an ions motion optimization (imo) algorithm for the ...

AN IONS MOTION OPTIMIZATION (IMO) ALGORITHM FOR THE CONTINUOUS ABSOLUTE P-CENTER LOCATION PROBLEM WITH EUCLIDEAN DISTANCE

LEY MEYNARD G. OPEÑA

SUBMITTED TO THE FACULTY OF THE COLLEGE OF SCIENCE AND MATHEMATICS UNIVERSITY OF THE PHILIPPINES MINDANAO IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF

BACHELOR OF SCIENCE IN APPLIED MATHEMATICS (Operations Research)

June 2017

UNIVERSITY OF THE PHILIPPINES MINDANAO

Bachelor of Science in Applied Mathematics Ley Meynard G. Opeña An Ions Motion Optimization (IMO) Algorithm for the Continuous Absolute pcenter Location Problem With Euclidean Distance

Special Problem Adviser Ritchie Mae T. Gamot, Ph.D. Department of Math, Physics, and Computer Science

Date of Submission June 2017

Permission is given for the following people to have access to this special problem: Available to the general public

No

Available only after consultation with author/thesis adviser Available only to those bound by confidentiality agreement

Yes Yes

Student’s signature: Signature of special problem adviser:

ii

The special problem manuscript attached hereto, entitled “AN IONS MOTION OPTIMIZATION (IMO) ALGORITHM FOR THE CONTINUOUS ABSOLUTE PCENTER LOCATION PROBLEM WITH EUCLIDEAN DISTANCE”, prepared and submitted by LEY MEYNARD G. OPEÑA in partial fulfillment of the requirements for the degree of Bachelor of Science in Applied Mathematics is hereby accepted.

RITCHIE MAE T. GAMOT, Ph.D. Adviser ____________________ Date

VICENTE B. CALAG, MSCS, MICT Panelist

LEO MANUEL B. ESTAÑA, M.Sc. Panelist

____________________ Date

____________________ Date

LEO MANUEL B. ESTAÑA, M.Sc. Department Chair ____________________ Date

DOMINICA DM. DACERA, Ph.D. Dean ____________________ Date

Recorded by: NOREEN GRACE V. FUNDADOR, Ph.D. College Secretary ____________________ Date

iii

BIOGRAPHICAL SKETCH The author, Ley Meynard G. Opeña, was born on February 22, 1997 in Tagum City. He is the eldest among the two children of Luis Lemuel Opeña III and Janet Opeña. Ley spent most of his childhood years together with her sister, Jade, at a small town in Sto. Tomas, Davao del Norte. Currently, he resides at Villa Paraiso Subd., Visayan Village, Tagum City. He took his elementary education at Visayan Village Central Elementary School, where he was a consistent honor student and graduated as the class valedictorian. He spent his secondary education life at Tagum City National High School under the Engineering and Science Education Program (ESEP). During those years, he discovered what are his potentials, especially those related on music and mathematics. He was also a member of the Student Government body on his 4th year. In 2013, he was admitted at the University of the Philippines Mindanao under the BS Applied Mathematics Major in Operations Research program. Aside from academics, he also engaged in extracurricular activities. He is a member of the Society of Math Majors, an academic organization which promotes service and leadership through camaraderie and passion in mathematics. He also joined the UP Mindanao Association of Musicians Playing Loud Instruments (AMPLI), an organization of bands union, where he found his band NEICLACE. To pursue his passion in singing, he also joined the UP Mindanao’s university choir, Koro Kantahanay, where they performed in various events such as the Musikahan sa Davao. They also competed in the 2nd Gawad Pangulo Choral Competition held at University of the Philippines Diliman.

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ACKNOWLEDGEMENT This special problem owes its existence to the help, support and inspiration of several people. First, I would like to thank the DMPCS faculty for shaping me during my entire college life. Without them, my college life wouldn’t have turned out to be a roller coaster ride. I would like to thank my panelists, Sir Leo and Sir Vic, for being able to pull out every needed information for my SP. I would like to give my sincere appreciation to my adviser, Maam Chimie, for giving me her unyielding support, guidance and knowledge in helping me finish this SP. My knowledge on metaheuristics and combinatorial optimization would not be expounded without her. I would also like to thank my two best friends, Jaenni and Rocel, for their continuous support ever since high school. To my bros Jerome, Ze, Jeffrey and Ace, thank you for the four years of fun and experience. I will never forget the lame jokes and puns you guys always threw randomly. May we still see each other again in the future. To my SMM and AMPLI family, thank you for making my college life wholesome. Special thanks to Koro Kantahanay for making my last year the best year of my entire college life. The memories we shared will be forever treasured in my heart. To all my friends and acquaintances. Thank you! Lastly, I would like to mention the most important group of people in my life. Maam Sarilla, my 4th year high school math teacher who inspired me to pursue my passion in the field of mathematics, thank you. To Mama Janet, Papa Luis, Jade and my family, thank you for being my support system and for everything. To the last person whom I owe everything, God, all of these wouldn’t be possible without your glory. I will always be grateful with your grace! v

TABLE OF CONTENTS

PAGE INTRODUCTION

1

REVIEW OF LITERATURE

6

p-center Problem

6

Computational complexity of the p-center problem

8

Continuous absolute p-center problem

8

Solving the p-center Problem

8

Ions Motion Optimization (IMO) Algorithm

13 17

MATERIALS AND METHODS Requirement Phase

17

Test Data

18

Objective Function

18

Solution Representation

18

Termination Criterion

19

Ions Motion Optimization (IMO) Algorithm

19

Distribution of Ions

19

Liquid Phase (Diversification)

20

Crystal Phase (Intensification)

21

Pseudocode 1: solid phase (intensification) General steps for the IMO algorithm.

22 22

Pseudocode 2: ions motion optimization algorithm

vi

23

Parameter Settings

25

p-center Problem to Solve

25

Software and Hardware Requirements

26

Performance Criteria

26 27

RESULTS AND DISCUSSION Initial Results

27

Test run

27

Probability criterion for re-initialization in solid phase

28

Smaller population size and iterations

29

Results from Egypt 5-center Problem Test Run

30

Egypt 5-center Problem Final Run

34

Results obtained

35

Initial vs. final best fitness

42

Initial run vs. final Run

44

Additional Results for the p-center problem

44

Increased number of center

44

Higher number of demand points

47

Complexity of the Continuous p-center Problem

52

SUMMARY AND CONCLUSION

55

LITERATURE CITED

58

APPENDICES

61

vii

LIST OF TABLES

TABLE

TITLE

PAGE

1

Types of p-center problems (Lifted from Biazaran and SeyediNezhad, 2009).

7

2

List of Parameter settings and its values.

25

3

List of Parameter settings for wi29.tsp and its values.

27

4

Results obtained from wi29.tsp test run.

28

5

List of Parameter settings for eg7146.tsp test run and its values.

30

6

Best fitness value over 5 runs for Egypt 5-center problem with MaxIter = 200.

32

7

Best fitness value over 10 runs for Egypt 5-center problem with MaxIter = 500.

32

8

List of Parameter settings for eg7146.tsp final run and its values.

35

9

Best fitness value over 30 runs for Egypt 5-center problem with MaxIter = 300.

35

10

Location of the centers at run number 11.

38

11

The time and iteration at which the best fitness value was attained.

40

12

The time and iteration at which the top 5 best fitness value was attained.

42

13

The Initial and Final locations of the centers for Egypt 5-center problem run 30.

43

14

List of Parameter settings for Egypt 6-center problem and its values.

44

15

Best fitness value over 5 runs for Egypt 6-center problem with MaxIter = 300.

44

viii

16

The time and iteration at which the best fitness value was attained.

45

17

Location of the centers for Egypt 6-center problem at run number 4.

46

18

List of Parameter settings for USA 5-center problem and its values.

48

19

List of Parameter settings for Italy 5-center problem and its values.

48

20

Best fitness value over 5 runs for USA 5-center problem with MaxIter = 100.

49

21

Best fitness value over 5 runs for Italy 5-center problem with MaxIter = 50.

49

22

Location of the centers for USA 5-center problem at run number 3.

50

23

Location of the centers for Italy 5-center problem at run number 1.

50

ix

LIST OF FIGURES

FIGURE

TITLE

PAGE

1

A set of demand points and service points and the maximum distance between them (Illustration by L.M.G. Opeña).

1

2

Repulsion and attraction force between cation and anion (Recreated based on Chakraborty et al., 2016).

13

3

In liquid phase, ions move towards its best opposite charge (Recreated based on (Recreated based on Hatamlou et al, 2015).

14

4

In crystal phase, ions have lesser room to move hence repulsion force is applied. Ions are then distributed around the best and worst ions (Recreated based on Hatamlou et al, 2015).

15

5

General flow of Methodology.

17

6

General Steps of the IMO algorithm.

24

7

Convergence Map for wi29.tsp of 30 runs with n = 29, p = 5 and probability for re-initialization of Anion and Cation in solid phase = 0.05.

29

8

Convergence Map for wi29.tsp of 30 runs with n = 29, p = 5 and probability for re-initialization of Anion and Cation in solid phase = 0.3.

30

9

Convergence Map for Egypt 5-center problem with MaxIter = 200.

31

10

Convergence Map for Egypt 5-center problem with MaxIter = 500.

31

11

Location of facilities (indicated by blue dot) for the Egypt 5center problem with MaxIter = 200 and Fitness = 2466.6361.

33

12

Location of facilities (indicated by blue dot) for the Egypt 5center problem with MaxIter = 500 and Fitness = 2439.2929.

34

13

The convergence map over 30 runs (green line) and its average per iteration (red line).

37

x

14

The values of the best fitness over 30 runs.

38

15

Location of facilities (indicated by blue dot) for the Egypt 5center problem with MaxIter = 300 and Fitness = 2434.4277.

39

16

The values of the time in seconds (s) at which the best fitness was achieved over 30 runs.

41

17

The convergence map of the runs that yielded the top 5 best fitness.

42

18

Comparison for the coverage and points for the initial (given by black) and final (given by green) best fitness values in run number 30.

43

19

The Convergence Map for Egypt 6-center problem test run.

46

20

Location of facilities (indicated by blue dot) for the Egypt 6center problem with MaxIter = 300 and Fitness = 2113.6733.

47

21

The Convergence Map for USA 5-center problem test run.

49

22

The Convergence Map for Italy 5-center problem test run.

50

23

Location of facilities (indicated by blue dot) for the USA 5center problem with MaxIter = 100 and Fitness = 104492.92.

51

24

Location of facilities (indicated by blue dot) for the Italy 5center problem with MaxIter = 50 and Fitness = 2826.263.

51

25

Location and coverage of Egypt 5-center problem run number 9 (green) and 21 (blue) with fitness difference equal to 0.0057.

53

26

Location and coverage of USA 5-center problem run number 2 (green) and 5 (blue) with fitness difference equal to 107.1.

53

27

Location and coverage of USA 5-center problem run number 2 (green) and 5 (blue) with fitness difference equal to 5.1818.

54

xi

LIST OF APPENDICES

APPENDIX

TITLE

PAGE

1

The Main Program (command.sce).

61

2

The Parameter Settings Sub-function (swarmgen.sce).

63

3

The Population Initialization Sub-function (swarmgen.sce).

64

4

The Objective Function Sub-function (objective.sce).

65

5

The Liquid Phase Sub-function (liquid.sce).

66

6

The Solid Phase Sub-function (solid.sce).

67

7

The Hungarian Method Sub-function (sort.sce).

68

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LIST OF APPENDIX TABLES

APPENDIX TABLE

TITLE

PAGE

1

Fitness Values Attained by Probability Criterion 0.05.

70

2

Fitness Values Attained by Probability Criterion 0.3.

71

3

Fitness Values Attained by Probability Criterion 0.5.

72

4

Fitness Values Attained by Probability Criterion 0.75.

73

5

Fitness Values Attained by Probability Criterion 1.

74

6

Fitness Values On Each Iterations Runs 1-10 for the Egypt 5center Problem with MaxIter = 300.

75

7

Fitness Values On Each Iterations Runs 11-20 for the Egypt 5center Problem with MaxIter = 300.

86

8

Fitness Values On Each Iterations Runs 21-30 for the Egypt 5center Problem with MaxIter = 300.

97

9

Location of Centers for the Egypt 5-center Problem Over 30 Runs with MaxIter = 300.

108

10

Location of Centers for the Egypt 5-center Problem Over 5 Runs with MaxIter = 200.

109

11

Location of Centers for the Egypt 5-center Problem Over 10 Runs with MaxIter = 500.

109

12

Location of Centers for the Egypt 6-center Problem Over 5 Runs with MaxIter = 300.

110

13

Location of Centers for the USA 5-center problem over 5 runs with MaxIter = 100.

110

14

Location of Centers for the Italy 5-center Problem Over 5 Runs with MaxIter = 50.

110

xiii

LIST OF APPENDIX FIGURES

APPENDIX FIGURE

TITLE

PAGE

1

Convergence Map for wi29.tsp of 30 Runs with n = 29, p = 5 and Probability for Re-initialization of Anion and Cation in Solid Phase = 0.5.

111

2

Convergence Map for wi29.tsp of 30 Runs with n = 29, p = 5 and Probability for Re-initialization of Anion and Cation in Solid Phase = 0.75.

111

3

Convergence Map for wi29.tsp of 30 Runs with n = 29, p = 5 and Probability for Re-initialization of Anion and Cation in Solid Phase = 1.

112

4

The Average Convergence Map Over 30 runs for Egypt 5center Problem.

112

5

Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 1.

113

6

Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 2.

114

7

Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 3.

115

8

Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 4.

116

9

Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 5.

117

10

Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 1 Best Fitness Over 10 Runs.

118

11

Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 2 Best Fitness Over 10 Runs.

119

12

Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 3 Best Fitness Over 10 Runs.

120

xiv

13

Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 4 Best Fitness Over 10 Runs.

121

14

Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 5 Best Fitness Over 10 Runs.

122

15

Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 1 Best Fitness Over 30 Runs.

123

16

Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 2 Best Fitness Over 30 Runs.

124

17

Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 3 Best Fitness Over 30 Runs.

125

18

Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 4 Best Fitness Over 30 Runs.

126

19

Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 5 Best Fitness Over 30 Runs.

127

21

Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 1.

128

21

Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 2.

129

22

Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 3.

130

23

Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 4.

131

24

Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 5.

132

25

Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 1.

133

26

Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 2.

133

27

Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 3.

134

xv

28

Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 4.

134

29

Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 5.

135

30

Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 1.

135

31

Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 2.

136

32

Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 3.

137

33

Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 4.

138

34

Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 5.

139

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ABSTRACT LEY MEYNARD G. OPEÑA, University of the Philippines Mindanao, June 2017, AN IONS MOTION OPTIMIZATION (IMO) ALGORITHM FOR THE CONTINUOUS ABSOLUTE P-CENTER LOCATION PROBLEM WITH EUCLIDEAN DISTANCE. Adviser: Ritchie Mae T. Gamot, Ph.D. The Ions Motion Optimization (IMO) algorithm is a relatively new physicsinspired metaheuristic algorithm based the properties of ions in nature. IMO has been benchmarked to known test functions and produced a highly-competitive solutions compared to known metaheuristic algorithms such as Artificial Bee Colony (ABC), Differential Evolution (DE), Genetic Algorithm (GA) and Particle Swarm Optimization (PSO). The IMO algorithm was recently combined with a learning algorithm to solve hydrothermal scheduling problem and performed well compared to DE, GA and PSO. The p-center problem is a location-allocation problem thought to be a good candidate for testing the IMO’s robustness due to its NP-hard nature. The IMO was then tested on selected 2D p-center location data sets used by Atiya and Fayed (2012) and El-Khodary et al. (2013). The IMO provided good quality of solutions and gave fast convergence to the solution even after utilizing reduced values for the parameter settings. Results have shown that it is necessary to reinitialize the population to achieve good quality of solutions. It was also observed that the continuous p-center problem is multimodal in nature. Increasing the parameter settings such as the maximum number of iterations and population size can be done in order to exploit the algorithm. The IMO algorithm can also be combined with other algorithm such as GA and PSO. Keywords: ions motion optimization algorithm, metaheuristics, nature-inspired algorithms, NP-hard problems, optimization, p-center location problem

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1 INTRODUCTION The p-center problem aims to locate p facilities in a space. The main objective of this problem is to minimize the maximum distance of each demand points served by its nearest facility. This problem is also known as the minimax location problem and is often described as the problem which determines the location and the smallest possible radius for p identical circles that can cover all demand points as shown in figure 1. (Drezner and Suzuki, 1996). The most common application of the p-center problem is those for emergency facilities like hospitals, schools and fire stations. Some requires continuous space like warning sirens, sprinkler systems, television transmitters and cellular towers (Drezner and Suzuki, 1996).

Fig. 1. A set of demand points and service points and the maximum distance between them (Illustration by L.M.G. Opeña).

2 To define, the distance between a customer and the service facility is known as the Euclidean distance (Kaveh and Nasr, 2011). The Euclidian distance location problem seeks to locate p new facility at point (𝑥𝑗 , 𝑦𝑗 ), 𝑗 = 1, 2, … , 𝑝 in ℝ2 given an established demand (𝑎𝑖 , 𝑏𝑖 ), 𝑖 = 1, 2, … , 𝑛. Chen (1983) said that the location of p-center facilities in ℝ2 with Euclidean distances can be written as, 2

2 1/2

min max min [(𝑎𝑖 − 𝑥𝑗 ) + (𝑏𝑖 − 𝑦𝑗 ) ] 𝑥𝑗 ,𝑦𝑗

𝑖

𝑗

, 𝑗 = 1, … , 𝑝.

[1]

where, (𝑎𝑖 , 𝑏𝑖 ), 𝑖 = 1, 2, … , 𝑛 are the coordinates of demand points and; (𝑥𝑗 , 𝑦𝑗 ) , 𝑗 = 1, 2, … , 𝑝 are the coordinates of the facilities, which are to be determined. The Euclidean p-center problems were found to be a Non-Deterministic Polynomial-time hard (NP-hard) problem by proving that Circle Covering is also NP-Hard (Meggido and Suppowit, 1984). Instead of unit circle, circles of radius R ≥ 1 (general assumption for the p-center problem) were used. When 1 ≤ R
0.5 ASOL(:,:,1) = A(:,:,1) + (O1*(repmat(CBESTPOINTS(:,:,1),aswarmsize,1)-1)); ASOL(:,:,2) = A(:,:,2) + (O1*(repmat(CBESTPOINTS(:,:,2),aswarmsize,1)-1)); else ASOL(:,:,1) = A(:,:,1) + (O1*(repmat(CBESTPOINTS(:,:,1),aswarmsize,1))); ASOL(:,:,2) = A(:,:,2) + (O1*(repmat(CBESTPOINTS(:,:,2),aswarmsize,1))); end if rand() > 0.5 CSOL(:,:,1) = C(:,:,1) + (O2*(repmat(ABESTPOINTS(:,:,1),cswarmsize,1)-1)); CSOL(:,:,2) = C(:,:,2) + (O2*(repmat(ABESTPOINTS(:,:,2),cswarmsize,1)-1)); else CSOL(:,:,1) = C(:,:,1) + (O2*(repmat(ABESTPOINTS(:,:,1),cswarmsize,1))); CSOL(:,:,2) = C(:,:,2) + (O2*(repmat(ABESTPOINTS(:,:,2),cswarmsize,1))); end endfunction

68 Appendix 7. The Hungarian Method Sub-function (sort.sce). //sort.sce - a hungarian method for assigning the cation to its nearest anion function CBESTPOINTSORT = sort(p,CBESTPOINTS,ABESTPOINTS) timer(); VAL(1:p,1:p) = 0; COST = VAL; ROWCOST(1,1:p) = 0; COLUMNCOST(1:p,1) = 0; for i = 1:p VAL(i,:) = sqrt((ABESTPOINTS(:,i,1)-CBESTPOINTS(:,:,1)).^2 + (ABESTPOINTS(:,i,2)-CBESTPOINTS(:,:,2)).^2); end COST = VAL; ROWCOST = min(COST,'r'); COST = COST - repmat(ROWCOST,p,1); COLUMNCOST = min(COST,'c'); COST = COST - repmat(COLUMNCOST,1,p); liness = 0; while liness < p SOL = zeros(p,p); liness = 0; for i = 1:p countc = size(find(COST(i,:)==0))'; if countc(2) > 1 SOL(i,:) = SOL(i,:)+1; liness = liness+1; end end for i = 1:p countr = size(find(COST(:,i)==0))'; countrs = size(find(SOL(:,i)==0 & COST(:,i)==0))'; if countrs(2) > 1 & countrs(2)=1 SOL(:,i) = SOL(:,i)+1; liness = liness+1; end end

69 Appendix 7 (cont.). if liness < p IND1 = find(SOL == 0); MIN = min(COST(IND1)); COST(IND1) = COST(IND1) - MIN; IND2 = find(SOL == 2); COST(IND2) = COST(IND2) + MIN; end end OPTIMAL = zeros(p,p); IND3 = find(COST==0); OPTIMAL(IND3) = 1; MAPPING = [[1:p]' zeros(p,1)]; counts = 1; trapp = 0 while counts>0 & trapp

1); countss = size(IND6); counts = countss(2); trapp = trapp+1; end if trapp < p CBESTPOINTSORT = CBESTPOINTS(:,MAPPING(:,2),:); else CBESTPOINTSORT = CBESTPOINTS; end endfunction

70 Appendix Table 1. Fitness Values Attained by Probability Criterion 0.05. Run Number Best fitness Value 1 1596.0365 2 1683.1942 3 1576.8502 4 1648.3602 5 1700.7633 6 1700.5328 7 1654.4256 8 1642.7053 9 1652.6401 10 1621.8883 11 1753.3537 12 1666.9681 13 1607.843 14 1693.3152 15 1598.9837 16 1508.6338 17 1593.288 18 1649.3028 19 1665.2104 20 1708.97 21 1710.1011 22 1693.5911 23 1671.3486 24 1627.76 25 1641.1733 26 1718.6018 27 1714.4213 28 1730.443 29 1665.8127 30 1587.1573 1656.122513 Mean Standard deviation 53.05552

71 Appendix Table 2. Fitness Values Attained by Probability Criterion 0.3. Run Number Best fitness Value 1 1571.5059 2 1575.2263 3 1607.444 4 1618.7668 5 1601.8557 6 1619.3883 7 1634.115 8 1634.6599 9 1647.1303 10 1660.5409 11 1634.3884 12 1611.3716 13 1570.7156 14 1607.1973 15 1585.3301 16 1583.3434 17 1556.6282 18 1599.2235 19 1616.3 20 1570.1978 21 1523.2033 22 1608.138 23 1618.002 24 1591.7204 25 1610.3026 26 1628.9528 27 1556.1423 28 1530.1525 29 1596.9181 30 1559.5156 Mean 1597.613 Standard deviation 32.55474

72 Appendix Table 3. Fitness Values Attained by Probability Criterion 0.5. Run Number Best fitness Value 1 1571.5328 2 1628.057 3 1610.9668 4 1498.145 5 1554.8306 6 1595.1994 7 1616.2019 8 1560.9226 9 1639.088 10 1552.5534 11 1580.5889 12 1580.699 13 1548.6734 14 1597.0333 15 1562.1144 16 1590.1769 17 1612.3001 18 1494.1008 19 1629.3785 20 1619.5881 21 1560.5864 22 1482.2701 23 1511.522 24 1543.4783 25 1500.5234 26 1544.2668 27 1599.0851 28 1542.6542 29 1604.7888 30 1591.5193 Mean 1570.76151 Standard deviation 42.59790227

73 Appendix Table 4. Fitness Values Attained by Probability Criterion 0.75. Run Number Best fitness Value 1 1589.2641 2 1572.3089 3 1597.7919 4 1607.1505 5 1612.757 6 1595.6279 7 1613.7059 8 1592.3752 9 1643.9545 10 1620.0785 11 1544.8155 12 1491.4083 13 1639.251 14 1613.1781 15 1580.6835 16 1623.6475 17 1594.2261 18 1579.479 19 1602.8129 20 1434.2824 21 1572.5518 22 1622.638 23 1530.803 24 1572.3348 25 1576.1849 26 1571.0695 27 1577.3512 28 1589.975 29 1547.3727 30 1643.2559 Mean 1585.078 Standard deviation 43.16925

74 Appendix Table 5. Fitness Values Attained by Probability Criterion 1. Run Number Best fitness Value 1 1620.2369 2 1592.3582 3 1594.9584 4 1542.6385 5 1569.9905 6 1619.9693 7 1584.3353 8 1570.8126 9 1542.3837 10 1560.7052 11 1595.5146 12 1536.8604 13 1603.0371 14 1522.8518 15 1611.0207 16 1556.6124 17 1564.6921 18 1580.0275 19 1524.5461 20 1515.455 21 1577.7299 22 1538.2836 23 1575.4952 24 1534.0043 25 1497.1347 26 1599.5968 27 1545.0253 28 1560.0497 29 1601.7059 30 1595.6624 Mean 1567.789803 Standard deviation 32.07270829

10 3008.596 2907.328 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344

75

Appendix Table 6. Fitness Values On Each Iterations Runs 1-10 for the Egypt 5-center Problem with MaxIter = 300. Run Number Iteration # 1 2 3 4 5 6 7 8 9 1 2851.053 2993.145 3032.147 2982.697 2804.039 3080.672 2772.988 2902.384 2698.169 2 2793.099 2929.480 2820.415 2930.311 2804.039 3017.800 2772.988 2858.548 2698.169 3 2599.482 2854.261 2772.822 2628.226 2573.498 2788.147 2771.800 2707.693 2628.196 4 2599.482 2854.261 2772.822 2628.226 2573.498 2788.147 2771.800 2707.693 2628.196 5 2599.482 2854.261 2772.822 2628.226 2573.498 2788.147 2771.800 2707.693 2628.196 6 2599.482 2854.261 2772.822 2628.226 2573.498 2788.147 2771.800 2707.693 2628.196 7 2599.482 2755.420 2772.822 2628.226 2573.498 2680.205 2771.800 2707.693 2628.196 8 2599.482 2755.420 2772.822 2628.226 2573.498 2680.205 2771.800 2707.693 2628.196 9 2599.482 2755.420 2772.822 2628.226 2573.498 2680.205 2771.800 2685.506 2628.196 10 2599.482 2755.420 2653.936 2628.226 2573.498 2680.205 2771.800 2685.506 2628.196 11 2599.482 2738.795 2653.936 2628.226 2477.246 2680.205 2771.800 2685.506 2628.196 12 2599.482 2738.795 2653.936 2628.226 2477.246 2680.205 2771.800 2685.506 2628.196 13 2599.482 2738.795 2653.936 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 14 2599.482 2738.795 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 15 2599.482 2738.795 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 16 2599.482 2738.795 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 17 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 18 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 19 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 20 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 21 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 22 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 23 2599.482 2717.934 2608.650 2628.226 2477.246 2680.205 2771.076 2685.506 2628.196 24 2599.482 2717.934 2608.650 2569.444 2477.246 2680.205 2771.076 2685.506 2628.196 25 2599.482 2717.934 2608.650 2569.444 2477.246 2680.205 2771.076 2685.506 2628.196 26 2599.482 2717.934 2608.650 2569.444 2477.246 2680.205 2771.076 2685.506 2628.196

2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650 2608.650

2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444 2569.444

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429

2771.076 2771.076 2771.076 2771.076 2771.076 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2648.384 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933

2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2685.506 2574.359 2495.087 2495.087

2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2628.196 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380

2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344

76

Appendix Table 6 (cont.). 27 2599.482 2717.934 28 2599.482 2717.934 29 2599.482 2717.934 30 2599.482 2717.934 31 2562.368 2717.934 32 2562.368 2717.934 33 2562.368 2717.934 34 2562.368 2717.934 35 2562.368 2615.230 36 2562.368 2615.230 37 2562.368 2615.230 38 2562.368 2615.230 39 2562.368 2615.230 40 2562.368 2615.230 41 2562.368 2615.230 42 2562.368 2615.230 43 2562.368 2615.230 44 2562.368 2615.230 45 2562.368 2615.230 46 2562.368 2615.230 47 2562.368 2615.230 48 2562.368 2615.230 49 2562.368 2615.230 50 2562.368 2615.230 51 2562.368 2615.230 52 2562.368 2615.230 53 2562.368 2615.230 54 2562.368 2615.230

2608.650 2608.650 2608.650 2494.949 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429

2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380

2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344

77

Appendix Table 6 (cont.). 55 2562.368 2615.230 56 2562.368 2615.230 57 2562.368 2615.230 58 2562.368 2615.230 59 2562.368 2615.230 60 2562.368 2615.230 61 2562.368 2615.230 62 2562.368 2615.230 63 2562.368 2615.230 64 2562.368 2615.230 65 2562.368 2615.230 66 2562.368 2615.230 67 2562.368 2615.230 68 2562.368 2615.230 69 2562.368 2615.230 70 2562.368 2615.230 71 2562.368 2615.230 72 2562.368 2615.230 73 2562.368 2615.230 74 2562.368 2615.230 75 2562.368 2615.230 76 2562.368 2615.230 77 2562.368 2615.230 78 2562.368 2615.230 79 2562.368 2615.230 80 2562.368 2615.230 81 2562.368 2615.230 82 2562.368 2615.230

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429 2632.429

2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380 2558.380

2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2588.344

78

Appendix Table 6 (cont.). 83 2562.368 2615.230 84 2562.368 2615.230 85 2562.368 2615.230 86 2562.368 2552.527 87 2562.368 2552.527 88 2562.368 2552.527 89 2562.368 2552.527 90 2562.368 2552.527 91 2562.368 2552.527 92 2562.368 2552.527 93 2562.368 2552.527 94 2562.368 2552.527 95 2562.368 2552.527 96 2562.368 2552.527 97 2562.368 2552.527 98 2562.368 2552.527 99 2562.368 2552.527 100 2562.368 2552.527 101 2562.368 2552.527 102 2562.368 2552.527 103 2562.368 2552.527 104 2562.368 2552.527 105 2562.368 2552.527 106 2562.368 2552.527 107 2562.368 2552.527 108 2562.368 2552.527 109 2562.368 2552.527 110 2562.368 2518.935

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2562.607 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2632.429 2632.429 2632.429 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934

2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2558.380 2558.380 2558.380 2558.380 2558.380 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147

2588.344 2588.344 2588.344 2588.344 2588.344 2588.344 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

79

Appendix Table 6 (cont.). 111 2562.368 2518.935 112 2562.368 2518.935 113 2562.368 2518.935 114 2562.368 2518.935 115 2562.368 2518.935 116 2562.368 2518.935 117 2562.368 2518.935 118 2562.368 2518.935 119 2562.368 2518.935 120 2562.368 2518.935 121 2562.368 2518.935 122 2562.368 2518.935 123 2562.368 2518.935 124 2562.368 2518.935 125 2562.368 2518.935 126 2562.368 2518.935 127 2562.368 2518.935 128 2562.368 2518.935 129 2562.368 2518.935 130 2562.368 2518.935 131 2562.368 2518.935 132 2562.368 2518.935 133 2562.368 2518.935 134 2562.368 2518.935 135 2562.368 2518.935 136 2562.368 2518.935 137 2562.368 2518.935 138 2562.368 2518.935

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934

2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147

2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

80

Appendix Table 6 (cont.). 139 2562.368 2518.935 140 2562.368 2518.935 141 2562.368 2518.935 142 2562.368 2518.935 143 2562.368 2518.935 144 2562.368 2518.935 145 2562.368 2518.935 146 2562.368 2518.935 147 2562.368 2518.935 148 2562.368 2518.935 149 2562.368 2518.935 150 2562.368 2518.935 151 2562.368 2518.935 152 2562.368 2518.935 153 2562.368 2518.935 154 2562.368 2518.935 155 2562.368 2518.935 156 2562.368 2518.935 157 2562.368 2518.935 158 2562.368 2518.935 159 2562.368 2518.935 160 2562.368 2518.935 161 2562.368 2518.935 162 2562.368 2518.935 163 2562.368 2518.935 164 2562.368 2518.935 165 2562.368 2518.935 166 2562.368 2518.935

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2575.934 2459.736 2459.736

2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2495.147 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405

2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

81

Appendix Table 6 (cont.). 167 2562.368 2518.935 168 2562.368 2518.935 169 2562.368 2518.935 170 2562.368 2518.935 171 2562.368 2518.935 172 2562.368 2518.935 173 2562.368 2518.935 174 2562.368 2518.935 175 2562.368 2518.935 176 2562.368 2518.935 177 2562.368 2518.935 178 2562.368 2518.935 179 2562.368 2518.935 180 2562.368 2518.935 181 2501.302 2518.935 182 2501.302 2518.935 183 2501.302 2518.935 184 2501.302 2518.935 185 2501.302 2518.935 186 2501.302 2518.935 187 2501.302 2518.935 188 2501.302 2518.935 189 2501.302 2518.935 190 2501.302 2518.935 191 2501.302 2518.935 192 2501.302 2502.768 193 2501.302 2502.768 194 2501.302 2502.768

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736

2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2514.933 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405

2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

82

Appendix Table 6 (cont.). 195 2501.302 2502.768 196 2501.302 2502.768 197 2501.302 2502.768 198 2501.302 2502.768 199 2501.302 2502.768 200 2501.302 2502.768 201 2501.302 2502.768 202 2501.302 2502.768 203 2501.302 2502.768 204 2501.302 2502.768 205 2501.302 2502.768 206 2501.302 2502.768 207 2501.302 2502.768 208 2501.302 2502.768 209 2501.302 2502.768 210 2501.302 2502.768 211 2501.302 2502.768 212 2501.302 2502.768 213 2501.302 2502.768 214 2501.302 2502.768 215 2501.302 2502.768 216 2501.302 2502.768 217 2501.302 2502.768 218 2501.302 2502.768 219 2501.302 2502.768 220 2501.302 2502.768 221 2501.302 2502.768 222 2501.302 2502.768

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736

2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405

2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

83

Appendix Table 6 (cont.). 223 2501.302 2502.768 224 2501.302 2502.768 225 2501.302 2502.768 226 2501.302 2502.768 227 2501.302 2502.768 228 2501.302 2502.768 229 2501.302 2502.768 230 2501.302 2502.768 231 2501.302 2502.768 232 2501.302 2502.768 233 2501.302 2502.768 234 2501.302 2502.768 235 2501.302 2502.768 236 2501.302 2502.768 237 2501.302 2502.768 238 2501.302 2502.768 239 2501.302 2502.768 240 2501.302 2502.768 241 2501.302 2502.768 242 2501.302 2502.768 243 2501.302 2502.768 244 2501.302 2502.768 245 2501.302 2502.768 246 2501.302 2502.768 247 2501.302 2502.768 248 2501.302 2502.768 249 2501.302 2502.768 250 2501.302 2502.768

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736

2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405

2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

84

Appendix Table 6 (cont.). 251 2501.302 2502.768 252 2501.302 2502.768 253 2501.302 2502.768 254 2501.302 2502.768 255 2501.302 2502.768 256 2501.302 2502.768 257 2501.302 2502.768 258 2501.302 2502.768 259 2501.302 2502.768 260 2501.302 2502.768 261 2501.302 2502.768 262 2501.302 2502.768 263 2501.302 2502.768 264 2501.302 2502.768 265 2501.302 2502.768 266 2501.302 2502.768 267 2501.302 2502.768 268 2501.302 2502.768 269 2501.302 2502.768 270 2501.302 2502.768 271 2501.302 2502.768 272 2501.302 2502.768 273 2501.302 2502.768 274 2501.302 2502.768 275 2501.302 2502.768 276 2501.302 2502.768 277 2501.302 2502.768 278 2501.302 2502.768

Appendix Table 6 (cont.). 279 2501.302 2502.768 280 2501.302 2502.768 281 2501.302 2502.768 282 2501.302 2502.768 283 2501.302 2502.768 284 2501.302 2502.768 285 2501.302 2502.768 286 2501.302 2502.768 287 2501.302 2502.768 288 2501.302 2502.768 289 2501.302 2502.768 290 2501.302 2502.768 291 2501.302 2502.768 292 2501.302 2502.768 293 2501.302 2502.768 294 2501.302 2502.768 295 2501.302 2502.768 296 2501.302 2502.768 297 2501.302 2502.768 298 2501.302 2502.768 299 2501.302 2502.768 300 2501.302 2502.768

2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452 2450.452

2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974 2511.974

2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246 2477.246

2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736 2459.736

2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930 2488.930

2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087 2495.087

2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405 2460.405

2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042 2495.042

85

20 3016.133 2878.489 2753.116 2753.116 2753.116 2753.116 2700.836 2700.836 2700.836 2700.836 2700.836 2700.836 2700.836 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474

86

Appendix Table 7. Fitness Values On Each Iterations Runs 11-20 for the Egypt 5-center Problem with MaxIter = 300. Run Number Iteration # 11 12 13 14 15 16 17 18 19 1 3031.272 2956.846 2752.706 2988.265 2991.818 3094.357 3054.731 2882.811 2981.676 2 2750.473 2912.046 2752.706 2974.471 2911.492 2908.705 2878.372 2857.117 2873.462 3 2677.029 2802.692 2709.580 2855.513 2797.528 2770.752 2662.156 2687.402 2756.061 4 2677.029 2776.979 2709.580 2855.513 2797.528 2611.535 2560.882 2687.402 2756.061 5 2677.029 2776.979 2709.580 2855.513 2797.528 2611.535 2560.882 2687.402 2756.061 6 2677.029 2776.979 2709.580 2855.513 2797.528 2611.535 2560.882 2687.402 2756.061 7 2677.029 2776.979 2709.580 2855.513 2797.528 2611.535 2560.882 2687.402 2542.561 8 2677.029 2776.979 2659.353 2855.513 2797.528 2611.535 2560.882 2687.402 2450.704 9 2677.029 2776.979 2659.353 2855.513 2797.528 2611.535 2560.882 2687.402 2450.704 10 2677.029 2691.840 2659.353 2853.725 2797.528 2611.535 2560.882 2687.402 2450.704 11 2677.029 2691.840 2659.353 2682.700 2797.528 2611.535 2560.882 2687.402 2450.704 12 2677.029 2691.840 2659.353 2594.487 2797.528 2611.535 2560.882 2687.402 2450.704 13 2677.029 2691.840 2659.353 2594.487 2797.528 2611.535 2560.882 2687.402 2450.704 14 2677.029 2691.840 2659.353 2594.487 2797.528 2611.535 2560.882 2687.402 2450.704 15 2677.029 2691.840 2659.353 2594.487 2797.528 2611.535 2560.882 2687.402 2450.704 16 2677.029 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2687.402 2450.704 17 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2687.402 2450.704 18 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2687.402 2450.704 19 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2687.402 2450.704 20 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704 21 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704 22 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704 23 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704 24 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704 25 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704 26 2663.790 2691.840 2659.353 2594.487 2664.239 2611.535 2560.882 2653.570 2450.704

2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840 2691.840

2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353

2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535

2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2560.882 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051

2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474

87

Appendix Table 7 (cont.). 27 2663.790 28 2663.790 29 2663.790 30 2663.790 31 2663.790 32 2663.790 33 2663.790 34 2663.790 35 2663.790 36 2663.790 37 2663.790 38 2663.790 39 2663.790 40 2663.790 41 2663.790 42 2663.790 43 2663.790 44 2663.790 45 2663.790 46 2663.790 47 2663.790 48 2663.790 49 2663.790 50 2663.790 51 2663.790 52 2663.790 53 2663.790 54 2663.790

2691.840 2691.840 2691.840 2691.840 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682

2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353

2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2594.487 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535

2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2546.051 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324

2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2653.570 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474

88

Appendix Table 7 (cont.). 55 2663.790 56 2663.790 57 2637.943 58 2621.621 59 2621.621 60 2621.621 61 2621.621 62 2621.621 63 2621.621 64 2621.621 65 2621.621 66 2621.621 67 2621.621 68 2621.621 69 2621.621 70 2621.621 71 2621.621 72 2621.621 73 2621.621 74 2621.621 75 2621.621 76 2621.621 77 2621.621 78 2621.621 79 2552.703 80 2552.703 81 2552.703 82 2552.703

2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2688.682 2665.450 2665.450 2665.450 2665.450 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429

2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2659.353 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2611.535 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588

2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2536.324 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474

89

Appendix Table 7 (cont.). 83 2552.703 84 2552.703 85 2552.703 86 2552.703 87 2552.703 88 2552.703 89 2552.703 90 2552.703 91 2552.703 92 2552.703 93 2552.703 94 2552.703 95 2552.703 96 2552.703 97 2552.703 98 2552.703 99 2552.703 100 2552.703 101 2552.703 102 2552.703 103 2552.703 104 2552.703 105 2552.703 106 2552.703 107 2552.703 108 2552.703 109 2552.703 110 2552.703

2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2591.429 2537.072 2537.072 2537.072 2537.072

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474

90

Appendix Table 7 (cont.). 111 2552.703 112 2552.703 113 2552.703 114 2552.703 115 2552.703 116 2552.703 117 2552.703 118 2552.703 119 2552.703 120 2552.703 121 2552.703 122 2552.703 123 2552.703 124 2552.703 125 2552.703 126 2552.703 127 2552.703 128 2552.703 129 2552.703 130 2552.703 131 2552.703 132 2552.703 133 2552.703 134 2552.703 135 2552.703 136 2552.703 137 2552.703 138 2552.703

2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2551.474 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843

91

Appendix Table 7 (cont.). 139 2552.703 140 2552.703 141 2552.703 142 2552.703 143 2552.703 144 2552.703 145 2552.703 146 2552.703 147 2552.703 148 2552.703 149 2552.703 150 2552.703 151 2552.703 152 2552.703 153 2552.703 154 2552.703 155 2552.703 156 2552.703 157 2552.703 158 2552.703 159 2552.703 160 2552.703 161 2552.703 162 2552.703 163 2552.703 164 2552.703 165 2552.703 166 2552.703

2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2606.814 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843

92

Appendix Table 7 (cont.). 167 2552.703 168 2552.703 169 2552.703 170 2552.703 171 2552.703 172 2552.703 173 2552.703 174 2552.703 175 2552.703 176 2552.703 177 2552.703 178 2552.703 179 2552.703 180 2552.703 181 2552.703 182 2552.703 183 2552.703 184 2539.485 185 2539.485 186 2539.485 187 2539.485 188 2539.485 189 2539.485 190 2539.485 191 2539.485 192 2539.485 193 2539.485 194 2539.485

2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2537.072 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2535.684 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2521.588 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843

93

Appendix Table 7 (cont.). 195 2539.485 196 2539.485 197 2539.485 198 2539.485 199 2539.485 200 2539.485 201 2539.485 202 2539.485 203 2539.485 204 2539.485 205 2539.485 206 2539.485 207 2539.485 208 2539.485 209 2539.485 210 2539.485 211 2539.485 212 2539.485 213 2539.485 214 2539.485 215 2539.485 216 2539.485 217 2539.485 218 2539.485 219 2539.485 220 2539.485 221 2539.485 222 2539.485

2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843

94

Appendix Table 7 (cont.). 223 2539.485 224 2539.485 225 2539.485 226 2539.485 227 2539.485 228 2539.485 229 2539.485 230 2469.126 231 2434.428 232 2434.428 233 2434.428 234 2434.428 235 2434.428 236 2434.428 237 2434.428 238 2434.428 239 2434.428 240 2434.428 241 2434.428 242 2434.428 243 2434.428 244 2434.428 245 2434.428 246 2434.428 247 2434.428 248 2434.428 249 2434.428 250 2434.428

2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751

2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2500.832 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843

95

Appendix Table 7 (cont.). 251 2434.428 252 2434.428 253 2434.428 254 2434.428 255 2434.428 256 2434.428 257 2434.428 258 2434.428 259 2434.428 260 2434.428 261 2434.428 262 2434.428 263 2434.428 264 2434.428 265 2434.428 266 2434.428 267 2434.428 268 2434.428 269 2434.428 270 2434.428 271 2434.428 272 2434.428 273 2434.428 274 2434.428 275 2434.428 276 2434.428 277 2434.428 278 2434.428

Appendix Table 7 (cont.). 279 2434.428 280 2434.428 281 2434.428 282 2434.428 283 2434.428 284 2434.428 285 2434.428 286 2434.428 287 2434.428 288 2434.428 289 2434.428 290 2434.428 291 2434.428 292 2434.428 293 2434.428 294 2434.428 295 2434.428 296 2434.428 297 2434.428 298 2434.428 299 2434.428 300 2434.428

2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2522.493 2497.735 2497.735 2497.735 2497.735 2497.735 2497.735 2497.735 2497.735 2497.735 2497.735 2497.735

2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2555.751 2518.444 2518.444 2518.444 2518.444 2518.444 2518.444 2518.444 2518.444 2518.444

2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926 2491.926

2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122 2513.122

2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515 2488.515

2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516 2501.516

2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917 2442.917

2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704 2450.704

2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843 2440.843

96

30 3076.909 2896.551 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585

97

Appendix Table 8. Fitness Values On Each Iterations Runs 21-30 for the Egypt 5-center Problem MaxIter = 300. Run Number Iteration # 21 22 23 24 25 26 27 28 29 1 2930.921 3012.123 2989.093 2959.700 3000.407 3036.947 2931.867 2933.291 2959.300 2 2834.160 3012.123 2938.874 2872.202 2968.002 2820.240 2735.151 2933.291 2927.860 3 2666.899 2778.972 2788.773 2654.953 2685.170 2798.094 2732.480 2705.154 2770.677 4 2666.899 2778.972 2788.773 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 5 2666.899 2778.972 2788.773 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 6 2666.899 2778.972 2788.773 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 7 2666.899 2778.972 2788.773 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 8 2666.899 2649.114 2783.848 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 9 2666.899 2649.114 2626.845 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 10 2666.899 2649.114 2584.312 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 11 2666.899 2649.114 2584.312 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 12 2666.899 2649.114 2584.312 2517.677 2685.170 2785.039 2732.480 2571.785 2770.677 13 2651.664 2649.114 2584.312 2517.677 2685.170 2691.402 2732.480 2571.785 2751.329 14 2651.664 2649.114 2584.312 2517.677 2685.170 2691.402 2732.480 2571.785 2751.329 15 2651.664 2649.114 2584.312 2517.677 2685.170 2691.402 2732.480 2571.785 2751.329 16 2651.664 2649.114 2584.312 2517.677 2639.059 2691.402 2732.480 2571.785 2751.329 17 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2732.480 2571.785 2751.329 18 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2732.480 2571.785 2751.329 19 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2732.480 2571.785 2751.329 20 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2732.480 2571.785 2751.329 21 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2732.480 2571.785 2751.329 22 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2732.480 2571.785 2751.329 23 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2620.422 2571.785 2751.329 24 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2620.422 2571.785 2751.329 25 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2620.422 2571.785 2719.413 26 2651.664 2649.114 2584.312 2517.677 2520.770 2691.402 2620.422 2571.785 2719.413

2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114

2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2584.312 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2517.677 2505.165 2505.165 2505.165 2505.165 2505.165 2505.165 2481.685 2481.685 2481.685

2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2520.770 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2691.402 2691.402 2691.402 2691.402 2691.402 2691.402 2691.402 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684

2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2719.413 2691.177 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472 2631.472

2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2671.585 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678

98

Appendix Table 8 (cont.). 27 2651.664 28 2651.664 29 2651.664 30 2651.664 31 2651.664 32 2651.664 33 2651.664 34 2651.664 35 2651.664 36 2651.664 37 2651.664 38 2651.664 39 2651.664 40 2651.664 41 2651.664 42 2651.664 43 2651.664 44 2617.350 45 2596.997 46 2596.997 47 2596.997 48 2596.997 49 2596.997 50 2596.997 51 2596.997 52 2596.997 53 2596.997 54 2596.997

2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2649.114 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2643.684 2635.174 2635.174 2635.174 2635.174

2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422 2620.422

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2631.472 2631.472 2631.472 2631.472 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669

2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678 2630.678

99

Appendix Table 8 (cont.). 55 2596.997 56 2596.997 57 2596.997 58 2596.997 59 2596.997 60 2596.997 61 2596.997 62 2596.997 63 2596.997 64 2596.997 65 2596.997 66 2596.997 67 2596.997 68 2596.997 69 2596.997 70 2596.997 71 2596.997 72 2596.997 73 2596.997 74 2511.916 75 2511.916 76 2460.399 77 2460.399 78 2460.399 79 2460.399 80 2460.399 81 2460.399 82 2460.399

2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2591.353 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174

2620.422 2620.422 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2534.669 2504.496

2630.678 2630.678 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780

100

Appendix Table 8 (cont.). 83 2460.399 84 2460.399 85 2460.399 86 2460.399 87 2460.399 88 2460.399 89 2460.399 90 2460.399 91 2460.399 92 2460.399 93 2460.399 94 2460.399 95 2460.399 96 2460.399 97 2460.399 98 2460.399 99 2460.399 100 2460.399 101 2460.399 102 2460.399 103 2460.399 104 2460.399 105 2460.399 106 2460.399 107 2460.399 108 2460.399 109 2460.399 110 2460.399

2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174 2635.174

2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496

2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2569.780 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360

101

Appendix Table 8 (cont.). 111 2460.399 112 2460.399 113 2460.399 114 2460.399 115 2460.399 116 2460.399 117 2460.399 118 2460.399 119 2460.399 120 2460.399 121 2460.399 122 2460.399 123 2460.399 124 2460.399 125 2460.399 126 2460.399 127 2460.399 128 2460.399 129 2460.399 130 2460.399 131 2460.399 132 2460.399 133 2460.399 134 2460.399 135 2460.399 136 2460.399 137 2460.399 138 2460.399

2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2635.174 2635.174 2635.174 2635.174 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495

2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940 2530.940

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2504.496 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964

2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360

102

Appendix Table 8 (cont.). 139 2460.399 140 2460.399 141 2460.399 142 2460.399 143 2460.399 144 2460.399 145 2460.399 146 2460.399 147 2460.399 148 2460.399 149 2460.399 150 2460.399 151 2460.399 152 2460.399 153 2460.399 154 2460.399 155 2460.399 156 2460.399 157 2460.399 158 2460.399 159 2460.399 160 2460.399 161 2460.399 162 2460.399 163 2460.399 164 2460.399 165 2460.399 166 2460.399

2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495 2580.495

2530.940 2530.940 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964

2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360

103

Appendix Table 8 (cont.). 167 2460.399 168 2460.399 169 2460.399 170 2460.399 171 2460.399 172 2460.399 173 2460.399 174 2460.399 175 2460.399 176 2460.399 177 2460.399 178 2460.399 179 2460.399 180 2460.399 181 2460.399 182 2460.399 183 2460.399 184 2460.399 185 2460.399 186 2460.399 187 2460.399 188 2460.399 189 2460.399 190 2460.399 191 2460.399 192 2460.399 193 2460.399 194 2460.399

2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2580.191

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2580.495 2580.495 2580.495 2580.495 2580.495 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2539.705 2499.645 2499.645 2499.645 2499.645

2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785

2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964

2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360

104

Appendix Table 8 (cont.). 195 2460.399 196 2460.399 197 2460.399 198 2460.399 199 2460.399 200 2460.399 201 2460.399 202 2460.399 203 2460.399 204 2460.399 205 2460.399 206 2460.399 207 2460.399 208 2460.399 209 2460.399 210 2460.399 211 2460.399 212 2460.399 213 2460.399 214 2460.399 215 2460.399 216 2460.399 217 2460.399 218 2460.399 219 2460.399 220 2460.399 221 2460.399 222 2460.399

2580.191 2580.191 2580.191 2580.191 2580.191 2580.191 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645

2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287

2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2571.785 2531.165 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868

2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964

2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360

105

Appendix Table 8 (cont.). 223 2460.399 224 2460.399 225 2460.399 226 2460.399 227 2460.399 228 2460.399 229 2460.399 230 2460.399 231 2460.399 232 2460.399 233 2460.399 234 2460.399 235 2460.399 236 2460.399 237 2460.399 238 2460.399 239 2460.399 240 2460.399 241 2460.399 242 2460.399 243 2460.399 244 2460.399 245 2460.399 246 2460.399 247 2460.399 248 2460.399 249 2460.399 250 2460.399

2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645

2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287

2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868

2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964

2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2522.360 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271

106

Appendix Table 8 (cont.). 251 2460.399 252 2460.399 253 2460.399 254 2460.399 255 2460.399 256 2460.399 257 2460.399 258 2460.399 259 2460.399 260 2460.399 261 2460.399 262 2460.399 263 2460.399 264 2460.399 265 2460.399 266 2460.399 267 2460.399 268 2460.399 269 2460.399 270 2460.399 271 2460.399 272 2460.399 273 2460.399 274 2460.399 275 2460.399 276 2460.399 277 2460.399 278 2460.399

Appendix Table 8 (cont.). 279 2460.399 280 2460.399 281 2460.399 282 2460.399 283 2460.399 284 2460.399 285 2460.399 286 2460.399 287 2460.399 288 2460.399 289 2460.399 290 2460.399 291 2460.399 292 2460.399 293 2460.399 294 2460.399 295 2460.399 296 2460.399 297 2460.399 298 2460.399 299 2460.399 300 2460.399

2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007 2465.007

2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220 2460.220

2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685 2481.685

2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120 2457.120

2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645 2499.645

2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287 2476.287

2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868 2454.868

2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964 2480.964

2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271 2460.271

107

Appendix Table 9. Location of Centers for the Egypt 5-center Problem Over 30 Runs with MaxIter = 300. 1 29583.370 30066.549 30117.065 26738.558 29102.992 30252.028 30665.062 30522.353 29135.590 30287.267 29816.307 30122.465 29951.221 23929.126 26284.249 24053.951 26908.869 28969.028 24039.427 28945.073 29635.864 29444.387 24098.473 28949.355 29140.202 29540.053

5 29142.468 29610.533 23974.563 29949.685 30545.872 23885.093 26086.251 23962.880 30395.284 26772.799 30530.738 29368.308 30563.295 29900.768 24072.373 25918.999 30189.918 23957.346 28939.300 30199.539 30359.001 23995.313 26312.462 30285.705 29791.914 26486.912

1 30450.793 30794.866 26862.610 29762.232 33211.208 27096.877 27242.621 30369.267 33420.870 32071.659 26411.825 27187.881 31418.913 33083.270 30054.170 33195.087 30407.423 33904.508 33154.805 33785.905 30947.645 30640.014 33061.871 33512.224 33902.114 30991.858

Y-coordinate of Center 2 3 4 29914.268 33213.810 26815.165 29534.172 33020.600 33884.985 30060.779 33513.405 30858.311 32941.240 33118.884 31855.251 30592.144 33139.103 29952.381 30252.220 30621.917 33565.835 33169.978 31990.133 33351.639 26812.069 33656.140 29726.692 30728.205 30144.333 33036.458 32895.242 33265.347 27287.710 33106.543 33787.672 30268.008 33032.873 29601.704 33443.982 33013.586 30055.679 34748.601 30192.488 33791.718 29978.504 30595.290 33406.004 26867.821 33868.895 26637.606 30535.521 33122.975 26852.799 33067.295 30767.800 29985.401 27035.810 31041.235 30145.582 26761.427 29887.102 33290.013 31309.612 33226.669 29969.321 33897.102 26861.063 33853.827 30248.992 26804.685 33540.270 30740.680 33134.363 30065.259 27072.145 33209.113 30400.929 27134.896 33375.474 26880.493 32998.403

5 33897.773 26693.617 33083.967 27000.503 26823.505 33213.526 29365.793 33294.879 26892.022 30059.025 30288.985 30735.589 26625.164 26379.395 32974.246 29886.799 29734.913 33109.930 33604.071 27026.358 27115.209 33139.291 30172.701 30628.755 31585.381 30073.751

108

Run # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

X-coordinate of Center 2 3 4 25502.077 23954.666 30298.828 26543.012 24217.175 29198.755 26686.853 28941.023 30095.701 28330.730 23954.826 30615.952 29876.216 23917.675 26600.790 26934.545 29913.640 29136.540 28074.378 30204.990 23857.371 29929.037 29187.045 26810.835 29340.785 26206.978 23978.941 28415.021 23996.373 30370.226 23968.896 28910.532 26643.081 24188.421 26162.207 28993.526 23925.074 26911.584 29007.799 26528.874 28917.450 30360.934 29481.069 28928.772 29866.017 29094.574 29930.177 29582.730 29099.955 30314.743 23923.576 30256.181 26194.176 30320.879 30199.036 26299.795 29801.555 26490.810 23893.854 30138.423 23938.851 26045.596 28883.078 30561.463 28904.177 26454.431 29908.043 29161.951 30361.940 23900.312 26525.154 30932.375 23931.091 26732.294 30490.845 29094.932 29800.034 24208.626

Appendix Table 9 (cont.). 27 28 29 30

24179.528 29370.453 29832.947 29538.405

29910.564 26817.496 29822.246 26153.773

26492.039 30512.545 23859.241 28994.841

30189.996 29005.119 29051.121 30091.315

29111.952 24089.986 26747.703 23948.633

33019.471 31044.493 30353.531 31004.212

26385.843 29955.034 26720.825 30001.331

30109.618 27079.843 33358.798 33839.697

30857.786 34045.480 33304.996 26984.717

33244.733 33103.189 30067.414 33092.088

Y-coordinate of Center 2 3 4 33345.154 33229.506 30784.023 33755.306 33195.622 30872.585 33948.002 26960.335 30467.938 27314.939 30103.503 33074.748 30261.114 33196.513 30488.376

5 30362.639 29846.439 30440.377 32822.156 33250.588

Appendix Table 10. Location of Centers for the Egypt 5-center Problem Over 5 Runs with MaxIter = 200. Run # 1 2 3 4 5

1 29878.536 30131.228 24025.965 30495.270 29893.447

X-coordinate of Center 2 3 4 29012.039 24108.284 29982.521 29142.259 23961.557 29743.842 28716.030 29947.909 27362.566 30789.348 26637.416 24029.222 26746.601 23999.371 29845.458

5 26466.670 26339.626 30407.371 28892.885 29114.733

1 27017.192 27155.944 33030.077 32106.438 26962.457

Appendix Table 11. Location of Centers for the Egypt 5-center Problem Over 10 Runs with MaxIter = 500. 1 26819.172 26502.111 29672.806 28886.912 29178.078 29687.807 23896.031 24139.151 28933.301 26793.287

5 29076.938 28841.251 29819.564 26949.069 30337.936 26184.763 29821.244 30100.963 29359.238 29426.346

1 30135.809 30401.094 26648.960 34048.298 33913.466 26717.024 33228.657 33091.522 33296.236 30233.048

Y-coordinate of Center 2 3 4 33049.736 26988.992 30818.463 26929.873 33169.792 31124.491 33716.032 30213.330 33047.554 30898.173 27284.596 33166.567 29665.229 26833.115 33118.015 33041.791 30853.020 33511.195 33382.496 26673.255 30117.796 33419.189 30736.204 30241.785 26479.821 33026.630 29798.539 33076.279 34140.365 26929.868

5 34206.885 34012.772 30801.151 30233.356 30488.391 29859.113 30237.474 27125.361 30816.624 31289.780

109

Run # 1 2 3 4 5 6 7 8 9 10

X-coordinate of Center 2 3 4 24099.497 30336.396 29701.571 29922.404 23951.683 29891.356 29058.801 26782.813 24076.726 29983.612 30550.089 24083.706 26421.964 29851.875 24017.429 24139.093 30121.528 28955.058 29068.154 30112.542 25895.785 29132.937 29701.601 26418.540 29906.316 24269.276 26194.249 24060.016 28919.797 30237.190

Appendix Table 12. Location of Centers for the Egypt 6-center Problem Over 5 Runs with MaxIter = 300. X-coordinate of Center

Y-coordinate of Center

Run #

1

2

3

4

5

6

1

2

3

4

5

6

1

25744.028

29794.388

30285.003

29551.742

26659.774

24317.286

34495.246

30807.857

26918.886

33952.568

29929.734

31698.482

2

30575.227

29804.653

29577.374

25183.589

26729.952

24045.704

26981.300

31217.891

34009.324

34059.865

30057.415

31548.315

3

23332.224

24938.809

30348.006

29280.749

27140.511

30331.914

30707.245

33569.217

30881.470

33934.916

30154.612

26651.318

4 5

30099.932 30365.977

30284.404 23957.931

29499.815 29328.931

24056.538 27029.527

25332.381 25425.720

26590.050 30642.680

30537.517 26996.562

26707.541 31010.965

33553.675 33651.859

31961.435 30018.732

33922.180 33923.093

30005.939 30832.706

Appendix Table 13. Location of Centers for the USA 5-center problem over 5 runs with MaxIter = 100. X-coordinate of Center

Y-coordinate of Center

Run #

1

2

3

4

5

1

2

3

4

5

1

425369.190

304976.480

448046.730

427950.210

341616.360

1155510.200

827849.770

956472.450

759210.680

1030361.500

2

299373.740

437238.930

426557.400

428336.540

301470.750

1036879.100

962439.230

1155324.500

765198.340

882209.540

3

439529.150

428341.900

316232.240

306216.800

432116.250

968038.090

1154120.800

881980.360

1044426.900

763517.380

4

344706.830

454690.970

418888.230

335983.180

425632.690

852426.730

958016.300

751117.490

1047119.600

1153513.800

5

426398.460

322805.760

431629.430

341006.530

440392.500

1165505.000

836318.890

770997.620

1025095.700

975310.660

Appendix Table 14. Location of Centers for the Italy 5-center Problem Over 5 Runs with MaxIter = 50. X-coordinate of Center

Y-coordinate of Center

Run #

1

2

3

4

5

1

2

3

4

5

1

40921.949

40985.672

45694.078

38852.625

44300.243

8619.199

16112.055

9358.674

13616.356

12282.086

2

45106.195

39280.676

38874.548

44293.585

40814.135

9325.283

9806.543

13473.844

12044.399

16070.889

3

40795.305

44255.481

40951.238

44840.439

39051.348

9700.598

12254.343

16018.349

9393.138

13606.745

4

44874.722

39094.827

44535.264

40109.450

40672.696

8844.317

13649.495

12602.327

10584.164

16215.099

5

40048.593

38920.198

44225.663

44393.663

40367.603

8783.023

13590.048

12217.252

9186.029

15912.251

110

111 Appendix Figure 1. Convergence Map for wi29.tsp of 30 Runs with n = 29, p = 5 and Probability for Re-initialization of Anion and Cation in Solid Phase = 0.5.

Appendix Figure 2. Convergence Map for wi29.tsp of 30 Runs with n = 29, p = 5 and Probability for Re-initialization of Anion and Cation in Solid Phase = 0.75.

112 Appendix Figure 3. Convergence Map for wi29.tsp of 30 Runs with n = 29, p = 5 and Probability for Re-initialization of Anion and Cation in Solid Phase = 1.

Appendix Figure 4. The Average Convergence Map Over 30 Runs for Egypt 5-center Problem.

113 Appendix Figure 5. Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 1.

114 Appendix Figure 6. Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 2.

115 Appendix Figure 7. Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 3.

116 Appendix Figure 8. Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 4.

117 Appendix Figure 9. Location of Facilities for the Egypt 5-center Problem with MaxIter = 200 for Run 5.

118 Appendix Figure 10. Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 1 Best Fitness Over 10 Runs.

119 Appendix Figure 11. Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 2 Best Fitness Over 10 Runs.

120 Appendix Figure 12. Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 3 Best Fitness Over 10 Runs.

121 Appendix Figure 13. Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 4 Best Fitness Over 10 Runs.

122 Appendix Figure 14. Location of Facilities for the Egypt 5-center Problem with MaxIter = 500 for the Top 5 Best Fitness Over 10 Runs.

123 Appendix Figure 15. Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 1 Best Fitness Over 30 Runs.

124 Appendix Figure 16. Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 2 Best Fitness Over 30 Runs.

125 Appendix Figure 17. Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 3 Best Fitness Over 30 Runs.

126 Appendix Figure 18. Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 4 Best Fitness Over 30 Runs.

127 Appendix Figure 19. Location of Facilities for the Egypt 5-center Problem with MaxIter = 300 for the Top 5 Best Fitness Over 30 Runs.

128 Appendix Figure 20. Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 1.

129 Appendix Figure 21. Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 2.

130 Appendix Figure 22. Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 3.

131 Appendix Figure 23. Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 4.

132 Appendix Figure 24. Location of Facilities for the Egypt 6-center Problem with MaxIter = 300 for Run 5.

133 Appendix Figure 25. Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 1.

Appendix Figure 26. Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 2.

134 Appendix Figure 27. Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 3.

Appendix Figure 28. Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 4.

135 Appendix Figure 29. Location of Facilities for the USA 5-center Problem with MaxIter = 100 for Run 5.

Appendix Figure 30. Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 1.

136 Appendix Figure 31. Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 2.

137 Appendix Figure 32. Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 3.

138 Appendix Figure 33. Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 4.

139 Appendix Figure 34. Location of Facilities for the Italy 5-center Problem with MaxIter = 50 for Run 5.