A Wave Analysis of the Subset Sum Problem

This paper introduces the wave model, a novel approach on analyzing the behavior of GAs. Our aim is to give techniques that have practical relevance and provide tools for improving the performance of the GA or for discovering simple and effective heuristics on certain problem classes. The wave analysis is the process of building wave models of problem instances of a problem class and extracting common features that characterize the problem class in question. A wave model is made of paths which are composed of subsets of the search space (features) that are relevant from the viewpoint of the search. The GA is described as a basicly {\em sequential} process; a wave motion along the paths that form the wave model. The method is demonstrated via an analysis of the NP-complete subset sum problem. Based on the analysis, problem specific GA modifications and a new heuristic will be suggested that outperform the original G