Journal of the Korean Operations Research and Management Science Society (한국경영과학회지)

The Korean Operations Research and Management Science Society (한국경영과학회)
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A Handling Method of Linear Constraints for the Genetic Algorithm

유전알고리즘에서 선형제약식을 다루는 방법

  • 성기석 (강릉원주대학교 산업정보경영공학과)
  • Received : 2012.09.01
  • Accepted : 2012.09.25
  • Published : 2012.12.31
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Abstract

In this paper a new method of handling linear constraints for the genetic algorithm is suggested. The method is designed to maintain the feasibility of offsprings during the evolution process of the genetic algorithm. In the genetic algorithm, the chromosomes are coded as the vectors in the real vector space constrained by the linear constraints. A method of handling the linear constraints already exists in which all the constraints of equalities are eliminated so that only the constraints of inequalities are considered in the process of the genetic algorithm. In this paper a new method is presented in which all the constraints of inequalities are eliminated so that only the constraints of equalities are considered. Several genetic operators such as arithmetic crossover, simplex crossover, simple crossover and random vector mutation are designed so that the resulting offspring vectors maintain the feasibility subject to the linear constraints in the framework of the new handling method.

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References

  1. Fang, S.C. and S. Puthenpura, Linear Optimization and Extensions-Theory and Algorithms, Prentice-Hall, 1993.
  2. Goldberg, D.E., Genetic algorithms in search, optimization, and machine learning. Addison-Wesley Pub. Co., Reading, Massachusetts, 1989.
  3. Koziel, S. and Z. Michalewicz, "Evolutionary Algorithms, Hormomorphous Mappins, and Constrained Parameter Optimization," Evolutionary Computation, Vol.7, No.1(1999), pp.124-141.
  4. Michalewicz, Z. and C. Janikow, "GENOCOP ：A Genetic Algorithm for Numerical Optimization Problems with Linear Constraints," Communications of the ACM, Vol.39, No.12 (1996), pp.175-201. https://doi.org/10.1145/272682.272711
  5. Michalewicz, Z., "Evolutionary Computation Techniques for Nonlinear Programming Problems," International Transactions in Operational Research, Vol.1, No.2(1994), pp.223-240. https://doi.org/10.1016/0969-6016(94)90022-1
  6. Renders, J.M. and S.P. Flasse, "Hybrid methods using genetic algorithms for global optimization," IEEE Transactions on Systems, Man and Cybernetics, Part B, Vol.26, No.2 (1996), pp.243-258. https://doi.org/10.1109/3477.485836
  7. Spendley, W., G.R. Hext, and F.R. Himsworth, "Sequential application of simplex designs in optimization and evolutionary opreation," Technometrics, Vol.4(1962), pp.441-461. https://doi.org/10.1080/00401706.1962.10490033
  8. Yen, J., J.C. Liao, L. Bogju, and D. Randolph, "A hybrid approach to modeling metabolic systems using a genetic algorithm and simplex method," IEEE Transactions on Systems, Man and Cybernetics, Part B, Vol.28, No.2(1998), pp.173-191.