Big valley in scheduling problems landscape — Metaheuristics with reduced searching area

Abstract

Created in the 90s of the past century methods of constructing algorithms (metaheuristic), inspired by the no free lunch theorem of Wolpert and Macready, using specific properties of problems, do not meet present expectations of practitioners. Commonly used artificial intelligence algorithms in recent years have also proved to be ineffective in solving a large group of extremely difficult instances of various problems. In the work we present some empirical methods of exploration of solution space in optimization problems whose solutions are represented by permutations. While sampling the set of permissible solutions we designate the histogram of the frequency of occurrence of local minima and on this basis we verify the statistical hypothesis concerning the (normal) distribution of occurrence of these minima. Due to this process we can flexibly change the “radius” of the searched area. Computational experiments performed on examples of the job shop problem are promising and inspire to conduct further research in this direction.