Skip to main content
SpringerLink
Log in

An Agent Based Evolutionary Approach for Nonlinear Optimization with Equality Constraints

  • Chapter
Agent-Based Evolutionary Search

Part of the book series: Adaptation, Learning, and Optimization ((ALO,volume 5))

  • 979 Accesses

Abstract

To represent practical problems appropriately, many mathematical optimization models require equality constraints in addition to inequality constraints. The existence of equality constraints reduces the size of the feasible space, which makes it difficult to locate feasible and optimal solutions. This paper shows the enhanced performance of an agent-based evolutionary algorithm in solving Constrained Optimization Problems (COPs) with equality constraints. In the early generations of the evolutionary process, the agents use a new learning process that is specifically designed for handling equality constraints. In the later generations, the agents improve their performance through other learning processes by exploiting their own potential. The performance of the proposed algorithm is tested on a set of well-known benchmark problems including two new problems. The experimental results confirm the improved performance of the proposed algorithm.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Ho, P.Y., Shimizu, K.: Evolutionary constrained optimization using an addition of ranking method and a percentage-based tolerance value adjustment scheme. Information Sciences 177, 2985–3004 (2007)

    Article  Google Scholar 

  2. Back, T., Hammel, U., Schwefel, H.P.: Evolutionary computation: comments on the history and current state. IEEE Transactions on Evolutionary Computation 1, 3 (1997)

    Article  Google Scholar 

  3. Chootinan, P., Chen, A.: Constraint handling in genetic algorithms using a gradient-based repair method. Computers & Operations Research 33, 2263–2281 (2006)

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  5. Venkatraman, S., Yen, G.G.: A Generic Framework for Constrained Optimization Using Genetic Algorithms. IEEE Transactions on Evolutionary Computation 9, 424–435 (2005)

    Article  Google Scholar 

  6. Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186, 311 (2000)

    Article  MATH  Google Scholar 

  7. Coello Coello, C.A.: Theoretical and numerical constraint-handling techniques used with evolutionary algorithms: a survey of the state of the art. Computer Methods in Applied Mechanics and Engineering 191, 1245–1287 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  8. Mezura-Montes, E., Coello, C.A.C.: A Numerical Comparison of Some Multiobjective-Based Techniques to Handle Constraints in Genetic Algorithms, Dept. Ing. Eléct., México (2002)

    Google Scholar 

  9. Barkat Ullah, A.S.S.M., Sarker, R., Lokan, C.: An Agent-based Memetic Algorithm (AMA) for Nonlinear Optimization with Equality Constraints. In: The 2009 IEEE Congress on Evolutionary Computation (CEC 2009), Norway (2009)

    Google Scholar 

  10. Merz, P., Freisleben, B.: Genetic local search for the TSP: new results. In: IEEE International Conference on Evolutionary Computation, pp. 159–164 (1997)

    Google Scholar 

  11. Cheng, R., Gen, M.: Parallel machine scheduling problems using memetic algorithms. In: IEEE International Conference on Systems, Man, and Cybernetics, pp. 2665–2670 (1996)

    Google Scholar 

  12. Burke, E.K., Smith, A.J.: A memetic algorithm to schedule planned maintenance for the national grid. Journal of Experimental Algorithmics 4 (1999)

    Google Scholar 

  13. Tang, J., Lim, M.H., Ong, Y.S., Er, M.J.: Solving large scale combinatorial optimization using PMA-SLS. In: Proceedings of the 2005 conference on Genetic and evolutionary computation. ACM Press, Washington (2005)

    Google Scholar 

  14. Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Transactions on Evolutionary Computation 4, 337–352 (2000)

    Article  Google Scholar 

  15. Alkan, A., Ozcan, E.: Memetic algorithms for timetabling. In: The 2003 Congress on Evolutionary Computation, pp. 1796–1802 (2003)

    Google Scholar 

  16. Vavak, F., Fogarty, T., Jukes, K.: A genetic algorithm with variable range of local search for tracking changing environments. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 376–385. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

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

    Google Scholar 

  18. Knowles, J.D., Corne, D.W.: M-PAES: a memetic algorithm for multiobjective optimization. In: Proceedings of the 2000 Congress on Evolutionary Computation, pp. 325–332 (2000)

    Google Scholar 

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

    Google Scholar 

  20. Knowles, J., Corne, D.: Memetic Algorithms for Multiobjective Optimization: Issues, Methods and Prospects. In: Recent Advances in Memetic Algorithms, pp. 313–352 (2005)

    Google Scholar 

  21. Tang, J., Lim, M., Ong, Y.: Diversity-adaptive parallel memetic algorithm for solving large scale combinatorial optimization problems. Soft Computing - A Fusion of Foundations, Methodologies and Applications 11, 873–888 (2007)

    Google Scholar 

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

    Google Scholar 

  23. Krasnogor, N., Smith, J.: A tutorial for competent memetic algorithms: model, taxonomy, and design issues. IEEE Transactions on Evolutionary Computation 9, 474–488 (2005)

    Article  Google Scholar 

  24. Moscato, P.: On Evolution, Search, Optimization, Genetic Algorithms and Martial Arts Towards Memetic Algorithms. Caltech Concurrent Computation Program Report 826, California Institute of Technology, Pasadena, CA, U.S.A (1989)

    Google Scholar 

  25. Hart, W.E.: Adaptive Global Optimization With Local Search. vol. PhD thesis: Univ. California, San Diego, CA (1994)

    Google Scholar 

  26. Krasnogor, N.: Studies on the Theory and Design Space of Memetic Algorithms. vol. Ph.D. Thesis, University of the West of England (2002)

    Google Scholar 

  27. Ong, Y.S., Keane, A.J.: Meta-Lamarckian learning in memetic algorithms. IEEE Transactions on Evolutionary Computation 8, 99–110 (2004)

    Article  Google Scholar 

  28. Merz, P., Freisleben, B.: A comparison of memetic algorithms, tabu search, and ant colonies for the quadratic assignment problem. In: Proceedings of the Congress on Evolutionary Computation, p. 2070 (1999)

    Google Scholar 

  29. Goldberg, D.E., Voessner, S.: Optimizing Global-Local Search Hybrids. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 220–228 (1999)

    Google Scholar 

  30. Tang, J., Lim, M.H., Ong, Y.S.: Adaptation for parallel memetic algorithm based on population entropy. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation. ACM Press, Seattle (2006)

    Google Scholar 

  31. Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)

    Google Scholar 

  32. Ferber, J.: Multiagent systems as introduction to distributed artificial intelligence. Addison-Wesley, Reading (1999)

    Google Scholar 

  33. Stan, F., Art, G.: Is It an agent, or just a program?: A taxonomy for autonomous agents. In: Jennings, N.R., Wooldridge, M.J., Müller, J.P. (eds.) ECAI-WS 1996 and ATAL 1996. LNCS, vol. 1193, pp. 21–35. Springer, Heidelberg (1997)

    Google Scholar 

  34. Chira, C., Gog, A., Dumitrescu, D.: 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, Atlanta, GA, USA, pp. 1953–1960 (2008)

    Google Scholar 

  35. Deb, K., Agrawal, R.B.: Simulated Binary Crossover for Continuous Search Space. Complex Systems 9, 115–148 (1995)

    MathSciNet  MATH  Google Scholar 

  36. Barkat Ullah, A.S.S.M., Sarker, R., Cornforth, D., Lokan, C.: An Agent-based Memetic Algorithm (AMA) for Solving Constrained Optimization Problems. In: IEEE Congress on Evolutionary Computation, CEC 2007, pp. 999–1006 (2007)

    Google Scholar 

  37. Barkat Ullah, A.S.S.M., Sarker, R., Cornforth, D., Lokan, C.: AMA: a new approach for solving constrained real-valued optimization problems. In: Soft Computing - A Fusion of Foundations, Methodologies and Applications, August 11 (2008)

    Google Scholar 

  38. Runarsson, T.P., Yao, X.: Stochastic ranking for constrained evolutionary optimization. IEEE Transactions on Evolutionary Computation 4, 284 (2000)

    Article  Google Scholar 

  39. Himmelblau, D.M.: Applied Nonlinear Programming. McGraw-Hill, USA (1972)

    MATH  Google Scholar 

  40. Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6, 182 (2002)

    Article  Google Scholar 

  41. Ray, T., Sarker, R.: Genetic algorithm for solving a gas lift optimization problem. Journal of Petroleum Science and Engineering 59, 84–96 (2007)

    Article  Google Scholar 

  42. Liu, H., Frazer, J.H.: Supporting evolution in a multi-agent cooperative design environment. Advances in Engineering Software 33, 319–328 (2002)

    Article  MATH  Google Scholar 

  43. Siwik, L., Kisiel-Dorohinicki, M.: Semi-elitist Evolutionary Multi-agent System for Multiobjective Optimization. In: Alexandrov, V.N., van Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3993, pp. 831–838. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  44. Zhong, W., Liu, J., Xue, M., Jiao, L.: A multiagent genetic algorithm for global numerical optimization. IEEE Transactions on Systems, Man and Cybernetics, Part B 34, 1128–1141 (2004)

    Article  Google Scholar 

  45. Davidsson, P., Persson, J., Holmgren, J.: On the Integration of Agent-Based and Mathematical Optimization Techniques. In: Agent and Multiagent Systems: Technologies and Applications, pp. 1–10 (2007)

    Google Scholar 

  46. Nakashima, T., Ariyama, T., Yoshida, T., Ishibuchi, H.: Performance evaluation of combined cellular genetic algorithms for function optimization problems, pp. 295–299 (2003)

    Google Scholar 

  47. De Jong, K.A.: Evolving intelligent agents: A 50 year quest. IEEE Computational Intelligence Magazine 3, 12–17 (2008)

    Article  Google Scholar 

  48. Vasile, M., Locatelli, M.: A hybrid multiagent approach for global trajectory optimization. Journal of Global Optimization (2008)

    Google Scholar 

  49. Bajo, J., Corchado, J.: Multiagent Architecture for Monitoring the North-Atlantic Carbon Dioxide Exchange Rate. In: Marín, R., Onaindía, E., Bugarín, A., Santos, J. (eds.) CAEPIA 2005. LNCS (LNAI), vol. 4177, pp. 321–330. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  50. Hasan, S.M.K., Sarker, R., Essam, D., Cornforth, D.: Memetic Algorithms for Solving Job-Shop Scheduling Problems. In: Memetic Computing. Springer, Heidelberg (2008) (in press)

    Google Scholar 

  51. Dobrowolski, G., Kisiel-Dorohinicki, M., Nawarecki, E.: Evolutionary multiagent system in multiobjective optimisation. In: Proc. of the IASTED Int. Symp. on Applied Informatics (2001)

    Google Scholar 

  52. Alba, E., Dorronsoro, B.: The exploration/exploitation tradeoff in dynamic cellular genetic algorithms. IEEE Transactions on Evolutionary Computation 9, 126–142 (2005)

    Article  Google Scholar 

  53. Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Inc., Chichester (2001)

    MATH  Google Scholar 

  54. Barkat Ullah, A.S.S.M., Sarker, R., Cornforth, D.: An Evolutionary Agent System for Mathematical Programming. In: Kang, L., Liu, Y., Zeng, S. (eds.) ISICA 2007. LNCS, vol. 4683, pp. 187–196. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  55. Barkat Ullah, A.S.S.M., Sarker, R., Cornforth, D.: Search space reduction technique for constrained optimization with tiny feasible space. In: Proceedings of the 10th annual conference on Genetic and evolutionary computation, Atlanta, GA, USA, pp. 881–888 (2008)

    Google Scholar 

  56. Elfeky, E.Z., Sarker, R.A., Essam, D.L.: A Simple Ranking and Selection for Constrained Evolutionary Optimization. In: Wang, T.-D., Li, X., Chen, S.-H., Wang, X., Abbass, H.A., Iba, H., Chen, G.-L., Yao, X. (eds.) SEAL 2006. LNCS, vol. 4247, pp. 537–544. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  57. Koziel, S., Michalewicz, Z.: Evolutionary algorithms, homomorphous mappings, and constrained parameter optimization. Evolutionary Computation 7 (1999)

    Google Scholar 

  58. Sarker, R., Ray, T.: Multiobjective Evolutionary Algorithms for solving Constrained Optimization Problems. In: International Conference on Computational Intelligence for Modelling, Control and Automation (CIMCA 2005), Vienna, Austria. IEEE Press, USA (2005)

    Google Scholar 

  59. Michalewicz, Z., Nazhiyath, G., Michalewicz, M.: A Note on Usefulness of Geometrical Crossover for Numerical Optimization Problems. In: 5th Annual Conference on Evolutionary Programming, Cambridge, MA, San Diego, CA, pp. 305–312 (1996)

    Google Scholar 

  60. Hock, W., Schittkowski, K.: Test Examples for Nonlinear Programming Codes. LNEMS. Springer, Heidelberg (1981)

    MATH  Google Scholar 

  61. Koziel, S., Michalewicz, Z.: Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization. Evolutionary Computation 7, 19–44 (1999)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Engineering and Information Technology (SEIT), UNSW@ADFA, Canberra ACT, 2600, Australia

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

Authors
  1. Abu S. S. M. Barkat Ullah
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Ruhul Sarker
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chris Lokan
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. School of Engineering and Information Technology, University of New SouthWales , ADFA Campus, Northcott Drive, 2600, Canberra, ACT, Australia

    Ruhul Amin Sarker  & Tapabrata Ray  & 

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Ullah, A.S.S.M.B., Sarker, R., Lokan, C. (2010). An Agent Based Evolutionary Approach for Nonlinear Optimization with Equality Constraints. In: Sarker, R.A., Ray, T. (eds) Agent-Based Evolutionary Search. Adaptation, Learning, and Optimization, vol 5. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13425-8_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-13425-8_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13424-1

  • Online ISBN: 978-3-642-13425-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation