An Adaptive Algorithm for Constrained Optimization Problems

Adaptivity has become a key issue in Evolutionary Algorithms, since early works in Evolution Strategies. The idea of letting the algorithm adjust its own parameters for free is indeed appealing. This paper proposes to use adaptive mechanisms at the population level for constrained optimization problems in three important steps of the evolutionary algorithm: First, an adaptive penalty function takes care of the penalty coefficients according to the proportion of feasible individuals in the current population; Second, a Seduction/Selection strategy is used to mate feasible individuals with infeasible ones and thus explore the region around the boundary of the feasible domain; Last, selection is tuned to favor a given number of feasible individuals. A detailed discussion of the behavior of the algorithm on two small constrained problems enlights adaptivity at work. Finally, experimental results on eleven test cases from the literature demonstrate the power of this approach.

[1]  Hans-Paul Schwefel,et al.  Numerical Optimization of Computer Models , 1982 .

[2]  Zbigniew Michalewicz,et al.  Handling Constraints in Genetic Algorithms , 1991, ICGA.

[3]  Thomas Bäck,et al.  A Survey of Evolution Strategies , 1991, ICGA.

[4]  Michael M. Skolnick,et al.  Using Genetic Algorithms in Engineering Design Optimization with Non-Linear Constraints , 1993, ICGA.

[5]  Alice E. Smith,et al.  Genetic Optimization Using A Penalty Function , 1993, ICGA.

[6]  Zbigniew Michalewicz,et al.  Evolutionary optimization of constrained problems , 1994 .

[7]  Abdollah Homaifar,et al.  Constrained Optimization Via Genetic Algorithms , 1994, Simul..

[8]  Christopher R. Houck,et al.  On the use of non-stationary penalty functions to solve nonlinear constrained optimization problems with GA's , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[9]  Raphael T. Haftka,et al.  A Segregated Genetic Algorithm for Constrained Structural Optimization , 1995, ICGA.

[10]  Edmund M. A. Ronald,et al.  When Selection Meets Seduction , 1995, ICGA.

[11]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms for Constrained Parameter Optimization Problems , 1996, Evolutionary Computation.

[12]  Zbigniew Michalewicz,et al.  Adaptation in evolutionary computation: a survey , 1997, Proceedings of 1997 IEEE International Conference on Evolutionary Computation (ICEC '97).

[13]  James C. Bean,et al.  A Genetic Algorithm for the Multiple-Choice Integer Program , 1997, Oper. Res..

[14]  Zbigniew Michalewicz,et al.  Boundary Operators for Constrained Parameter Optimization Problems , 1997, ICGA.

[15]  Zbigniew Michalewicz,et al.  Evolutionary Algorithms, Homomorphous Mappings, and Constrained Parameter Optimization , 1999, Evolutionary Computation.