Self-adaptive fitness formulation for constrained optimization

A self-adaptive fitness formulation is presented for solving constrained optimization problems. In this method, the dimensionality of the problem is reduced by representing the constraint violations by a single infeasibility measure. The infeasibility measure is used to form a two-stage penalty that is applied to the infeasible solutions. The performance of the method has been examined by its application to a set of eleven test cases from the specialized literature. The results have been compared with previously published results from the literature. It is shown that the method is able to find the optimum solutions. The proposed method requires no parameter tuning and can be used as a fitness evaluator with any evolutionary algorithm. The approach is also robust in its handling of both linear and nonlinear equality and inequality constraint functions. Furthermore, the method does not require an initial feasible solution.

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

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

[3]  K. Deb.  An Efficient Constraint Handling Method for Genetic Algorithms , 2000 .

[4]  Patrick D. Surry,et al.  The COMOGA Method: Constrained Optimisation by Multi-Objective Genetic Algorithms , 1997 .

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

[6]  Marc Schoenauer,et al.  Constrained GA Optimization , 1993, ICGA.

[7]  Alice E. Smith,et al.  Penalty guided genetic search for reliability design optimization , 1996 .

[8]  F. Cheng,et al.  Multiobjective Optimization Design with Pareto Genetic Algorithm , 1997 .

[9]  Zbigniew Michalewicz,et al.  A Note on Usefulness of Geometrical Crossover for Numerical Optimization Problems , 1996, Evolutionary Programming.

[10]  Xin Yao,et al.  Stochastic ranking for constrained evolutionary optimization , 2000, IEEE Trans. Evol. Comput..

[11]  Gunar E. Liepins,et al.  Some Guidelines for Genetic Algorithms with Penalty Functions , 1989, ICGA.

[12]  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.

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

[14]  Jonathan A. Wright,et al.  Genetic algorithms: a fitness formulation for constrained minimization , 2001 .

[15]  Peter J. Fleming,et al.  Multiobjective optimization and multiple constraint handling with evolutionary algorithms. I. A unified formulation , 1998, IEEE Trans. Syst. Man Cybern. Part A.

[16]  P Hajela,et al.  Constraint handling in genetic search - A comparative study , 1995 .

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

[18]  C. Coello.  TREATING CONSTRAINTS AS OBJECTIVES FOR SINGLE-OBJECTIVE EVOLUTIONARY OPTIMIZATION , 2000 .

[19]  Dr. Zbigniew Michalewicz,et al.  How to Solve It: Modern Heuristics , 2004 .

[20]  David W. Coit,et al.  Adaptive Penalty Methods for Genetic Optimization of Constrained Combinatorial Problems , 1996, INFORMS J. Comput..

[21]  Kalyanmoy Deb,et al.  A fast and elitist multiobjective genetic algorithm: NSGA-II , 2002, IEEE Trans. Evol. Comput..

[22]  Keigo Watanabe,et al.  Evolutionary Optimization of Constrained Problems , 2004 .

[23]  Hyun Myung,et al.  Constrained optimization using two-phase evolutionary programming , 1995, Proceedings of IEEE International Conference on Evolutionary Computation.

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

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

[26]  Zbigniew Michalewicz,et al.  Evolutionary Computation at the Edge of Feasibility , 1996, PPSN.

[27]  Sana Ben Hamida,et al.  An Adaptive Algorithm for Constrained Optimization Problems , 2000, PPSN.