Effectiveness of penalty function in solving the subset sum problem

We investigate the evolutionary heuristics used as approximation algorithm to the subset sum problem. We propose a graded penalty function in a fitness function of genetic algorithms to penalize an infeasible string in solving the subset sum problem. An exponential term of generation variable, t/sup 0/, is added into the penalty function for increasing penalty generation by generation. The experiments show that the proposed penalty function is more efficient, than other existing penalty functions. It is suggested that the penalty pressure is increased step by step.

[1]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[2]  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.

[3]  Lawrence Davis,et al.  Using a genetic algorithm to optimize problems with feasibility constraints , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[4]  Anne L. Olsen Penalty functions and the knapsack problem , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.