Performance evaluation of evolutionary class of algorithms—An application to 0–1 knapsack problem

The 0–1 knapsack [1] problem is a well-known NP-complete problem. There are different algorithms in the literature to attack this problem, two of them being of specific interest. One is a pseudo polynomial algorithm of order O(nK), K being the target of the problem. This algorithm works unsatisfactorily, as the given target becomes high. In fact, the complexity might become exponential in that case. The other scheme is a fully polynomial time approximation scheme (FPTAS) whose complexity is also polynomial time. The present paper suggests a probabilistic heuristic which is an evolutionary scheme accompanied by the necessary statistical formulation and its theoretical justification. We have identified parameters responsible for the performance of our evolutionary scheme which in turn would keep the option open for improving the scheme.