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.