Useful Infeasible Solutions in Engineering Optimization with Evolutionary Algorithms

We propose an evolutionary-based approach to solve engineering design problems without using penalty functions. The aim is to identify and maintain infeasible solutions close to the feasible region located in promising areas. In this way, using the genetic operators, more solutions will be generated inside the feasible region and also near its boundaries. As a result, the feasible region will be sampled well-enough as to reach better feasible solutions. The proposed approach, which is simple to implement, is tested with respect to typical penalty function techniques as well as against state-of-the-art approaches using four mechanical design problems. The results obtained are discussed and some conclusions are provided.

[1]  Carlos A. Coello Coello,et al.  Adding a diversity mechanism to a simple evolution strategy to solve constrained optimization problems , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[2]  Tapabrata Ray,et al.  Society and civilization: An optimization algorithm based on the simulation of social behavior , 2003, IEEE Trans. Evol. Comput..

[3]  Frank Hoffmeister,et al.  Problem-Independent Handling of Constraints by Use of Metric Penalty Functions , 1996, Evolutionary Programming.

[4]  Carlos A. Coello Coello,et al.  PASSSS: an implementation of a novel diversity strategy for handling constraints , 2004, Proceedings of the 2004 Congress on Evolutionary Computation (IEEE Cat. No.04TH8753).

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

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

[7]  Thomas Bäck,et al.  Evolutionary algorithms in theory and practice - evolution strategies, evolutionary programming, genetic algorithms , 1996 .

[8]  Kaisa Miettinen,et al.  Numerical Comparison of Some Penalty-Based Constraint Handling Techniques in Genetic Algorithms , 2003, J. Glob. Optim..

[9]  Shang He,et al.  An improved particle swarm optimizer for mechanical design optimization problems , 2004 .

[10]  D. Fogel Evolutionary algorithms in theory and practice , 1997, Complex..

[11]  Hans-Paul Schwefel,et al.  Numerical optimization of computer models , 1981 .

[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.