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Handling equality constraints with agent-based memetic algorithms

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Abstract

In addition to inequality constraints, many mathematical models require equality constraints to represent the practical problems appropriately. The existence of equality constraints reduces the size of the feasible space significantly, which makes it difficult to locate feasible and optimal solutions. This paper presents a new equality constraint handling technique which enhances the performance of an agent-based evolutionary algorithm in solving constrained optimization problems with equality constraints. The technique is basically used as an agent learning process in the agent-based evolutionary algorithm. The performance of the proposed algorithm is tested on a set of well-known benchmark problems including seven new problems. The experimental results confirm the improved performance of the proposed technique.

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References

  1. Sarimveis H, Nikolakopoulos A (2005) A line up evolutionary algorithm for solving nonlinear constrained optimization problems. Comput Oper Res 32: 1499–1514

    Article  MathSciNet  Google Scholar 

  2. Liang JJ, Suganthan PN (2006) Dynamic multi-swarm particle swarm optimizer with a novel constraint-handling mechanism. In: IEEE Congress on evolutionary computation, CEC 2006, pp 9–16

  3. Mezura-Montes, Ee (eds) (2009) Constraint-handling in evolutionary optimization. Springer, Berlin

    Google Scholar 

  4. Ho PY, Shimizu K (2007) Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Inf Sci 177: 2985–3004

    Article  Google Scholar 

  5. Back T, Hammel U, Schwefel HP (1997) Evolutionary computation: comments on the history and current state. IEEE Trans Evol Comput 1: 3

    Article  Google Scholar 

  6. Marczyk A (2004) Genetic algorithms and evolutionary computation. TalkOrigins Archive

  7. Sarker R, Kamruzzaman J, Newton C (2003) Evolutionary optimization (EvOpt): a brief review and analysis. Int J Computat Intell Appl 3: 311–330

    Article  Google Scholar 

  8. Chootinan P, Chen A (2006) Constraint handling in genetic algorithms using a gradient-based repair method. Comput Oper Res 33: 2263–2281

    Article  MATH  Google Scholar 

  9. Michalewicz Z, Schoenauer M (1996) Evolutionary algorithms for constrained parameter optimization problems. Evol Comput 4: 1–32

    Article  Google Scholar 

  10. Venkatraman S, Yen GG (2005) A generic framework for constrained optimization using genetic algorithms. IEEE Trans Evol Comput 9: 424–435

    Article  Google Scholar 

  11. Deb K (2000) An efficient constraint handling method for genetic algorithms. Comput Methods Appl Mech Eng 186: 311–338

    Article  MATH  Google Scholar 

  12. Coello Coello CA (2002) Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Comput Methods Appl Mech Eng 191: 1245–1287

    Article  MATH  MathSciNet  Google Scholar 

  13. Mezura-Montes E, Coello CAC (2002) A numerical comparison of some multiobjective-based techniques to handle constraints in genetic algorithms. Technical report EVOCINV-03-2002. Evolutionary Computation Group at CINVESTAV-IPN, Mexico

  14. Barkat Ullah ASSM, Sarker R, Lokan C (2009) An agent-based memetic algorithm (AMA) for nonlinear optimization with equality constraints. In: The 2009 IEEE Congress on evolutionary computation (CEC 2009), Norway

  15. Takahama T, Sakai S (2009) Solving difficult constrained optimization problems by the ɛ constrained differential evolution with gradient-based mutation. In: Mezura-Montes E (eds) Constraint-handling in evolutionary optimization. Springer, Berlin, pp 51–72

    Chapter  Google Scholar 

  16. Merz P, Freisleben B (1997) Genetic local search for the TSP: new results. In: Evolutionary Computation, 1997. IEEE international conference, pp 159–164

  17. Cheng R, Gen M (1996) Parallel machine scheduling problems using memetic algorithms. IEEE Int Conf Syst Man Cybern 4: 2665–2670

    Google Scholar 

  18. Burke EK, Smith AJ (1999) A memetic algorithm to schedule planned maintenance for the national grid. J Exp Algorithmics 4(1): 1–13

    Article  Google Scholar 

  19. Tang J, Lim MH, Ong YS, Er MJ (2005) Solving large scale combinatorial optimization using PMA-SLS. In: Proceedings of the 2005 conference on genetic and evolutionary computation. ACM Press, Washington DC, pp 621–628

  20. Merz P, Freisleben B (2000) Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Trans Evol Comput 4: 337–352

    Article  Google Scholar 

  21. Alkan A, Ozcan E (2003) Memetic algorithms for timetabling. In: The 2003 Congress on evolutionary computation, vol 3, pp 1796–1802

  22. Vavak F, Fogarty T, Jukes K (1996) A genetic algorithm with variable range of local search for tracking changing environments. Parallel problem solving from Nature—PPSN IV. Springer, Berlin, pp 376–385

    Google Scholar 

  23. Handoko S, Kwoh CK, Ong YS (2009) Feasibility structure modeling: an effective chaperon for constrained memetic algorithms. IEEE Trans Evol Comput (in press)

  24. Handoko SD, Kwoh CK, Ong YS (2009) Classification-assisted memetic algorithms for equality-constrained optimization problems. AI 2009: advances in artificial intelligence, vol 5866. Springer, Berlin, pp 391–400

  25. Knowles J, Corne DW (2001) A comparative assessment of memetic, evolutionary and constructive algorithms for the multi-objective d-msat problem. In: GECCO-2001 workshop program, pp 162–167

  26. Knowles J, Corne DW (2000) M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of the 2000 Congress on evolutionary computation, vol 1, California, pp 325–332

  27. Hu X, Huang Z, Wang Z (2003) Hybridization of the multi-objective evolutionary algorithms and the gradient-based algorithms. In: The 2003 Congress on evolutionary computation, vol 2, pp 870–877

  28. Knowles J, Corne DW (2005) Memetic algorithms for multiobjective optimization: issues, methods and prospects. In: Recent advances in memetic algorithms, pp 313–352

  29. Tang J, Lim M, Ong Y (2007) Diversity-adaptive parallel memetic algorithm for solving large scale combinatorial optimization problems. Soft Comput Fusion Found Methodol Appl 11: 873–888

    Google Scholar 

  30. Dawkins R (1976) The selfish gene. Oxford University Press, New York

    Google Scholar 

  31. Hart WE (1994) Adaptive global optimization with local search. PhD thesis, University of California, San Diego

  32. Krasnogor N (2002) Studies on the theory and design space of memetic algorithms. PhD thesis, University of the West of England

  33. Krasnogor N, Smith J (2005) A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Trans Evol Comput 9: 474–488

    Article  Google Scholar 

  34. Ong YS, Keane AJ (2004) Meta-Lamarckian learning in memetic algorithms. IEEE Trans Evol Comput 8: 99–110

    Article  Google Scholar 

  35. Merz P, Freisleben B (1999) A comparison of memetic algorithms, tabu search, and ant colonies for the quadratic assignment problem. In: Proceedings of the 1999 Congress on evolutionary computation, CEC 99, vol 3, pp 2063–2070

  36. Goldberg DE, Voessner S (1999) Optimizing global-local search hybrids. In: Proceedings of the genetic and evolutionary computation conference, pp 220–228

  37. Tang J, Lim MH, Ong YS (2006) Adaptation for parallel memetic algorithm based on population entropy. In: Proceedings of the 8th annual conference on genetic and evolutionary computation. ACM Press, Seattle

  38. Davis L (1991) Handbook of genetic algorithms. Van Nostrand Reinhold, New York

    Google Scholar 

  39. Ferber J (1999) Multiagent systems as introduction to distributed artificial intelligence. Addision-Wesley, Boston

    Google Scholar 

  40. Stan F, Art G (1997) Is it an agent, or just a program? A taxonomy for autonomous agents. Intelligent agents III agent theories, architectures, and languages. Springer, Berlin, pp 21–35

    Google Scholar 

  41. Chira C, Gog A, Dumitrescu D (2008) Exploring population geometry and multi-agent systems: a new approach to developing evolutionary techniques. In: Proceedings of the 2008 GECCO conference companion on genetic and evolutionary computation. ACM, Atlanta, pp 1953–1960

  42. Deb K, Agrawal RB (1995) Simulated binary crossover for continuous search space. Complex Syst 9: 115–148

    MATH  MathSciNet  Google Scholar 

  43. Barkat Ullah ASSM, Sarker R, Cornforth D, Lokan C (2007) An agent-based memetic algorithm (AMA) for solving constrained optimization problems. In: IEEE Congress on evolutionary computation, CEC 2007, Singapore, pp 999–1006

  44. Barkat Ullah ASSM, Sarker R, Cornforth D, Lokan C (2008) AMA: a new approach for solving constrained real-valued optimization problems. Soft Comput Fusion Found Methodol Appl 13(8–9): 741–762. doi:10.1007/s00500-008-0349-1

    Google Scholar 

  45. Runarsson TP, Yao X (2000) Stochastic ranking for constrained evolutionary optimization. IEEE Trans Evol Comput 4: 284

    Article  Google Scholar 

  46. Himmelblau DM (1972) Applied nonlinear programming. McGraw-Hill, Boston

    MATH  Google Scholar 

  47. Hillier FS, Lieberman GJ (2005) Introduction to operations research. McGraw-Hill, Boston

    Google Scholar 

  48. Hock W, Schittkowski K (1981) Test examples for nonlinear programming codes. Springer-Verlag, New York

    MATH  Google Scholar 

  49. Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6: 182

    Article  Google Scholar 

  50. Ray T, Sarker R (2007) Genetic algorithm for solving a gas lift optimization problem. J Petroleum Sci Eng 59: 84–96

    Article  Google Scholar 

  51. Kisiel-Dorohinicki M (2002) Agent-oriented model of simulated evolution. In: SOFSEM 2002: theory and practice of informatics, pp 253–261

  52. Siwik L, Kisiel-Dorohinicki M (2006) Semi-elitist evolutionary multi-agent system for multiobjective optimization. Computational Science—ICCS 2006. Springer, Berlin, pp 831–838

  53. Zhong W, Liu J, Xue M, Jiao L (2004) A multiagent genetic algorithm for global numerical optimization. IEEE Trans Syst Man Cybern B 34: 1128–1141

    Article  Google Scholar 

  54. Byrski A, Schaefer R (2009) Formal model for agent-based asynchronous evolutionary computation. In: IEEE Congress on evolutionary computation (CEC) 2009, Norway, pp 78–85

  55. Dobrowolski G., Kisiel-Dorohinicki M, Nawarecki E (2001) Evolutionary multiagent system in multiobjective optimisation. In: Hamza M (ed) Proceedings of the IASTED international symposium: applied informatics. IASTED/ACTA Press

  56. Socha K, Kisiel-Dorohinicki M (2002) Agent-based evolutionary multiobjective optimisation. In: Proceedings of the 2002 Congress on evolutionary computation, vol 1, pp 109–114

  57. Dreżewski R, Kisiel-Dorohinicki M (2006) Maintaining diversity in agent-based evolutionary computation. In: Computational Science—ICCS 2006, pp 908–911

  58. Zhong W, Liu J, Jiao L (2005) Job-shop scheduling based on multiagent evolutionary algorithm. In: Lecture notes in computer science: advances in natural computation. Springer, Berlin, pp 925–933

  59. Yan C, Zeng-Zhi L, Zhi-Wen W (2004) Multi-agent based genetic algorithm for JSSP. In: Proceedings of 2004 international conference on machine learning and cybernetics, vol 1, pp 267–270

  60. Liu J, Zhong W, Jiao L (2006) A multiagent evolutionary algorithm for constraint satisfaction problems. IEEE Trans Syst Man Cybern B 36: 54–73

    Article  Google Scholar 

  61. Liu H, Frazer JH (2002) Supporting evolution in a multi-agent cooperative design environment. Adv Eng Softw 33: 319–328

    Article  MATH  Google Scholar 

  62. Choi SPM, Liu J, Chan S-P (2001) A genetic agent-based negotiation system. Comput Netw 37: 195–204

    Article  Google Scholar 

  63. Meng A, Ye L, Roy D, Padilla P (2007) Genetic algorithm based multi-agent system applied to test generation. Comput Educ 49: 1205–1223

    Article  Google Scholar 

  64. Lim MK, Zhang Z (2002) Iterative multi-agent bidding and co-ordination based on genetic algorithm. In: Proceeding of 3rd international symposium on multi-agent systems, large complex systems, and e-businesses, Erfurt, pp 682–689

  65. Pendharkar PC (2007) The theory and experiments of designing cooperative intelligent systems. Decis Support Syst 43: 1014–1030

    Article  Google Scholar 

  66. Smith RE, Kearney PJ, Merlat W (1999) Evolutionary adaptation in autonomous agent systems—a paradigm for the emerging enterprise. BT Technol J 17: 157–167

    Article  Google Scholar 

  67. Jeong IK, Lee JJ (1997) Evolving multi-agents using a self-organizing genetic algorithm. Appl Math Comput 88: 293

    Article  MATH  MathSciNet  Google Scholar 

  68. Yang A, Abbass H, Sarker R (2006) Land combat scenario planning: a multiobjective approach. Simulated evolution and learning. Springer, Berlin, pp, pp 837–844

    Google Scholar 

  69. Sahin CS, Urrea E, Uyar MU, Conner M, Hokelek I, Conner M, Bertoli G, Pizzo C (2008) Genetic algorithms for self-spreading nodes in MANETs. In: Proceedings of the 10th annual conference on Genetic and evolutionary computation. ACM, Atlanta, pp 1141–1142

  70. Sahin CS, Urrea E, Uyar MU, Conner M, Hokelek I, Bertoli G, Pizzo C (2008) Uniform distribution of mobile agents using genetic algorithms for military applications in MANETs. In: IEEE military communications conference, 2008. MILCOM 2008, pp 1–7

  71. Davidsson P, Persson J, Holmgren J (2007) On the integration of agent-based and mathematical optimization techniques. Agent and multi-agent systems: technologies and applications, pp 1–10

  72. Nakashima T, Ariyama T, Yoshida T, Ishibuchi H (2003) Performance evaluation of combined cellular genetic algorithms for function optimization problems. In: Proceedings of 2003 IEEE international symposium on computational intelligence in robotics and automation, vol 1, pp 295–299

  73. De Jong KA (2008) Evolving intelligent agents: a 50 year quest. Comput Intell Mag IEEE 3: 12–17

    Article  MathSciNet  Google Scholar 

  74. Vasile M, Locatelli M (2008) A hybrid multiagent approach for global trajectory optimization. J Glob Optim 44: 461–479

    Article  MathSciNet  Google Scholar 

  75. Thornton C, Boulay Bd (1999) Artificial intelligence: strategies, applications, and models through SEARCH. AMACOM, New York

    Google Scholar 

  76. Bajo J, Corchado J (2006) Multiagent architecture for monitoring the North-Atlantic carbon dioxide exchange rate. In: Current topics in artificial intelligence, pp 321–330

  77. Hasan SMK, Sarker R, Essam D, Cornforth D (2008) Memetic algorithms for solving job-shop scheduling problems. Memetic Comp 1: 69–83

    Article  MATH  Google Scholar 

  78. Alba E, Dorronsoro B (2005) The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Trans Evol Comput 9: 126–142

    Article  Google Scholar 

  79. Deb K (2001) Multi-objective optimization using evolutionary algorithms. Wiley, New York

    MATH  Google Scholar 

  80. Barkat Ullah ASSM, Sarker R, Cornforth D (2007) An evolutionary agent system for mathematical programming. In: Advances in computation and intelligence. Lecture notes in computer science. Springer, Berlin, pp 187–196

  81. Barkat Ullah ASSM, Sarker R, Cornforth D (2008) Search space reduction technique for constrained optimization with tiny feasible space. In: Proceedings of the 10th annual conference on genetic and evolutionary computation. ACM, Atlanta, pp 881–888

  82. Elfeky EZ, Sarker RA, Essam DL (2006) A simple ranking and selection for constrained evolutionary optimization. In: Lecture notes in computer science: simulated evolution and learning, pp 537–544

  83. Koziel S, Michalewicz Z (1999) Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evol Comput 7: 19–44

    Article  Google Scholar 

  84. Joines JA, Houck CR (1994) On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA’s. In: Proceedings of the first IEEE conference on evolutionary computation, vol 2, pp 579–584

  85. Surry PD, Radcliffe NJ (1997) The COMOGA method: constrained optimization by multi-objective genetic algorithms. Control Cybern 26: 391–412

    MathSciNet  Google Scholar 

  86. Schaffer JD (1985) Multiple objective optimization with vector evaluated genetic algorithms. In: Proceedings of the 1st international conference on genetic algorithms. L. Erlbaum Associates Inc., pp 93–100

  87. Coello CAC (2000) Treating constraints as objectives for single-objective evolutionary optimization. Eng Optim 32: 275–308

    Article  Google Scholar 

  88. Fonseca CM, Fleming PJ (1993) Genetic algorithms for multiobjective optimization: formulation, discussion and generalization. In: Forrest S (ed) Proceedings of the fifth international conference on genetic algorithms. Morgan Kauffman Publishers, San Mateo, California University of Illinois at Urbana-Champaign, pp 416–423

  89. Coello CAC (2000) Constraint-handling using an evolutionary multiobjective optimization technique. Civil Eng Environ Syst 17: 319–346

    Article  Google Scholar 

  90. Horn J, Nafploitis N, Goldberg DE (1994) A niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of the first IEEE conference on evolutionary computation. IEEE Press, pp 82–87

  91. Coello CAC, Mezura-Montes E (2002) Handling constraints in genetic algorithms using dominance-based tournaments. In: Parmee IC (ed) Proceeding of the fifth international conference on adaptive computing design and manufacture (ACDM 2002), vol 5. Springer-Verlag, Devon, pp 273–284

  92. Wanner EF, Guimaraes FG, Saldanha RR, Takahashi RHC, Fleming PJ (2005) Constraint quadratic approximation operator for treating equality constraints with genetic algorithms. In: The 2005 IEEE Congress on evolutionary computation, vol 3, pp 2255–2262

  93. Sarker R, Ray T (2005) Multiobjective evolutionary algorithms for solving constrained optimization problems. In: International conference on computational intelligence for modelling, control and automation (CIMCA2005). IEEE Press, Vienna, pp 197–202

  94. Michalewicz Z, Nazhiyath G, Michalewicz M (1996) A note on usefulness of geometrical crossover for numerical optimization problems. In: Proceeding of the 5th annual conference on evolutionary programming. MIT Press, Cambridge, pp 305–312

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  1. School of Engineering and Information Technology, University of New South Wales at the Australian Defence Force Academy, Canberra, 2600, Australia

    Abu S. S. M. Barkat Ullah, Ruhul Sarker & Chris Lokan

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  1. Abu S. S. M. Barkat Ullah
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Correspondence to Abu S. S. M. Barkat Ullah.

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Barkat Ullah, A.S.S.M., Sarker, R. & Lokan, C. Handling equality constraints with agent-based memetic algorithms. Memetic Comp. 3, 51–72 (2011). https://doi.org/10.1007/s12293-010-0051-6

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