Neighborhood Reduction Strategy for Tabu Search Implementation in Asymmetric Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is one of the most widely discussed problems in combinatorial optimization. It has many practical applications in fields of distribution and logistics management, scheduling problems etc. Since these problems are hard, in addition to exact algorithms, research has focused on heuristic techniques to solve TSPs. Computational time is a major concern while solving large TSPs. This problem intensifies further if the graph becomes asymmetric (ATSP). Metaheuristics like tabu search are widely used to find a reasonably good tour fast. Given the practical relevance of ATSPs the lack of literature on it is surprising. The primary objective of our work is to implement tabu search for large ATSPs to obtain good tours in reasonable time. To do that, we make the underlying graph sparse by developing an elite tour based preprocessing scheme. Tabu search is implemented on this reduced graph which results in a reduction of computational time. We also create diversified initial tours suitable for multi-start tabu search in this process. We present our computational experiences both on randomly generated instances and benchmark instances.