CFP last date
20 December 2024
Call for Paper
January Edition
IJCA solicits high quality original research papers for the upcoming January edition of the journal. The last date of research paper submission is 20 December 2024

Submit your paper
Know more
The week's pick
Responsive image
Improved Shuffled Frog Leaping Algorithm with Self-Adaptive Shuffling for Fuzzy Logic PD+G Controller Optimization in Robotic Manipulators

Duc Hoang Nguyen
Random Articles
Reseach Article

Survey of Metaheuristic Algorithms for Combinatorial Optimization

by Malti Baghel, Shikha Agrawal, Sanjay Silakari
journal cover thumbnail

International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 58 - Number 19
Year of Publication: 2012
Authors: Malti Baghel, Shikha Agrawal, Sanjay Silakari
10.5120/9391-3813

Malti Baghel, Shikha Agrawal, Sanjay Silakari . Survey of Metaheuristic Algorithms for Combinatorial Optimization. International Journal of Computer Applications. 58, 19 ( November 2012), 21-31. DOI=10.5120/9391-3813

@article{ 10.5120/9391-3813,
author = { Malti Baghel, Shikha Agrawal, Sanjay Silakari },
title = { Survey of Metaheuristic Algorithms for Combinatorial Optimization },
journal = { International Journal of Computer Applications },
issue_date = { November 2012 },
volume = { 58 },
number = { 19 },
month = { November },
year = { 2012 },
issn = { 0975-8887 },
pages = { 21-31 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume58/number19/9391-3813/ },
doi = { 10.5120/9391-3813 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T21:02:57.614070+05:30
%A Malti Baghel
%A Shikha Agrawal
%A Sanjay Silakari
%T Survey of Metaheuristic Algorithms for Combinatorial Optimization
%J International Journal of Computer Applications
%@ 0975-8887
%V 58
%N 19
%P 21-31
%D 2012
%I Foundation of Computer Science (FCS), NY, USA
Abstract

This paper is intended to give a review of metaheuristic and their application to combinatorial optimization problems. This paper comprises a snapshot of the rapid evolution of metaheuristic concepts, their convergence towards a unified framework and the richness of potential application in combinatorial optimization problems. Over the years, combinatorial optimization problems are gaining awareness of the researchers both in scientific as well as industrial world. This paper aims to present a brief survey of different metaheuristic algorithms for solving the combinatorial optimization problems. Basically we have divided the metaheuristic into three broad categories namely trajectory methods, population based methods and hybrid methods. Trajectory methods are those that deal with a single solution. These include simulated annealing, tabu search, variable neighborhood search and greedy randomized adaptive search procedure. Population based methods deal with a set of solutions. These include genetic algorithm, ant colony optimization and particle swarm optimization. Hybrid methods deal with the hybridization of single point search methods and population based methods. These are further categorized into five different types. Finally we conclude the paper by giving some issues which are needed to develop a well performed metaheuristic algorithm.

References
  1. A. Nagar, S. S. Heragu & J. Haddock. 1995. A meta-heuristic algorithm for a bi-criteria scheduling problem. Ann. Oper. Res. Vol. 63, pp. 397-414.
  2. A. Yu Bin, Y. Zhong-Zhen & Y. Baozhen. 2009. An improved ant colony optimization for vehicle routing problem. Eur. J. Oper. Res. Vol. 196, pp. 171-176.
  3. A. Al-khedhairi. 2008. Simulated annealing metaheuristic for solving P-median problem. Int. J. Contemp. Math. Sciences vol. 3. pp. 1357-1365.
  4. Alfonsas Misevicius. 2003. A modified simulated annealing algorithm for the quadratic assignment problem. Informatica. vol. 14, pp. 497–514.
  5. Andrade, D. V. , Resende & M. G. C. 2007. GRASP with evolutionary path-relinking. Proceedings of The Seventh Metaheuristics International Conference.
  6. Arnaldo Vieira Moura, Rafael Augusto Scaraficci. 2010. A grasp strategy for a more constrained school timetabling problem. Int. J. Oper. Res. Vol. 7, pp. 152-170.
  7. A. Roli and C. Blum. 2003. Metaheuristics in combinatorial optimization: overview and conceptual comparison. ACM Computing Surveys. vol. 35 pp. 268–308.
  8. Atkinson, J. B . 1998. A greedy randomized search heuristic for time-constrained vehicle scheduling and the incorporation of a learning strategy. J. Oper. Res. Soc. Vol. 49, pp. 700–708.
  9. Ayed A. Salman, Imtiaz Ahmad, Sabah Al-Madani. 2002. Particle swarm optimization for task assignment problem. Microprocess and Microsyst. Vol. 26, pp. 363-371.
  10. B. Hu and G. R. Raidl. Effective neighborhood structures for the generalized traveling salesman problem. In J. I. van Hemert, C. Cotta (Eds. ), Evolutionary Computation in Combinatorial Optimization—EvoCOP 2008, Vol. 4972 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany. pp. 36–47.
  11. B. Meyer. Hybrids of constructive meta-heuristics and constraint programming. A case study with ACO. In Chr. Blum, M. J. Blesa, A. Roli, and M. Sampels, editors, Hybrid Metaheuristics-An emergent approach for optimization. Springer Verlag, New York, 2008.
  12. Barnes, J. W and M. Laguna. Solve the multiple-machine weighted flow time problem using tabu search. IIE Trans. vol. 25, 1993, pp. 121-128.
  13. Barnes, J. W. , V. Wiley, J. Moore, and D. Ryer. 2004. Solving the aerial fleet refueling problem using group theoretic tabu search. Math and Comput Model. pp. 6-8.
  14. Battiti, R. and G. Tecchiolli. 1994. The Reactive Tabu Search. ORSA J Comput. Vol, 6, pp. 126–140.
  15. Bell, J. E. , McMullen, P. R. 2004. Ant colony optimization techniques for the vehicle routing problem. Adv. Eng. Inform. Vol. 1, pp. 41–48.
  16. Binato, S. , Faria, H. Jr. , Resende, M. G. C. 2001. Greedy randomized adaptive path relinking. Proceedings of the 4th Metaheuristics International Conference, pp. 393–397.
  17. Bullnheimer, B. , Hartl, R. F. , Strauss, C. 1999. An improved ant system algorithm for the vehicle routing problem. Ann. Oper. Res. vol. 89, pp. 319–328.
  18. C. Avanthay, A. Hertz, and N. Zufferey. 2003. A Variable Neighborhood Search for Graph Coloring. Eur. J. Oper. Res. Vol. 151, pp. 379–388.
  19. Christian Blum, Jakob Puchinger, Günther R. Raidl, Andrea Roli. 2011. Hybrid metaheuristics in combinatorial optimization. A survey Appl. Soft. Comput. Vol. 11, pp. 4135-4151.
  20. C. Blum, M. J. Blesa. 2009. Solving the KCT problem: large-scale neighborhood search and solution merging. In. E. Alba, C. Blum, P. Isasi, C. León, J. A. Gómez (Eds. ), Optimization Techniques for Solving Complex Problems. Hoboken, NJ,Wiley & Sons. pp. 407–421.
  21. C. C. Ribeiro and M. C. Souza. 2002. Variable neighborhood search for the degree-constrained minimum spanning tree problem. Discret. Appl. Math. vol. 118, pp. 43-54.
  22. C. H. Papadimitriou and K. Steiglitz. 1982. Combinatorial Optimization - Algorithms and Complexity Dover Publications, Inc. , New York
  23. C. Walshaw. 2004. Multilevel refinement for combinatorial optimization problems. Ann. Oper. Res. Vol. 131, pp. 325–372.
  24. C. Wilbaut, S. Hanafi, A. Fréville& S. Balev. 2009. Tabu search: global intensification using dynamic programming. Control Cybern. Vol. 35, pp. 579–598.
  25. Carlton, W. and J. W. Barnes. Solving the Traveling Salesman Problem with Time Windows Using Tabu Search. IIE Trans. Vol. 28,1996, pp. 617-629.
  26. Chen, A. L. , G. K. Yang and Z. M. Wu. 2006. Hybrid discrete particle swarm optimization algorithm for capacitated vehicle routing problem. J. Zhejiang University Sci. vol. 7, pp. 607-614.
  27. Chiung Moon et al. 2002. An efficient GA for the TSP with precedence constraints. Eur. J. Oper. Res. Vol. 140, pp. 606-617.
  28. Chu, P. C. and J. E. Beasley. 1998. A Genetic Algorithm for the Multidimensional Knapsack Problem. J Heuristics. Vol. 4, pp. 63-86.
  29. Colorni A. , Dorigo M. , Maniezzo V. & Trubian M. 1994. Ant system for job-shop scheduling. Belgian J. Oper. Res. Stat. and Comput. Sci. vol. 34, pp. 39-54.
  30. Consoli S, Darby-Dowman K, Mladenovic N and Moreno J. 2009. Variable neighborhood search for the minimum labelling Steiner tree problem. Ann. Oper. Res. Vol. 172, pp. 71-96.
  31. Consoli, S. , Moreno-Perez, JA. , Darby-Dowman, K. and Mladenovi? N. 2010. Discrete particle swarm optimization for the minimum labelling Steiner tree problem. Nat. Comput. Vol. 9 pp. 29- 46.
  32. D. T. Connolly. 1990. An improved annealing scheme for the QAP. Eur. J. Oper. Res. Vol. 46, pp. 93-100.
  33. D. L. Applegate, R. E. Bixby, V. Chvátal & W. J. Cook. 1998. On the solution of the traveling salesman problem. Doc. Math. , Extra Volume ICM III, pp. 645–656.
  34. Dorigo M and Gambardella LM. Ant colony system: a cooperative learning approach to the traveling salesman problem. IEEE T. Evol. Comput. vol. 1, 1997, pp. 53–66.
  35. Dorigo M, Maniezzo V, Colorni A. 1991. Positive feedback as a search strategy. Technical Report 91-016, Politecnico di Milano, Italy.
  36. Duarte A, Escudero LF, Marti R, Mladenovic N, Pantrigo JJ and Sanchez-Oro J. 2012. Variable Neighborhood Search for the Vertex Separation Problem. Comput. and Oper. Res.
  37. E. Danna, E. Rothberg, C. Le Pape. 2003. Integrating mixed integer programming and local search: a case study on job-shop scheduling problems. In:Fifth International Workshop on Integration of AI and OR techniques in Constraint Programming for Combinatorial Optimization Problems (CP-AI-OR'2003), pp. 65–79.
  38. E. J. Teoh, Huajin Tang and K. C Tan. 2006. A Columnar Competitive Model with Simulated Annealing for Solving Combinatorial Optimization Problems. Proc. IEEE Int Jt Conf Neural Netw, Vancouver, BC, Canada, July 16-21 pp. 3254-3259.
  39. E. Rothberg. 2007. An evolutionary algorithm for polishing mixed integer programming solutions. INFORMS. J. Comput. Vol. 19 pp. 534–541.
  40. E-G. Talbi, O. Roux, C. Fonlupt, and D. Robilliard. 2001. Parallel ant colonies for the quadratic assignment problem. Future. Gener. Comput. Syst. vol. 17,pp. 441–449.
  41. F. Glover. 1986. Future paths for integer programming and links to artificial intelligence. Comput. & Oper. Res. Vol. 13, pp. 533-549.
  42. F. Glover and G. Kochenberger. 2003. Handbook of Metaheuristics. Vol. 57 of International Series in Oper. Res. and Manag. Sci, Kluwer Academic Publishers.
  43. F. Glover. 1968. Surrogate constraints, Oper. Res. Vol. 16,741–749.
  44. Feo, T. A. , & Resende, M. G. C. 1995. Greedy randomized adaptive search procedure. J. Glob. Optim. Vol. 6, pp. 109-133.
  45. Fleurent, C. , Glover F. 1999. Improved constructive multistart strategies for the quadratic assignment problem using adaptive memory. INFORMS J. Comput. Vol. 11, pp. 198–204.
  46. Frank Neumann, Carsten Witt. 2006. Ant Colony Optimization and the Minimum Spanning Tree Problem. Electron. Colloq. Comput. Complex. (ECCC) 13.
  47. G. R. Raidl and H. Feltl. 2004. An improved hybrid genetic algorithm for the generalized assignment problem. In: H. M. Haddadd, et al. (Eds. ), Proceedings of the 2003 ACM Symposium on Appl Comput ACM Press, pp. 990–995.
  48. González-Velarde, J. L. and M. Laguna. 2002. Tabu search with simple ejection chains for coloring graphs. Ann. Oper. Res. Vol. 117, pp. 165-174.
  49. H. Tamura, A. Hirahara, I. Hatono, M. Umano. 1994. An approximate solution method for combinatorial optimization. Trans. Soc. Instrum. Control. Eng. Vol. 130 pp. 329–336.
  50. Hansen P and Mladenovi? N. 1997. Variable neighborhoods search for the p-median. Locat. Sci. Vol. 5, pp. 207-226.
  51. Harwig, J. , J. W. Barnes, J. T. Moore. 2006. An adaptive tabu search approach for 2-dimensional orthogonal packing problems. Mil. Oper. Res. Vol. 11, pp. 5-26.
  52. Hirsch, M. J. , Meneses, C. N. , Pardalos, P. M. , Resende, M. G. C. 2007. Global optimization by continuous GRASP. Optim. Lett. Vol. 1, pp. 201–212.
  53. J. Balakrishnan, C. H. Cheng, D. G. Conway, C. M. Lau. 2003. A hybrid genetic algorithm for the dynamic plant layout problem. Prod. Econ. Vol. 86, pp. 107–120.
  54. J. Bautista and J. Pereira. 2009. A dynamic programming based heuristic for the assembly line balancing problem. Eur. J. Oper. Res. Vol. 194, pp. 787–794.
  55. J. E. Beasley and P. C. Chu(1996) A genetic algorithm for the set covering problem. Eur. J. Oper. Res. Vol 94, pp. 392–404.
  56. J. H. Holland. 1975. Adaptation in natural and artificial systems, The University of Michigan Press, Ann Harbor, MI
  57. J. Kennedy and R. C. Eberhart. 1995. Particle swarm optimization. Proc. of IEEE Int Conf. on Neural Netw Piscataway, NJ, USA , pp. 1942-1948.
  58. J. Lazi?, S. Hanafi, N. Mladenovi?, D. Uroševi?. 2010. Variable neighborhood decomposition search for 0–1 mixed integer programs. Comput. and Oper. Res. Vol. 37, pp. 1055–1067.
  59. J. C. Beck. 2007. Solution-guided multi-point constructive search for job shop scheduling. J. Artif. Intel. Vol. 29, Res. pp. 49–77.
  60. J. E. Gallardo, C. Cotta and A. J. Fernández. 2007 On the hybridization of memetic algorithms with branch-and-bound techniques. IEEE Trans. on Syst. Man. and Cybern. —Part B Vol. 37, pp. 77–83.
  61. James, T. , Rego, C. , Glover, F. 2009. Multistart tabu search and diversi?cation strategies for the quadratic assignment problem. IEEE Trans. Syst. Man. and Cybern. Part A: Systems and Humans. Vol. 39, pp. 579–596.
  62. Jingfa Liu, Yu Zheng, Wenjie Liu. 2009. A Heuristic Simulated Annealing Algorithm for the Circular Packing Problem. Genet. Evol. Comput. pp. 802-805.
  63. Kinney, G. , J. W. Barnes, and B. Colletti. 2007. A Reactive Tabu Search algorithm with variable clustering for the Unicost Set Covering Problem. Int. J. Oper. Res. Vol. 2, pp. 156-172.
  64. Kirkpatrick, S. , Gelatt, C. D. , Vecchi, M. P. 1983. Optimization by simulated annealing. Sci. Vol. 220, pp. 671-680.
  65. Korycinski, D. , M. M. Crawford, J. W. Barnes, and J. Ghosh. 2003. Adaptive feature selection for hyperspectral data analysis using a binary hierarchical classifier and tabu search. Proc. 2003 International Geoscience and Remote Sensing Symposium, Toulouse, France, pp. 297-299.
  66. KP Wang, L Huang, CG Zhou, W Pang. 2003. Particle swarm optimization for traveling salesman problem. Int. Conf. Mach. Learn. and Cybern. Vol. 3, pp. 1583-1585.
  67. Kunpeng KANG. 2012. A Fast Particle Swarm Optimization Algorithm for Large Scale Multidimensional Knapsack Problem. J. Comput. Inform. Syst. Vol. 8, pp. 2709–2716.
  68. Kusum Deep and Hadush Mebrathu. 2011. Combined Mutation Operators of Genetic Algorithm for the Travelling Salesman Problem. Int. J. Comb. Optim. Probl. Inform. Vol. 2, pp. 2-24.
  69. L. Shi and S. Ólafsson. 2000. Nested partitions method for global optimization. Oper. Res. Vol. 48, pp. 390–407.
  70. Laguna, M. , J. P. Kelly, J. L. González Velarde, and F. Glover. 1995. Tabu search for the multilevel generalized assignment problem. Eur. J. Oper. Res. Vol. 82,pp. 176-189.
  71. Laguna, M. , J. W. Barnes, F. W. Glover. 1991. Tabu search methods for a single machine scheduling problem. J. Intel. Manuf. Vol. 2, pp. 63-74.
  72. Laguna, M. , Mart?´, R. 1999. GRASP and path relinking for 2-layer straight line crossing minimization. INFORMS. J. Comput. Vol. 11, pp. 44–52.
  73. Lei Yuan, Zhendong Zhao. A Modified Binary Particle Swarm Optimization Algorithm for Permutation Flow Shop Problem. In Proceedings of the Sixth Int Conf Mach Learn Cyberns (ICMLC 2007), Hong Kong (19-22) August 2007, pages 902-907.
  74. Lokketangen, A. , F. Glover. 1998. Solving zero-one mixed integer programming problems using tabu search. Eur. J. Oper. Res. vol. 106, pp. 624-658.
  75. M. Haouari and J. C. Siala. 2006. A hybrid Lagrangian genetic algorithm for the prize collecting Steiner tree problem. Comput. Oper. Res. vol. 33, pp. 1274–1288.
  76. M. Khichane, P. Albert, C. Solnon. Integration of ACO in a constraint programming language. In: Proceedings of ANTS 2008—6th International Workshop on Ant Colony Optimization and Swarm Intelligence. Vol. 5217 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, 2008, pp. 84–95.
  77. M. López-Ibáñez and C. Blum. 2010. Beam-ACO for the travelling salesman problem with time windows. Comput. Oper. Res. vol. 37, pp. 1570–1583.
  78. M. Lozano and C. García-Martínez. 2010. Hybrid metaheuristics with evolutionary algorithms specializing in intensification and diversification: overview and progress report. Comput. Oper. Res. vol. 37, pp. 481–497.
  79. M. Prandtstetter and G. R. Raidl. 2008. An integer linear programming approach and a hybrid variable neighborhood search for the car sequencing problem. Eur. J. Oper. Res. Vol. 191, pp. 1004–1022.
  80. M. Reimann. Guiding ACO by problem relaxation: a case study on the symmetric TSP. In: T. Bartz-Beielstein, M. J. Blesa Aguilera, C. Blum, B. Naujoks, A. Roli, G. Rudolph, M. Sampels (Eds. ) Proceedings of HM 2007—Fourth International Workshop on Hybrid Metaheuristics, Vol. 4771 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany,2007, pp. 45–55.
  81. M. Vasquez & Y. Vimont. 2005. Improved results on the 0–1 multidimensional knapsack problem. Eur. J. Oper. Res. vol. 165, pp. 70–81.
  82. M. G. C. Resende, R. Martí, M. Gallego & A. Duarte. 2010. GRASP and path relinking for the max–min diversity problem. Comput. Oper. Res. vol. 37, pp. 498–508.
  83. M. J. Geiger, M. Sevaux & Stefan Vo?. 2011. Neighborhood selection in VNS. Metaheuristic international conference 25-28.
  84. Matheus Rosendo & Aurora Pozo. 2010. A hybrid Particle Swarm Optimization algorithm for combinatorial optimization problems. IEEE Congr. Evol. Comput. pp. 1-8.
  85. Mladenovic N , Urosevic D, Perez-Brito D and Garcia-Gonzalez CG. 2010. Variable neighborhood search for bandwidth reduction. Eur. J. Oper. Res. vol. 200, pp. 14-27.
  86. N. Mladenovic and P. Hansen. 1997. Variable Neighborhood Search. Comput. Oper. Res. vol. 24,pp. 1097-1100.
  87. N. Mladenovi? and D. Urosevi?. 2001. VNS for the k-cardinality tree. In. Proceedings of 4th Metaheuristics International Conference, MIC'2001, Edited by J. Sousa, Porto, Portugal.
  88. Nanry, W. P. and J. W. Barnes. 2000. Solving the pickup and delivery problem with time windows using reactive tabu search. Trans. Res. Part B vol. 34, pp. 107-121.
  89. Neelam Tyagi and Varshney R. G. 2012. A Model To Study Genetic Algorithm For The Flowshop Scheduling Problem. J. Inform. Oper. Manag. ISSN: 0976–7754 & E-ISSN: 0976–7762, Volume 3, pp-38-42.
  90. Olli Braysy. 2001. Genetic algorithms for the vehicle routing problem with time windows. Technical Report, 1/2001, University of Vaasa, Vaasa, Finland.
  91. Omar M. Sallabi and Younis El-Haddad. 2009. An Improved Genetic Algorithm to Solve the Travelling Salesman Problem. World Acad. Sci. Eng. and Technol. vol. 52, pp. 471-474.
  92. Ou, G. , Tamura, H. , Tanno, K. and Tang, Z. 2010. A method of solving scheduling problems using an improved guided genetic algorithm. Electron. Comm. Jpn. vol. 93, pp. 15–22.
  93. P Shaw. 1998. Using constraint programming and local search methods to solve vehicle routing problems. In: M. Maher, J. -F. Puget (Eds. ), Principle and Practice of Constraint Programming—CP98, Vol. 1520 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany , pp. 417–431.
  94. P. C, Chu and J. E. Beasley. 1997. A genetic algorithm for the generalized assignment problem. Comput. Oper. Res. vol. 24, pp. 17–23.
  95. P. J. M. Van Laarhoven, E. H. L. Aarts, and J. K. Lenstra. 1992. Job Shop Scheduling by Simulated Annealing. Oper. Res. vol. 40,pp. 113-125.
  96. P. C, Chu & J. E. Beasley. 1998. A genetic algorithm for the multidimensional knapsack problem. J. Heuristics. vol. 4, pp. 63–86.
  97. PIEROBOM , JL DELGADO, RSB Kaestner, CAA. 2011. Particle Swarm Optimization Applied to task assignment problem. In: X Brazilian Congr on Comput Intel. Fortaleza, CE: Proceedings of the 2011 CBIC
  98. Prais, M. , Ribeiro, C. C. 2000. Reactive GRASP: an application to a matrix decomposition problem in TDMA traffic assignment. INFORMS. J. Comput. vol. 12, pp. 164–176.
  99. Puchinger, J. and G. R. Raidl. 2005. Relaxation Guided Variable Neighborhood Search. In Proceedings of the XVIII Mini EURO Conference on VNS, Tenerife, Spain
  100. R. K. Ahuja, J. B. Orlin and A. Tiwari. 2000. A descent genetic algorithm for the quadratic assignment problem. Comput. Oper. Res. vol. 27, pp. 917–934.
  101. R. Montemanni and D. H. Smith. 2010. Heuristic manipulation, tabu search and frequency assignment. Comput. Oper. Res. vol. 37, pp. 543–551.
  102. R. K. Congram, C. N. Potts, S. L. van de Velde. 2002. An iterated dynasearch algorithm for the single-machine total weighted tardiness scheduling problem. INFORMS J. Comput. vol. 14, pp. 52–67.
  103. Ribeiro, C. C. , Uchoa, E. , Werneck, R. F. 2002. A hybrid GRASP with perturbations for the Steiner problem in graphs. INFORMS. J. Comput. vol. 14, pp. 228–246.
  104. S. Pirkwieser, G. R. Raidl, J. Puchinger. Combining Lagrangian decomposition with an evolutionary algorithm for the knapsack constrained maximum spanning tree problem. In: C. Cotta, J. I. van Hemert (Eds. ), Evol Comput Comb Optim—EvoCOP 2007, Vol. 4446 of Lecture Notes in Computer Science, Springer-Verlag, Berlin, Germany, 2007, pp. 176–187.
  105. S. Prestwich, S. Tarim, R. Rossi & B. Hnich. 2009. Evolving parameterized policies for stochastic constraint programming. In: I. Gent (Ed. ), Principles and Practice of Constraint Programming—CP 2009, Vol. 5732 of Lecture Notes in Computer Science, Springer-Verlag, Berlin Heidelberg, Germany, pp. 684–691.
  106. S. -M. Tse, Y. Liang, K. -S. Leung, K. -H. Lee, T. S. -K. Mok. A memetic algorithm for multiple-drug cancer chemotherapy schedule optimization. IEEE Trans on Syst Man, Cybern—Part B, vol. 37, 2007, 84–91.
  107. Scrich, C. R. , V. A. Armentano and M. Laguna. 2004. Tardiness minimization on a flexible job shop: a tabu search approach. J. Intel. Manuf. vol. 15,pp. 103-115.
  108. Sevkli, M. , Aydin,. M. E. A variable neighborhood search implementation for job shop scheduling problems. In Pro. Of EvoCOP 2006 , Lecture Notes in Computer Science 3906, Budapest, Hungary, (10-12 April 2006), pp. 261271.
  109. Sevkli, M. , Guner, A. R. 2008. A Discrete Particle Swarm Optimization Algorithm for Uncapacitated Facility Location Problem. J. Artif. Evol. Appl. Vol. 2008, pp. 1-9.
  110. Surekha P. 2010. Solving fuzzy based job shop scheduling problems using GA and ACO. J Emerg Trends Comput and Inform Sci, vol. 1, pp. 95-102.
  111. T Stützle. 2006. Iterated local search for the quadratic assignment problem. Eur. J. Oper. Res. vol. 174, pp. 1519–1539.
  112. Tasgetiren MF, Sevkli M, Liang YC, Gencyilmaz G. Particle swarm optimization algorithm for single machine total weighted tardiness problem. In: Proc. of the IEEE Congr Evol Comput, Portland,vol. 2, 2004, pp. 1412–1419.
  113. Tate David M. , Smith Alice E. 1995. A Genetic Approach to the Quadratic Assignment Problem. Comput. Oper. Res. vol. 22, pp. 73-83.
  114. Thomas Stutzle. An ant approach to the ?ow shop problem. In Proceedings of the 6th European Congress on Intelligent Techniques & Soft Computing (EUFIT'98), Verlag Mainz, Aachen, volume 3, 1998, pp. 1560–1564.
  115. Ulrike Schneider. 2011. A Tabu search tutorial based on a real world scheduling problem. Cent. Eur. J. Oper. Res. vol. 19, pp. 467-493.
  116. V. J. Rayward-Smith and A. S. Wade. 2000. Effective Local Search for the Steiner Tree Problem. In Advances in Steiner Trees ed. by Ding-Zhu Du, J. M. Smith and J. H. Rubinstein, Kluwer.
  117. Xu Hao. 2010. Optimization Models and Heuristic Method Based on simulated annealing Strategy for Solving Travelling Solution Problem. Appl. Mech. Mater. vols (34-35),pp 1180-1184.
  118. Yannis Marinakis. 2012. Multiple phase neighborhood search GRASP for the capacitated vehicle routing problem. Expert. Syst. Appl. vol. 39, pp. 6807-6815.
  119. Zar Chi Su Su Hlaing, May Aye Khine. 2011. An Ant Colony Optimization Algorithm for Solving Traveling Salesman Problem. Int Proc of Comput Sci Inform Technol, vol. 16, pp. 54-59.
Index Terms

Computer Science
Information Sciences

Keywords

Ant Colony optimization Combinatorial optimization problems Genetic algorithm Greedy randomized adaptive search procedure Particle swarm optimization Simulated Annealing Tabu search variable neighborhood search

Powered by PhDFocusTM