Multi-Objective Fruit Fly Optimization Algorithm for ...

Paper code: 01A4

Multi-Objective Fruit Fly Optimization Algorithm for Solving Economic Power Dispatch Problem A. Abou El-Ela (1)

Ragab A. El Sehiemy(2,*)

R. M. Rizk-Allah (3)

D. Abdel Fatah (4)

1)

Electrical Engineering Department, Faculty of Engineering, Menoufia University, Egypt Electrical Engineering Department, Faculty of Engineering, Kafrelsheikh University, Egypt 3) Basic Engineering Department, Faculty of Engineering, Menoufia University, Egypt 4) M. Sc Student, Electrical Engineering Department, Faculty of Engineering, Menoufia University, Egypt * Corresponding author: [email protected] 2)

Abstract–In this paper the economic power dispatch involves the simultaneous optimization of fuel cost and emission objectives which are conflicting ones in nature. However, there is no single optimal solution which simultaneously optimizes all the objective functions. This paper presents a novel robust multi-objective fruit fly optimization algorithm (MOFOA) incorporated with Pareto optimal solutions. The algorithm is initialized by a population of random fruit flies. During this initialization, the objective functions are simulated into single objective function. Then, the evolutions of these fruit flies are performed by flying randomly around the Pareto optimal solution or around the best solution so far. The application to the standard 30-bus IEEE system demonstrates the efficiency and robustness of the proposed approach to generate well-distributed Pareto optimal solutions for the multi-objective economic power dispatch problem. Key words: fruit fly algorithm, multi-objective, economic load dispatch.

of emitted pollutants in the power system cannot be ignored and must be minimized simultaneously with the reduction of fuel cost. As a result of these objectives ED becomes a multi objective problem and must achieve the system constraints [1].In regulated and deregulated market the electricity price can be determined with the help of economic operation in power system therefore the important of ED increases [4]. Considering valve-point effect constraint, the difficult of non convexity economic dispatch problem is increased in addition a significant increase in losses occurs as a result of opening the steam admission valves [4]. The multi-objective or vector optimization is considered as an important research point for the researchers and engineers since most of the real world problems need to optimize a group of objectives simultaneously. ED is the most important one of these problems so the researchers pay a great significant attention to solve the ED as a multi-objective problem. In the beginning, the classical ED is solved using traditional deterministic methods such as Lambda iteration method, Newton method, gradient method, Dynamic programming, and General Algebraic Modeling System method (GAMS). These classical methods are inefficient to find the global solutions of the difficult optimization problems and are not suitable for continuous problems. Due to the computational drawbacks of the existing traditional methods and complexity of non-linear optimization problems, the researchers have to concentrate their studies in meta-heuristic algorithms such as genetic algorithm (GA), the particle swarm optimization (PSO), ant

I. INTRODUCTION Economic load dispatch problem is a great subject in modern power system because of its non linearity constraints. Due to this reason economic dispatch (ED) becomes a great challenge for researchers and engineers [1]. The main objective of economic dispatch of electric power generation is to make the generating units within limits to meet the requirements of load demand with minimum total generation cost at the same time satisfying the system equality and inequality constraints [2]. The passage of the United State (US) clean air act amendments of 1990 forced the utilities to modify their operational strategies of power system generating units to make the environmental impacts within limits [1, 3]. The environmental impacts have attracted significant attention so that the amount

71

A. Abou El-Ela et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] colony optimization (ACO), evolutionary algorithm (EA), simulated annealing algorithm (SA) and bat algorithm (BA). Over the last decades, there are many meta-heuristic algorithms which have been successfully applied to solve the economical emission dispatch problems in addition they are providing better solutions for some difficult and complicated real world optimization problems [5, 6, 7, 8]. A promising new meta-heuristic algorithm denotes as fruit fly optimization algorithm (FFOA). This technique was invented by Prof. Pan, a scholar of Taiwan and was developed from the foraging behavior of the fruit fly (drosophila). There are two important issues in the fruit fly algorithm. These are the smell and the vision. The main features of fruit fly that makes it different from other species are osphresis and vision [8, 9]. The FFOA can be used to simulate several types of complex optimization problems. The drosophila has such a strong osphresis that it can smell the food source 40 km away then it flies toward the location of the food. The implementation of FFOA can be divided into two stages. In the first stage, the population of flies search for the location of the food then they fly towards the food. When the flies approach the food, the second stage begins then the grope of flies fly towards the corresponding location of the food by using their sensitive vision. This process is repeated to determine the best location until the flies reach the food [10]. This technique can be constructed simply, which code can be understood easily. The problems can be solved fast and accurate solutions can be obtained. The FFOA have few adjustment parameters and fast to acquire solutions [10,11,12]. Compared with other optimization methods fruit fly algorithm is simple and more efficient. In this paper, a novel robust multi-objective fruit fly optimization algorithm (MOFOA) is proposed. It is used to solve the constrained economic load dispatch problem as a multi objective optimization problem. Firstly, the algorithm is initialized by a population of random fruit flies. During this initialization, the objective functions are simulated into single objective function. Secondly, the evolutions of these fruit flies are performed by flying randomly around the Pareto optimal solution or around the best solution so far. II.

The total fuel cost function is considered the essential part of the overall power plant unit cost. This total operating cost is consists of fixed costs such as the maintenance, supplies and personal cost so they are represented as constant values in the cost function. Therefore, the cost function is depended on the fuel cost as a controllable objective in the total cost in addition this fuel cost has a direct relation with active output power and can be represented by a quadratic function as described below [1, 13, 14]: min Ft 

NG

 (a

i

 bi PG i  c i PG i 2 )

(1)

i 1

In case of considering the valve open effect, the part of sine component (which represents the ripple effect produced by this action) will be added to this equation as [1, 14]: min Ft 

NG

 (a

i

 bi PG i  ci PG i 2 )  d i sin[ei [ PG i  PG i min ]]

(2)

i 1

Where, Ft is the non-linear fitness function which represents the overall power generation cost of the system. NG is the number of generation buses. ai , bi , ci are the coefficients of power generation cost and d i , ei are the objective function coefficients due to the valve open effect, PGi is the power generation on bus i , PG i min is the minimum production capability. This objective aims to minimize the total fuel cost in ($/h) Ft [1, 14]. The second objective aims to minimize the environmental impacts which proposed by the fossil fueled thermal units. The total emission in (ton/hr) of the atmospheric pollutants, such as nitrogen oxides and sulpher oxides, can be represented by the following equation: min E t 

NG

10

2

( i   i PG i   i PG i 2 )   i exp[i PG i ]

(3)

i 1

Where i , i and  i are the coefficients of power generation emissions. The two previous objectives must achieve the following constraints:  The total output electric power generation of all power plant units must meet load demand in addition cover the power loss in transmission lines as follows:

PROBLEM FORMULATION

NG



Economic load dispatch is a non-linear problem which aims to minimize the total fuel cost while satisfying the load requirements and the system constraints simultaneously and the minimization of fuel cost is considered the main objective of ED problem. When the generation emission is considered the ED becomes a multi-objective problem so the complexity of this problem will be increased. These main objectives can be illustrated as follows [2].

i 1

PGi 

NG

P

Dj

 Ploss

(4)

j 1

Where, PDj is the load demand at bus j , Ploss is the



total power losses in the system, NG is the number of generation buses, NL is the number of load buses. The real power generation outputs must be restricted by their lower and upper limits hence this constraint can be expressed as follow:

PGi min  PGi  PGi max

71

(5)

A. Abou El-Ela et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] fruit fly is superior to the other species in sensing and perception especially in smell and vision. The search process of the drosophila has two main functions smell and vision [10, 12]. The main steps of classical FFOA are summarized as follows: Step1: random initialize fruit fly swarm position (randomly distribute the fruit fly warm in the search space) Step2: give random direction and distance for each individual fruit fly in the search space using osphresis to find the food. .The random search distance for each fruit fly can be obtained from the following equation: (9) X i  X axis  Randomvalue

Where PGi min is the minimum power generated,

PGi max is the maximum power generated. 

The following constraint is concerned with congestion constraint. Equation (6) evaluates the power flow in transmission lines in terms of the injected power generation as follow [1]: n

T j ( PGi ) 

 (D

ji

PGi )

(j  1, 2,........ NG )

(6)

i 1

where D ji is a sensitivity factor called generalized generation distributed factor (GGDF), i is the number of lines, j is the number of generators,

Y i Y axis  Random value

T j (PGi ) is the power flows in transmission lines.

Where, X i and Y i are the random directions and distances for

In order to obtain secure and stable operation for power system the transmission line loading must be

the search of food by an individual fruit fly to x, y coordinate. Where X axis and Y axis are the random initial fruit fly swarm

restricted by it is upper bending limit PF max as follow [1]: PFk  PF

max

k  1, 2,...nl

(10)

coordinate. Step3: The location of the fruit fly cannot be known therefore the distance (Dist) of the fruit fly to the origin is calculated then the smell concentration (S) judgment value is computed which is equal to the reciprocal of distance. These calculations are represented as follow:

(7)

Where, nl is the number of transmission line. The economic load dispatch problem can be reformatted as a multi-objective problem where multi-objective optimization can be defined as the process that optimizing a collection of objective functions at the same time. Min F (x)  (f1 (x), f 2 (x),.....f k (x)) (8) s .t x  S , x  (x1 , x 2 ,....., x n )

Dist  x 2  y 2

(11)

S  1/ Dist (12) Where, Dist is the distance of the fruit fly to the origin, and S is the smell concentration judgment value. Step4: Evaluate the fitness function by substituting the smell concentration into concentration judgment function. (13) Smell  Function (S)

Where, (f1 (x),f 2 (x),.....f k (x)) are the k objective functions,

(x1 , x 2 ,....., x n ) are the n optimization parameters and S is the solution or parameter space. The ED problem has two main objectives which are conflicted in nature one of them is the minimization of fuel cost and the other is the minimization of environmental impacts. In this paper, firstly the problem is solved with considering the cost function as a single objective then the proposed algorithm is applied to minimize the combined of cost and emission function as multi-objective problem while satisfying equality and inequality constraints. Here it uses the weighted sum method which can be formulated as follow [1,15,16]: (8) F W 1  F1 (x)  W2  F2 (x)

Where, Smell is the smell concentration of the individual location of the fruit fly, Function (S) is the fitness function. Step5: Identify the best drosophila which gives the maximum concentration value. (14) [bestSmell bestIndex ]  max (Smell) Where, bestSmell is the best smell concentration value. Step6: save the smell concentration value corresponding to the best drosophila which have the best smell and keep x, y coordinates afterwards the group of fruit flies fly towards the food location depended on the sensitive vision. Smellbest  bestSmell (15) (16) X axis  X (bestindex )

Where F represents the two objective functions fuel cost and emission, F1 (x) is cost function, F2 (x) is emission function ,

W 1 and W2 are the weighting factors.

Y axis Y (bestindx )

III. FRUIT FLY OPTIMIZATION ALGORITHM In recent years, a new meta-heuristic algorithm was developed, called fruit fly optimization algorithm. This algorithm is essentially depended on the foraging behavior of fruit flies or vinegar flies in finding food. This algorithm is proposed to solve single and multi-objective optimization problems. The

(17)

Step7: Enter the iteration optimization loop, repeat the implementation of the steps from 2-5 then compare the smell concentration value with the pervious, if it is smaller, implement step 6 and repeat these steps until reaching the best location of the food(maximum iteration number) then stop the execution of the FOA searching.

71

A. Abou El-Ela et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] IV. PROPOSED ALGORITHM In this section, a framework for the proposed approach that involves two stages is presented. The first one employs the heuristic search by MOFOA to obtain approximate Pareto solution, while the other phase employs efficient local search to improve the obtained solution quality. Here the MOFOA is used to solve the economic load dispatch problem dealing with several objectives (cost and emission). The main steps of this technique are demonstrated as [16]: Step1: construct S swarms In multi objective functions, the objective functions F  (f1 ,f 2 ,....,fS ) need to be optimized at the same time, the existence of a solution that is best with respect to all objectives is not necessary. Here, the number of swarms is set to S with

V. APPLICATIONS A. Case study The IEEE 30-bus system with six generators units is selected to propose the robustness of fruit fly algorithm. The test system consists of 41 lines and six generators located at buses 25-30. The following Tables represent the upper and lower limits of the six generators of the test system in addition they represent the coefficients of cost and emission and the down ramp rate is considered as  10% [1]. Table1. Generation limits and cost coefficients [1].

G1 G2 G3 G4 G5 G6

its own pheromone structure, where S  F is the number of optimizing objective functions [16]. Step2: Initialization Firstly, the MOFOA sets the control parameters i.e. population size (number of fruit flies) N and number of iterations T. Then, randomly initialize the fruit fly swarm location in the search space where the MOFOA assigns a random vector for each fruit fly N P1 , P2 , P3 ,........Png ,Where n g is the number



Min MW 0.05 0.05 0.05 0.05 0.05 0.05

Generator

Max MW 0.5 0.6 1 1.2 1 0.6

A ($/MW) 10 10 20 10 20 10

B ($/MW) 200 150 180 100 180 150

C $ 100 120 40 60 40 100

D $ 32.4 32.4 32.4 23.4 24 24

E MW 0.047 0.047 0.047 0.063 0.063 0.063

Table2. Generator emission coefficients [1] . Coefficient α β γ ζ λ



of generator unit. The random power generation values are obtained from the following relation: PGij  pG min j  (pG max j  pG min j )  rand(); (18)

G1 4.091 -5.554 6.490 2.0E-4 2.857

G2 2.543 -6.047 5.638 5.0E-4 3.333

G3 4.258 -5.094 4.586 1.0E-6 8.000

G4 5.326 -3.550 3.380 2.0E-3 2.000

G5 4.258 -5.094 4.586 1.0E-6 8.000

G6 6.131 -5.555 5.151 1.0E-5 6.667

B. Studied states To estimate the robustness and efficiency of the proposed MOFOA, it is applied to solve constrained economic load dispatch problem in the following order [1]: State1: minimizing the fuel cost as a single objective function. State2: minimizing the generation emissions as a single objective function. State3: minimizing the two objective functions (fuel cost and generation emission) as a multi-objective problem using weighted sum method. The results obtained by the proposed algorithm are compared with those obtained by the multi-objective algorithms such as non dominated sorting genetic algorithm "NSGA" [9,19], niched Pareto genetic algorithm "NPGA" [9,19], strength Pareto Evolutionary algorithm "SPEA" [9,19] and multi objective fuzzy based on particle swarm optimization algorithm [20], Modified Shuffled Frog Leaving Algorithm "MSFLA" [21] and improved real coded genetic algorithm "RCGA" [22].

Where i  (1, 2,..., N), j  (1, 2,..., n g 1) Step3: constraints handling The previously generated values are restricted between upper and lower bounds, in addition, they are limited by power balance constraint [16, 17, 18].

pGi min  pGi  pGi max pGi  pd  ploss Where, pd is the load demand and p loss is the power loss in the system. Step4: evaluation Evaluate the objective function by substituting with the obtained solutions produced by flies based on smell sense while satisfying upper and lower limits of power generation i.e. these calculations must achieve the equality and inequality constraints. The generation reserve is used to satisfy these constraints. Smell  Function (S) (19) Afterwards, the weighted sum method is employed to solve the problem as a multi-objective function as illustrated in equation (8). Step5: pheromone update. After evaluating each fruit fly according to objective function, new solutions are generated from the following equation:

C. Results & comments State 1: minimization of fuel cost Table 3 represents the results of the ED problem solution solved by the proposed MOFOA. These results compared to Dynamic Random Neighborhood particle swarm optimization algorithm "DRN-PSO" [1] and real coded genetic algorithm "RCGA" [22] for state1. From Table 3, the fuel cost and the generation emission have minimum values 564.8935$/hr and 0.2036 ton/hr, respectively, compared to RCGA and DRNPSO. The fuel cost is reduced by 26.2582$/hr compared to DRN-PSO.

PG  PGi min  (PGi max  PGi min ) Step6: evaluate Pareto solutions. Step7: repeat the steps from 3:6. Step8: (Stopping criteria), the search will terminate if the number of iteration reaches the allowable number.

02

A. Abou El-Ela et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] Table 3 represents the evaluation of the proposed algorithm in terms of mean, best and worst values for 100 iterations (runs) and the related standard deviation for each state using the optimization algorithms reported in the literature [1]. Table 3 Best fuel cost solution for state1

Figure 1 illustrates the covergence characteristics of fuel cost against iteration number for state1 using the proposed MOFOA.

Variable

Proposed algorithm MOFOA

RGGA[22] DRN-PSO[1]

684

PG1(per unit) PG2(per unit) PG3(per unit) PG4(per unit) PG5(per unit) PG6(per unit) Mean (Fuel cost) $/hr Best (Fuel cost) $/hr Worst (Fuel cost) $/hr Standard-deviation Emission at best fuel costs ton/hr

682

fuel cost

680 678 676 674 672 670 0

50

100

150

200

250 iteration

300

350

400

450

0.1727 0.3966 0.5679 1.1079 .0.2194 0.3949 623.3722 615.5482 634.9026 5.7289

0.1764 0.2852 0.4691 0.8981 0.6350 0.3029 602.2351 591.1517 619.1436 6.0778

0.2443 0.1939 0.7416 0.4624 0.5918 0.6000 619.3516 564.8935 693.9891 53.1308

0.2285

0.215

0.2036

0.1967

500

0.1966

Fig.1. Convergence characteristics of fuel cost generation emition

0.1965

State 2: minimization of generation emission In this state, the minimization of generation emission is considered a single objective. Table 4 shows the emission economic dispatch (EED) solution considering the environmental impacts as the primary objective. The total emissions equal 0.1949 ton/hr. while the fuel cost equal 609.5658 $/hr. It is proven that the emission impacts are improved, also the fuel cost obtained using MOFOA are competitive compared to those obtained using the two other optimization algorithms (DRN-PSO, RCGA) [1].

RGGA[23]

DRN-PSO[1]

PG1(per unit) PG2(per unit) PG3(per unit) PG4(per unit) PG5(per unit) PG6(per unit) Mean (Emission) ton/hr Best (Emission) Worst (Emission ) Standarddeviation fuel costs $/hr

0.3969 0.4566 0.6015 0.3853 0.5366 0.5064

0.3850 0.4396 0.6230 0.4218 0.4702 0.5200

Proposed algorithm MOFOA 0.1344 0.5850 0.3927 1.1738 0.1838 0.3142

0.2018

0.2016

0.1968

0.1932 0.2194

0.1949 0.2128

0.1949 0.1998

0.0056

0.0036

0.0015

691.3766

643.8616

609.5658

0.1963 0.1962 0.1961 0.196 0.1959

0

10

20

30

40

50 iteration

60

70

80

90

100

Fig.2. Convergence characteristics of emission function Table 5 presents a comparison between the proposed algorithm and other optimization algorithms for solving the fuel cost and emission as a single objective. Table 5. A comparison between different algorithms solutions for states 1 and 2

Table 4 Best emission ED solution for state 2 Variable

0.1964

Algorithm

Figure 2 shows the convergence characteristics of generation emission and number of iterations for state2. The proposed algorithm gives a robust solution and good convergence characteristics.

07

State 1

State 2

Cost ($/h)

Emission (Ton/h)

Cost($/h)

Emission (Ton/h)

NSGA [9]

600.3100

0.2238

633.8300

0.1946

NPGA [9]

600.2200

0.2206

636.0400

0.1943

SPEA

[9]

600.3400

0.2241

640.4200

0.1942

FCPSO

[20]

600.1300

0.2223

638.3577

0.1942

MSFLA [21]

600.1114

0.22215

638.2425

0.1942

RCGA

[22]

611.6935

0.2285

648.5301

0.1932

DRN-PSO [1]

591.1517

0.215

643.8616

0.1949

Proposed Approach

478.2092

0.2118

609.5658

0.1994

A. Abou El-Ela et. Al. – International Conference on New Trends for Sustainable Energy 2016 [ICNTSE] [9]

State 3: Multi-objective state Table 6 presents a comparison between the multi-objective proposed algorithm and the other optimization algorithms. The featured performance of the proposed algorithm is proven from the good convergence characteristics and robust solution.

[10]

[11]

Table 6 A comparison between the different algorithms [12] Algorithm

Emission (Ton/h)

Cost ($/h)

SPEA

[9]

0.2004

610.3

NSGA

[9]

0.2041

606.03

NPGA

[9]

0.2015

608.90

MSLFA [21]

0.2006

610.0783

RCGA

[22]

0.2159

578.8774

DRN-PSO [1]

0.2119

614.8176

Proposed approach MOFOA

0.2124

604.4262

VI.

[13]

[14]

[15]

[16]

[17]

CONCLUSIONS

This paper investigates the economic load dispatch problem solution using a novel technique called multi-objective fruit fly optimization algorithm. The comparisons and results proved that the proposed method is more efficient and fast for solving non-linear multi-objective optimization problems. More economical solutions have been obtained compared to previous solutions those reported in the literature. The proposed method can be considered as an efficient alternative method.

[18]

[19]

[20]

REFERENCES [1]

[2]

[3]

[4]

[5]

[6]

[7]

[8]

[21]

M. A. El-Hosseiny, R.A. El-Sehiemy and A.Y.Haikal. "Multiobjective optimization algorithm for secure economical/emission dispatch problems." Journal of engineering and applied science 1.2, pp. 83-103, 2014. Abido, Mohammad Ali. "Multiobjective evolutionary algorithms for electric power dispatch problem." Evolutionary Computation, IEEE Transactions on10.3, pp.315-329, 2006. Niknam, T., Narimani, M. R., Aghaei, J., & Azizipanah-Abarghooee, R. "Improved particle swarm optimisation for multi-objective optimal power flow considering the cost, loss, emission and voltage stability index." Generation, Transmission & Distribution, IET 6.6, pp.515-527, 2012. Chakraborty, S., Senjyu, T., Yona, A., Saber, A. Y., & Funabashi, T. "Solving economic load dispatch problem with valve-point effects using a hybrid quantum mechanics inspired particle swarm optimisation." Generation, Transmission & Distribution, IET 5.10, pp. 1042-1052, 2011. Balasubbareddy, M. "Multi-objective optimization in the presence of ramp-rate limits using non-dominated sorting hybrid fruit fly algorithm." Ain Shams Engineering Journal (2016). R. M. Rizk-Allah, , Elsayed M. Zaki, and Ahmed Ahmed El-Sawy. "Hybridizing ant colony optimization with firefly algorithm for unconstrained optimization problems." Applied Mathematics and Computation 224, pp. 473-483, 2013. Puri, Vinod, and Yogesh K. Chauhan. "A Solution to Economic Dispatch Problem Using Augmented lagrangian Particle Swarm Optimization."International Journal of Emerging Technology and Advanced Engineering2.8, pp. 511-517, 2012. Xing, Bo, and Wen-Jing Gao. "Fruit Fly Optimization Algorithm." Innovative Computational Intelligence: A Rough Guide to 134 Clever Algorithms. Springer International Publishing, pp. 167-170, 2014.

[22]

[23]

[24]

[25]

[26]

[27]

[28]

00

Abido, M.A., "Multiobjective Evolutionary Algorithms for Electric Power Dispatch Problem", IEEE Trans. On Evolutionary computation, Vol. 10, pp. 315-329, 2006. Iscan, Hazim, and MesutGunduz. "A Survey on Fruit Fly Optimization Algorithm." 2015 11th International Conference on Signal-Image Technology & Internet-Based Systems (SITIS). IEEE, 2015. Pan, Q. K., Sang, H. Y., Duan, J. H., & Gao, L. "An improved fruit fly optimization algorithm for continuous function optimization problems." Knowledge-Based Systems 62, pp. 69-83, 2014. Lu, M., Zhou, Y., Luo, Q., & Huang, K. "An Adaptive Fruit Fly Optimization Algorithm Based on Velocity Variable." network 8.3 (2015). Hadji, B., Mahdad, B., Srairi, K., & Mancer, N. "Multi-objective PSOTVAC for Environmental/Economic Dispatch Problem." Energy Procedia 74, pp. 102-111, 2015. Soleymani, Soodabeh, and Mahdi Hayatdavudi. "Solving Economic Load Dispatch Using A Novel Method Based On PSO Algorithm And GAMS Software." International Journal of Technology Enhancements and Emerging Engineering Research 3.12, pp.8-13, 2014. Marler, R. Timothy, and Jasbir S. Arora. "Survey of multi-objective optimization methods for engineering." Structural and multidisciplinary optimization 26.6, pp.369-395, 2004. Mousa, A. A., Waiel F. Abd El-Wahed, and R. M. Rizk-Allah. "A hybrid ant colony optimization approach based local search scheme for multiobjective design optimizations." Electric Power Systems Research 81.4, pp.1014-1023, 2011. Ahmed Ahmed El-Sawy , Elsayed M. Zaki , R. M. Rizk-Allah, A Novel Hybrid Ant Colony Optimization and Firefly Algorithm for Solving Constrained Engineering Design Problems. Journal of Natural Sciences and Mathematics, Vol. 6, No. 1, PP 1-22, 2013 Ahmed Ahmed El-Sawy , Elsayed M. Zaki , R. M. Rizk-Allah, Novel Hybrid Ant Colony Optimization and Firefly Algorithm for Multiobjective Optimization Problems . International Journal of Mathematical Archive-4(1), pp.152-161, 2013. Hota, P.K., Barisal, A.K., and Chakrabarti, R., "Economic Emission Load Dispatch Through Fuzzy Based Bacterial Foraging Algorithm", International Journal of Electrical Power and Energy Systems, 2010. Agrawal, S., Panigrahi , B.K. and Tiwari, M.K., " Multiobjective Particle Swarm Algorithm With Fuzzy Clustering for Electrical Power Dispatch", IEEE Trans. on Evolutionary Computation. Vol. 12, No. 5, PP. 529-541, 2008. Reddy, A. Srinivasa, and K. Vaisakh. "Economic Emission Load Dispatch by Modified Shuffled Frog Leaping Algorithm." International Journal of Computer Applications 31.11, pp. 35-42, 2011. El-Sehiemy, R., El-Hosseini, M. A., and Hassanien, A. E. " Multiobjective Real-Coded Genetic Algorithm for Economic/Environmental Dispatch Problem", Studies in Informatics and Control, Vol. 22, No.2, PP. 113-122,2013. Zheng, Xiaolong, Ling Wang, and Shengyao Wang. "An enhanced nondominated sorting based fruit fly optimization algorithm for solving environmental economic dispatch problem." Evolutionary Computation (CEC), 2014 IEEE Congress on. IEEE, 2014 Vaishnavi, V. Jaya, and A. Srinivasa Reddy. "Multi-Objective Economic Emission Dispatch using Backtracking Search Optimization Algorithm."International Journal of Emerging Science and Engineering (IJESE) 3.2, pp. 39-46, 2014. Wang, Ling, Xiao-long Zheng, and Sheng-yao Wang. "A novel binary fruit fly optimization algorithm for solving the multidimensional knapsack problem."Knowledge-Based Systems 48, pp. 17-23, 2013. Hadji, B., Mahdad, B., Srairi, K., & Mancer, N. "Multi-objective Economic Emission Dispatch Solution Using Dance Bee Colony with Dynamic Step Size." Energy Procedia74, pp.65-76, 2015. R. M. Rizk-Allah, "A novel multi-ant colony optimization for multiobjective resource allocation problems." International Journal of Mathematical Archive (IJMA) ISSN 2229-5046 5.9 (2014). Yuan, X., Dai, X., Zhao, J., & He, Q. "On a novel multi-swarm fruit fly optimization algorithm and its application." Applied Mathematics and Computation 233, pp.260-271, 2014.