International Journal of Advanced Robotic Systems
ARTICLE
Ant Colony Optimization Combined With Immunosuppression and Parameters Switching Strategy for Solving Path Planning Problem of Landfill Inspection Robots Regular Paper
Chao Zhang1, Qing Li1*, Peng Chen1 and Yi-nan Feng1 1 School of Automation and Electrical Engineering, University of Science and Technology Beijing, Beijing, China *Corresponding author(s) E-mail:
[email protected] Received 02 February 2016; Accepted 15 April 2016 DOI: 10.5772/63737 © 2016 Author(s). Licensee InTech. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/3.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
1. Introduction
An improved ant colony optimization (ACO) combined with immunosuppression and parameters switching strategy is proposed in this paper. In this algorithm, a novel judgment criterion for immunosuppression is introduced, that is, if the optimum solution has not changed for default iteration number, the immunosuppressive strategy is carried out. Moreover, two groups of parameters in ACO are switched back and forth according to the change of optimum solution as well. Therefore, the search space is expanded greatly and the problem of the traditional ACO such as falling into local minima easily is avoided effec‐ tively. The comparative simulation studies for path planning of landfill inspection robots in Asahikawa, Japan are executed, and the results show that the proposed algorithm has better performance characterized by higher search quality and faster search speed.
Nowadays, robots are more and more widely applied in production process and our daily life, and path planning is a very important branch in robotics, especially for mobile robots. Path planning is often treated as finding an opti‐ mum path from a start node to a goal node, and certain optimization criteria (e.g., shortest distance, minimum running time, or lowest energy consumption) must be satisfied [1]. Generally, robot is regarded as a particle in this process.
Keywords Robots, Path Planning Improved Ant Colony Optimization, Immunosuppression, Parameters Switching Strategy
In recent years, scholars have done lots of fruitful work for path planning of mobile robots, and several methods, such as artificial potential field method (APF) [2], genetic algorithm (GA) [3], particle swarm optimization (PSO) [4], and ant colony optimization (ACO), have been developed to tackle this problem [5-9]. Among them, ACO is a typical swarm intelligence optimization method, and it is wildly used recently for its convenient realization [10, 11]. How‐ ever, it has some problems, such as slow search speed, Int J Adv Robot Syst, 2016, 13:130 | doi: 10.5772/63737
1
falling into the local convergence easily, and randomness of the optimum solution, because the initial pheromone of ACO is deficient. To overcome above shortcomings, some improved ACO algorithms based on immunosuppression are presented by scholars. Immunosuppression refers to a process that keeps the individuals with high fitness and low concentration, while making obsolete the individuals with low fitness and high concentration. Liu et al. present a highly efficient algorithm-binary state ant colony algo‐ rithm based on immunodominance strategy. In this algorithm, different pheromone update methods were used, aiming at two groups of ants. Moreover, elitist ants were got from tabu table, which was optimized through immune operator such as clone expansion and hyper mutation, and then local optimization immunodominance operating was applied to enhance the explorative capacity [12]. Liu Yong et al. propose a hybrid model combined with ACO and immune clone algorithm. In this model, the pheromone distribution for ants is generated through immune memory operator at the early stage, and the concentration of pheromone is adjusted through immuno‐ suppression at the last period, so that the diversity of ant colony is preserved [13]. Lin and Huo present a modified ACO based on immune system, making use of the positive feedback of ACO and the global search capability of immune genetic algorithm, and dynamic route guidance simulation result illustrates the effectiveness of the pro‐ posed algorithm [14]. Zhang et al. use immune algorithm to obtain the iterative optimization of associated parame‐ ters of ACO, raising the efficiency of the method [15]. In the dump rebuilding project of Asahikawa, Japan, the landfill inspection robot is required for collecting the gas emission information of dump. That means all the gas emission pipelines should be traversed by land inspection robots with the minimum distance, and the inspection path planning problem can be treated as traveling salesman problem (TSP) because there is no obstacle in routing environment. Besides, the location of gas emission pipe‐ lines is distributed in rugged mountain, so they are not in the same plane, and the path planning problem could be regarded as 3D TSP. In this paper, each data collecting point in dump are viewed as a city in TSP, and the cost function is measured by 3D geometric distance, thus the way solving TSP could be used for path planning of land inspection robots. The research work of this paper is aiming at path planning for inspection robots in landfill reconstructing project, Asahikawa, Hokkaido, Japan, and its contributions can be summarized as follows:
2
1.
The environment without obstacle, such as the situation in this paper, can be converted into TSP, and it is a new mathematical model abstraction method.
2.
A modified ACO for solving path planning problem of landfill inspection robots is proposed. The proposed algorithm has a novel, targeted, and effective judg‐
Int J Adv Robot Syst, 2016, 13:130 | doi: 10.5772/63737
ment criterion for immunosuppression that the optimum solution has not changed in default iteration number; its search space is expanded by parameters switching strategy, and the defect of ACO, which falling into local minima easily, is avoided to some extent. 2. Project Background and Environment Modeling The research environment of this paper is the landfill in Etanbetsuchonakazono, Asahikawa, Hokkaido, Japan. In this section, the research background is described, then the environmental information is processed, so that path planning problem for landfill inspection robots can be converted into a TSP. 2.1 Background description The central landfill is located in No. 197 address, Etanbet‐ suchonakazono, Asahikawa, Hokkaido, Japan, which covers an area of 179.7 hectares. A mass of household garbage and some construction waste, total about 6.5 million tons, was filled here from June 1979 to June 2003 [16]. The settlement of landfill was affected, and under‐ ground water was polluted by lots of water left in garbage because of poor drainage in the landfill. Moreover, serious anaerobic environment was formed, and a great quantity of combustible gas was also accumulated in the landfill for lacking in air circulation. Therefore, potential safety hazards were increased due to deficiency of gas emission pipes [17]. Asahikawa ministry of environment reconstructed this landfill to solve the above problems. Catchpits, drainage‐ way for penetrating fluids and gas emission pipelines, have been built from 2004 to 2009. Ninety-seven gas emission pipes were erected by this project, and the number of them is expected to reach 109 [17]. The planning topographic map of landfill is shown in Figure 1, pointing out different colors in graph stands for gas emission pipes, and the altitude of gas pipes is expressed by contour line. To prevent relevant workers from encroaching of harmful gas, inspection robots are applied to collect gas concentra‐ tion of the gas emission pipes, and the route should be predetermined by simulation studies, so that the robot could travel all the pipes with minimum distance. 2.2 Environmental information processing From the above environment, path planning problem for landfill inspection robots can be converted into a TSP because there are no barriers in the dump. Due to the uneven distribution of gas emission pipes, the cost function between cities in TSP is substituted by 3D geometrical Euclidean distance between each gas emission pipeline. The horizontal plane with an altitude of 200 m is selected as X-Y plane for the 109 pipes that are mostly constructed
Figure 1. The planning topographic map of landfill in Asahikawa
Figure 2. The 3D view for all gas emission pipelines
Figure 3. The projection for the location of gas emission pipelines in X-Y plane
with a height near to 200 m. After projecting these 109 points to X-Y plane, we can find that point 8-5 is located in the center of the 109 points. So, point 8-5 is set as the origin
of 3D coordinates, and 3D view for all gas emission pipelines is shown in Figure 2, whose projection in X-Y plane is shown in Figure 3.
Chao Zhang, Qing Li, Peng Chen and Yi-nan Feng: Ant Colony Optimization Combined With Immunosuppression and Parameters Switching Strategy for Solving Path Planning Problem of Landfill Inspection Robots
3
No.
1
2
3
4
5
6
7
8
Code
8-5
9-5
10-5
11-d
12-d
A18
A19
A20
X
0
-50
-100
-150
-200
-250
-350
-400
Y
0
0
0
0
0
-7
-7
-7
Z
5.6
6.4
7.5
8.2
8.3
8.7
0
0
No.
9
10
11
12
13
14
15
16
Code
7-5
6-5
A17
8-4
9-4
10-4
11-c
12-c
X
50
100
150
0
-50
-100
-150
-200
Y
0
0
0
50
50
50
-52
52
Z
6.3
6.2
4.3
6
6.5
6.5
6.5
6.8
No.
17
18
19
20
21
22
23
24
Code
A14
A15
A16
7-4
6-4
A13
A12
A11
X
-250
-350
-400
50
100
150
200
250
Y
46
45
45
50
50
50
50
50
Z
6.8
0
0
6
6.5
2.3
-3.1
-13.5
No.
98
98
99
100
101
102
103
104
Code
B19
B17
B18
C7
B23
B22
B21
B27
X
104
200
266
0
-70
245
339
-12
Y
-256
-229
-252
-300
-306
-306
-306
-360
Z
8.5
8.3
4
16
16
10.4
5
17.4
No.
105
106
107
108
109
Code
B26
B25
B24
B29
B28
X
80
275
375
217
311
Y
-364
-360
-360
-404
-412
Z
14.6
8.6
7.4
16.6
8.8
Table 1. The coordinates of gas emission pipeline (partial)
According to the location of 109 pipelines and the origin set above, the 3D coordinates of all pipelines could be deter‐ mined, and part of them are listed in Table 1 (there are only coordinates of 37 gas emission pipelines for length limita‐ tion). The 3D geometrical distance between i th and j th gas emission pipeline could be computed by Equation (1). Dij = ( xi - x j )2 + ( yi - y j )2 + ( zi - z j )2
(1)
where (xi ,yi ,zi ) and (xj ,yj ,zj ) represent the 3D coordinates of
i th and j th gas emission pipeline separately, as listed in
Table 1.
Therefore, the path planning problem for landfill inspec‐ tion robot has already converted into a 3D traveling salesman problem. 3. Improved Ant Colony Algorithm Combined With Immunosuppression and Parameters Switching Strategy In this section, ACO and its mathematical model are introduced, a modified ACO combined with immunosup‐ 4
Int J Adv Robot Syst, 2016, 13:130 | doi: 10.5772/63737
pression and parameters switching strategy is proposed, and the steps of proposed algorithm are described. 3.1 ACO and its mathematical model The optimum solutions are built in parallel by different ants when ACO is used for TSP solving process. The probability Pijk (t) where node j is selected as the next node from current
node i by k th ant is shown as Equation (2) when the ant system (AS) model is taken as an example [18].
ì t ija (t )hijb (t ) ï a b ï Pijk (t ) = í å t is (t )his (t ) sÎallowed k ï ïî 0
j Î allowedk
(2)
otherwise
In the equation above, τij (t) and ηij (t) stand for the phero‐
mone amount and heuristic factor between nodes i and j 1
at t moment respectively. Typically ηij (t) = d , where dij is ij the distance between nodes i and j . α and β are the weights controlling the influence τij (t) and ηij (t) separately. allowedk
is the node set where all selectable nodes by k th ant are included. The route of an ant is a sequence including all serial numbers of gas emission pipes and it is also a feasible solution of TSP when all nodes are visited by the ant. If all ants completed the iteration processes, the pheromone between nodes i and j is updated by Equations (3) and (4).
t ij (t + 1) = (1 - r )t ij (t ) + Dt ij (t )
(3)
Dt ij (t ) = åDt ijk (t )
(4)
In the equation above, ρ is the pheromone evaporation coefficient. Δτijk (t) is the pheromone amount that the k th
ant released on path from node i to node j at t moment and Δτij (t) is the increment of the pheromone for all ants on path from node i to node j at the same time.
The computational equation of Δτijk (t) is shown as Equation
(5) when the ant-cycle model is chosen as the pheromone evaporation style. ìQ ï Dt ijk (t ) = í Lk ï0 î
Situation 1
(5)
otherwise
where Q is the total pheromone amount and L
k
is the
distance of the path obtained by the k th ant In Situation 1 k th ant passes through the path from node i to node j During the optimization process, the pheromone amount in the environment is accumulated or evaporated until the default maximum iteration number is reached. 3.2 Immunosuppressive ACO In ACO, the more ants pass through a path, the more pheromone is accumulated, and the higher concentration is obtained in the path. Therefore, the path will be selected in high probability in the next recursive loop. This positive feedback mechanism ensures the rapidity and convergence of ACO. However, premature phenomenon appears accordingly, and the algorithm is fall into local minima easily. To overcome the problem, some scholars take the basic idea of immunosuppression into consideration for concentration adjusting. The path concentration Cij (t) is defined as a ratio between
the amount of ants which pass through the path from node i to node j and the amount of all ants [12]. When the concentration of a path is higher than default value C0 the pheromone on this path will be inhibited. Otherwise, the
inhibition will be relieved. The immunosuppression equation is shown in Equation (6). ìt k (t )e lCij ( t ) C (t ) > C ï 0 ij t ijk (t + 1) = í ij k otherwise ïî t ij (t )
(6)
where λ is an adjusting factor and it is a negative constant. Compared with simple ACO, higher quality solution has achieved by immunosuppression algorithm proposed by Liu et al. for small-scale TSP, such as Oliver30 [12]. But in the project as mentioned above, it is a complex process in which a certain amount of pheromone accumulated in a particular path because the number of gas emission pipes is large and they are distributed uniformly, so the paths selected by ants are dispersive at the early stage. Therefore, a suitable C0, which has a direct influence on search quality, is difficult to determine under such environment. If C0 is set
too big, then the concentration value would be hard to reach and the immunosuppression may lose its efficiency. On the contrary, if C0 is set too small, then the pheromone
could not be accumulated fully, thereby the convergence speed would be slow.
Aiming at this circumstance, a novel judgment criterion for immunosuppression is introduced in this paper. The concentration of a path should be inhibited if the optimum solution has not changed successively for default iteration number and the inhibition is released when optimum solution with higher fitness value appears. The improved immunosuppression equation can be described as Equa‐ tion (7). ìt k (t )e lCij ( t ) ï t (t + 1) = í ij k ïî t ij (t ) k ij
Situation2 otherwise
(7)
In Situation 2, the optimum solution has not changed successfully for default iteration number. In this improved method, immunosuppressive strategy is utilized in accordance with the optimum solution. On the one hand, the difficulty in C0 selecting is avoided. On the other hand,
it has strong pertinency and high efficiency because it is carried out only in the circumstance where the optimum solution has no change successively for default iteration number. In addition, all the paths passed by ants are inhibited instead of some certain paths so that the paths which have not selected in early stage are more likely chosen by ants in the next iteration. As a result, the ran‐ domness information is exploited sufficiently, and the search space is expanded greatly. 3.3 Parameters switching strategy Besides immunosuppression, the parameters switching strategy is also introduced to improve the algorithm. In ACO, different selection of parameters has direct influence
Chao Zhang, Qing Li, Peng Chen and Yi-nan Feng: Ant Colony Optimization Combined With Immunosuppression and Parameters Switching Strategy for Solving Path Planning Problem of Landfill Inspection Robots
5
on problemsolving process. A group of parameters with strong randomness is usually selected for expanding the search space when ACO is trapped into stagnating state and another group of parameters with better convergence is chosen when optimum solution with higher fitness value appears so that the heuristic information can be used adequately. In this paper, three parameters ρ , α , and β are chosen as the switching parameters. Among them, ρ is the pheromone evaporation coefficient, the bigger ρ is, the faster pheromone evaporates, and the randomness of ACO is stronger. However, α and β are the parameters stand for the influence of pheromone and heuristic information to the algorithm. Bigger α leads to stronger convergence and bigger β means that ACO is easily influenced by heuristic information so that the node with local shortest path will be chosen more frequently. 3.4 Parameters switching strategy The algorithm combined with immunosuppression and parameters switching strategy proposed in this paper has six steps as follows: Step 1. Select a group of parameters with strong random‐ ness in the initial stage of algorithm. Step 2. After running for default iteration number, choose another group of parameters with better convergence to enhance the influence of pheromone and heuristic infor‐ mation. Step 3. If the optimum solution unchanged continuously for default iteration number, then switch back to parame‐ ters with strong randomness to enlarge the search space. Step 4. Inhibit the concentration with Equation (7) to expand the search space further. Step 5. If there is solution with high fitness value appearing, go back to Step 2, relieving immune suppression. Other‐ wise, keep the immunosuppression and still choose parameters with strong randomness. Step 6. Continue the algorithm until the default maximum iteration is reached.
Algorithm
Optimum solution(m)
Computing times(s)
Average
Minimal
Average
Minimal
A
6374.9001
6223.8737
51.433
50.016
B
6411.9024
6295.5747
51.192
49.313
C
6335.7857
6164.4252
50.469
47.781
D
6391.4104
6250.2623
53.547
51.217
E
6512.7402
6482.3676
52.632
50.515
Table 2. Simulation results obtained by five ant colony algorithms
6
Asahikawa. The general parameters of ACO are selected as AntCount = 150 and Q = 2000. The default maximum iteration number is set as 200. According to the experience men‐ tioned in Section 3.3, parameters with strong randomness are chosen as ρ = 1, α = 1 and β = 3, whereas parameters with strong convergence are chosen as ρ = 0.5, α = 2, and β = 4 after a large number of trial and error tests. The determination of default iteration number X is the most difficult thing in proposed algorithm. If X is too small, then the immunosuppression operator will be so frequent in which the convergence speed will be slow down. On the contrary, if X is too big, the algorithm could not handle the stagnating problem timely and the effect of immunosup‐ pression will be obviously reduced within the same maximum iteration number. After a lot of statistical experiments, the default iteration number X is set as 20. All the simulations are completed in ASUS laptop with Intel core i5 CPU, 2.40 GHz basic frequency, 2G RAM. The software running environment is Visual Studio 2008 and program language is C++. Comparative simulate studies using five algorithms defined later are investigated for path planning of landfill inspection robots in 3D TSP environ‐ ment mentioned earlier Algorithm A (Improved immunosuppressive ACO): If the optimum solution has not changed for consecutive 20 generations, the concentration of path would be adjusted by using of Equation (7) with λ = − 1.8 until optimum solution with higher fitness value appears. Parameters are chosen as ρ = 0.5, α = 2 and β = 4 Algorithm B (Parameters switching ACO): At the early stage of algorithm, select a group of parameters with strong randomness as ρ = 1, α = 1 and β = 3 to ensure the diversity of solutions. After 20 generations, another group of parame‐ ters with better convergence are selected as ρ = 0.5, α = 2 and β = 4 to utilize the pheromone and heuristic information until optimum solution with higher quality is not obtained for continuous 20 generations. Then initial group of parameters with strong randomness is switched back until optimum solution with higher fitness value appears and the group of parameters with better convergence is called again. Algorithm C (Improved ACO combined with immuno‐ suppression and parameters switching strategy): Its steps are described in Section 2.4, the values of ρ , α and β are the same as Algorithm B. Algorithm D (Immunosuppressive ACO in Ref [12]): Equation (6) is used as immunosuppression model if the concentration of certain path is larger than the default value C0. Parameters are selected as ρ = 0.5, α = 2, β = 4 and C0 = 0.6 Algorithm E (Traditional ACO): Parameters are selected as
4. Simulation Studies
ρ = 0.5, α = 2 and β = 4
The proposed algorithm is applied for path planning of landfill inspection robots in dump rebuilding project in
The simulation experiments are implemented five times for each algorithm defined above to reduce the randomness
Int J Adv Robot Syst, 2016, 13:130 | doi: 10.5772/63737
existing in problemsolving process of ACO. The average optimum solution, average computing time, minimal optimum solution and minimal computing time are shown in Table 2. Some facts can be concluded from Table 2 as follows: 1.
Algorithm E (Traditional ACO) has worst performan‐ ces no matter in computing time or search quality.
2.
Compared with Algorithm D (Immunosuppressive ACO in Ref [12]), Algorithm A (Improved immuno‐ suppressive ACO) has better performances in com‐ puting time and search quality. That indicates that the novel judgment criterion for immunosuppression proposed in this paper is effective.
3.
Algorithm C (Improved ACO combined with immu‐ nosuppression and parameters switching strategy) has achieved optimum solution with higher fitness value than Algorithm A (Improved immunosuppressive ACO) in relatively short computer time. That demon‐ strates that the parameters switching strategy has a positive impact on search quality improving and search speed accelerating. The minimal optimum solution is selected as the final result for each algo‐ rithm after five times experiments. The changes of path lengths for minimal optimum solution corresponding to each algorithm are shown in Figure 4.
The path length of optimum solution achieved by proposed algorithm is 6164.425159 and its relative sequence numbers are: V = {57, 52, 51, 53, 54, 55, 56, 59, 58, 43, 46, 38, 34, 35, 44, 45, 36, 27, 15, 16, 17, 28, 37, 29, 18, 19, 8, 7, 65, 64, 6, 5, 4, 62, 63, 72, 73, 89, 82, 88, 81, 80, 79, 71, 74, 66, 60, 61, 2, 3, 14, 13, 26, 25, 30, 20, 12, 1, 9, 10, 21, 22, 11, 68, 67, 75, 83, 91, 90, 86, 87, 96, 95, 100, 104, 101, 97, 105, 108, 103, 107, 109, 106, 102, 99, 94, 98, 93, 92, 84, 76, 77, 85, 78, 70, 69, 24, 23, 33, 32, 31, 39, 40, 41, 42, 50, 49, 48, 47}. The inspection route is shown in Figure 5.
Figure 5. Optimum inspection route for robots achieved by the proposed algorithm
5. Conclusion The main contributions of this paper are a new mathemat‐ ical model abstraction method which can convert path planning problem of inspection robots to TSP and a modified ACO combined with immunosuppression and parameters switching strategy. Simulation results of path planning for inspection robots in landfill reconstructing project in Asahikawa, Hokkaido, Japan show that the proposed algorithm obtains the shortest path with the least amount of time consumption, illustrating that immuno‐ suppression and parameters switching strategy proposed in this paper can expand the search space, avoid falling into local minima, improve the solution quality and reduce the computing time effectively. 6. Acknowledgements We are extremely grateful to College of Design and Manufacturing Technology, Muroran Institute of Technol‐ ogy, Japan for accepting one of our co-authors, Peng Chen as an international exchanging student and providing him all the conviences. We also deeply appreciate Professor Hanajima Naohiko for his scientific and rigorous guidance to Peng Chen. 7. References [1] Liu J, Yang Q D, Ma Y, Tang Z H. Global Path Planning Based on Improved Ant Colony Optimi‐ zation Algorithm for Geometry. Journal of North‐ eastern University (Natural Science). 2015;36(7): 923–928. [2] Khatib O. Real-Time Obstacle Avoidance for Manipulators and Mobile Robots. In: Proceedings of IEEE International Conference on Robotics and Automation; 1985; St. Louis, MO, USA. IEEE; p. 500–505.
Figure 4. The changes of path lengths for minimal optimum solution corresponding to each algorithm
[3] Eberhart R C, Shi Y. Comparison Between Genetic Algorithms and Particle Swarm Optimization. Evolutionary Programming VII Lecture Notes in Computer Science. 1998;1447:611–616.
Chao Zhang, Qing Li, Peng Chen and Yi-nan Feng: Ant Colony Optimization Combined With Immunosuppression and Parameters Switching Strategy for Solving Path Planning Problem of Landfill Inspection Robots
7
[4] Kennedy J, Ebehart R. Particle Swarm Optimiza‐ tion. In: Proceedings of the IEEE International Conference on Neural Networks; 1995; Perth, WA. IEEE; p. 1942–1948. [5] Peng Y, Guo, W Q, Liu M, Cui J X, Xie S R. Obstacle Avoidance Planning Based on Artificial Potential Field Optimized by Point of Tangency in ThreeDimensional Space. Journal of System Simulation. 2014;26(8): 1758–1762. [6] Li J W, Li S S Genetic Algorithm Based on Polygon Segmentation AUV Global Path Planning. Comput‐ er Engineering and Design. 2013;34(7): 2556–2560. [7] Wang X W, Shi Y P, Gu X S. Welding Robot Path Planning Based on Partition PSO. Journal of East China University of Science and Technology (Natural Science Edition). 2014;40(5):95–101. [8] Li L, Tang X L, Zhang L, Chen L. Mobile Robot Path Planning Method Based on Multi-Agent Particle Swarm Optimization in Dynamic Environment. Journal of Sichuan University (Engneering Science Edition). 2015;47(Suppl. 2):149–154. [9] Li Q, Zhang C, Chen P, Yin Y X. Improved Ant Colony Optimization Algorithm Based on Particle Swarm Optimization. Control and Decision. 2013;28(6):873–878. [10] Colorni A, Dorigo M, Maniezzo V. Distributed Optimization by Ant Colonies. In: Proceedings of European Conference on Artificial Life (ECAL91); 1991; Paris p. 134–142. [11] Colorni A, Dorigo M, Maniezzo V. An Investigation of Some Properties of An Ant Algorithm. In: Proceedings of the Parallel Problem Solving From
8
Int J Adv Robot Syst, 2016, 13:130 | doi: 10.5772/63737
Nature Conference (PPSN92); 1992; Brussels. p. 509–520. [12] Liu Z H, Zhang Y J, Li X H, Wu J H. Research of Using Binary State ACA Based on Immunodomi‐ nance to Solve TSP. Journal of Chinese Computer Systems. 2010;31(5):937–941. [13] Liu Y, Liu N, Liu S J. A TSP Solving Model Based on Immune Ant Colony Hybrid Algorithm. Journal of Sichuan University(Engineering Science Edition). 2010;42(3):121–126. [14] Li N, Huo Z S. An Ant Colony Dynamic Route Guidance of Multi-Searching Based on Immmune Genetic. Jounal of Chinese Computer Systems. 2013;34(3):590–594. [15] Zhang Y Y, Hou Y B, Li C Ant Path Planning for Handling Robot Based on Artificial Immune Algorithm. Computer Measurement and Control. 2015;23(12):4124–4127. [16] Monitoring Committee of Asahikawa Nakazono Final Disposal Site. Summary for the Nakazono Final Disposal Site. In: Proceedings of Monitoring Committee of Asahikawa Nakazono Final Disposal Site; 2010; Asahikawa. p. 1–10. [17] Kamata A, Tobita A, Matsufuji T, Yoshida H, Katayama N. Stabilizing Treatment and Closure Work for Nakazono Final Disposal Site in Asahika‐ wa City. Japan Waste Management Association. 2011;64(301):282–285. [18] Dorigo M, Maniezzo V, Colorni A. The Ant System: Optimization by a Colony of Cooperating Agents. IEEE Transaction on Systems, Man, and Cybernet‐ ics-Part B. 1996;26(1):29–41.
