International Journal of Control, Automation, and Systems

Institute of Control, Robotics and Systems (제어로봇시스템학회)
권호 표지

Game Model Based Co-evolutionary Solution for Multiobjective Optimization Problems

  • Sim, Kwee-Bo (School of Electrical and Electronic Engineering, ChungAng University) ;
  • Kim, Ji-Yoon (School of Electrical and Electronic Engineering, ChungAng University) ;
  • Lee, Dong-Wook (School of Electrical and Electronic Engineering, ChungAng University)
  • Published : 2004.06.01
Download PDF
⟨ Previous Next ⟩

Abstract

The majority of real-world problems encountered by engineers involve simultaneous optimization of competing objectives. In this case instead of single optima, there is a set of alternative trade-offs, generally known as Pareto-optimal solutions. The use of evolutionary algorithms Pareto GA, which was first introduced by Goldberg in 1989, has now become a sort of standard in solving Multiobjective Optimization Problems (MOPs). Though this approach was further developed leading to numerous applications, these applications are based on Pareto ranking and employ the use of the fitness sharing function to maintain diversity. Another scheme for solving MOPs has been presented by J. Nash to solve MOPs originated from Game Theory and Economics. Sefrioui introduced the Nash Genetic Algorithm in 1998. This approach combines genetic algorithms with Nash's idea. Another central achievement of Game Theory is the introduction of an Evolutionary Stable Strategy, introduced by Maynard Smith in 1982. In this paper, we will try to find ESS as a solution of MOPs using our game model based co-evolutionary algorithm. First, we will investigate the validity of our co-evolutionary approach to solve MOPs. That is, we will demonstrate how the evolutionary game can be embodied using co-evolutionary algorithms and also confirm whether it can reach the optimal equilibrium point of a MOP. Second, we will evaluate the effectiveness of our approach, comparing it with other methods through rigorous experiments on several MOPs.

Keywords

References

  1. A dissertation submitted to the Swiss Federal Institute of Technology Zurich for the degree of Doctor of Technical Sciences Evolutionary algorithms for multiobjective optimization: Methods and applications E. Zitzler
  2. IEEE Trans. on Evolutionary Computation v.3 no.4 Multiobjective evolutionary algorithms: a comparative case study and the strength pareto approach E. Zitzler;L. Thiele https://doi.org/10.1109/4235.797969
  3. Doctoral dissertation, Vanderbilt University Some experiments in machine learning using vector evaluated genetic algorithms J. D. Schaffer
  4. Proc. Int. Conf. on Genetic Algorithms and their Applications Multiple objective optimization with vector evaluated genetic algorithms J. D. Schaffer
  5. Proc. IEEE Conf. on Evolutionary Computation, IEEE World Congress on Computational Intelligence (ICEC '94) v.1 A niched pareto genetic algorithm for multiobjective optimization J. Horn;N. Nafpliotis;D. E. Goldberg
  6. Genetic Algorithms and Their Applications: Proc. 1st Int. Conf. Genetic Algorithms Compaction of symbolic layout using genetic algorithms M. P. Fourman
  7. Parallel Problem Solving from Nature, 1st Workshop Proc.:Lecture Notes in Computer Science v.496 A variant of evolution strategies for vector optimization F. Kursawe
  8. Struct. Optim. v.4 Generic search strategies in multicriterion optimal design P. Hajela;C.-Y. Lin https://doi.org/10.1007/BF01759923
  9. IEEE Trans. on Systems, Man, and Cybernetics-Part A: Systems and Humans v.28 no.1 Multiobjective optimization and multiple constraint handlling with evolutionary algorithms-part i: a unified formulation C. M. Fonseca;P. J. Fleming https://doi.org/10.1109/3468.650319
  10. Genetic Algorithms in Search, Optimization and Machine Learing D. E. Goldberg
  11. Proc. Fifth Int. Conf. Genetic Algorithms Genetic algorithms for multiobjective optimization: Formulation, discussion and generalization C. M. Fonseca;P. J. Fleming
  12. Evolutionary Computation v.3 no.1 An overview of evolutionary algorithms in multiobjective optimization C. M. Fonseca;P. J. Fleming https://doi.org/10.1162/evco.1995.3.1.1
  13. IlliCAL Reprot 93005 Multiobjective optimization using niched pareto genetic algorithm J. Horn;N. Nafpliotis
  14. Genetic Algorithms and Their Application: Proc. 2nd Int. Conf. Genetic Algorithms Genetic algorithms with sharing for multi-modal function optimization D. E. Goldberg;J. J. Richardson
  15. Evolutionary Computation v.2 no.3 Multiobjective optimization using non-dominated sorting in genetic algorighms N. Srinival;K. Deb https://doi.org/10.1162/evco.1994.2.3.221
  16. Genetic Algorithms in Engineering and Computer Science Hybrid GA for multi objective aerodynamic shape optimization C. Poloni
  17. Parallel CFD 96 Parallel genetic solution for multiobjective MDO R. Makinen;P. Neittaanmaki;J. Periaux;M. Sefrioui;J. Toivonen
  18. Proc. Congress on Evolutionary Computation Nash genetic algorithms: examples and applications M. Sefrioui;J. Periaux
  19. Proc. Fifth Annual Conf. on Evolutionary Programming Fast convergence thanks to diversity M. Sefrioui;J. Periaux;J.-G. Ganascia
  20. Evloution and the Theory of Games J. Maynard-Smith
  21. GECCO 2001 Workshop on Coevolution: Turning Adaptative Algorithms upon Themselves Geme theory and the simple convolutionary algorithm:Some preliminary results on fitness sharing S. G. Ficici;J. B. Pollack
  22. Theoretical Population Biology v.37 Evolutionary stability: One Concept, several meanings S. Lessard https://doi.org/10.1016/0040-5809(90)90033-R
  23. Journal of Theoretical Biology v.115 The essential properties of evoputionary stability G. W. Rowe;I. F. Harvey;S. F. Hubbard https://doi.org/10.1016/S0022-5193(85)80100-4
  24. Nonlinear Dynamics and Chaos S. H. Strogatz
  25. Proc. 1999 Genetic and Evolutionary Computation Conf. Comparison of multiobjective evolutionary algorithms: empirical results E. Zitzler;K. Deb;L. Thiele
  26. Proc. Fifth Int. Conf. on Parallel Problem Solving from Nature (PPSN-V) Multiobjective optimization using evolutionary algorithms-a comparative case study E. Zitzler;L. Thiele
  27. IEEE Trans. on Evolutionary Computation v.3 no.4 Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach E. Zitzler;L, Thiele https://doi.org/10.1109/4235.797969
  28. Proc. 1999 Genetic and Evolutionary Computation Conf. Workshop Program Comparison of multiobjective evolutionary algorthms: Empirical results E. Zitzler;K. Deb;L. Thiele
  29. Evolutionary Computation v.7 no.3 Multi-objective genetic algorithms: Problem difficulties and construction of test problems K. Deb https://doi.org/10.1162/evco.1999.7.3.205