Integrating Local Search Methods in Metaheuristic Algorithms for Combinatorial Optimization: The Traveling Salesman Problem and its Variants

Metaheuristic Algorithms (MAs) have demonstrated exceptional competence in solving Combinatorial Optimization Problems (COP) such as the Minimum Spanning Tree Problem (MSTP), the Features Selection Problem (FSP) with the most popular and oldest being the Traveling Salesman Problem (TSP). However, this class of algorithms many a time suffers from local optima stagnation leading to sub-optimal performance. Thus, there is a need for such algorithms to be supported with specific Local Search (LS) procedures either as an inner component or as a post-processing mechanism to enhance the search process for better performance. This paper presents a comprehensive review of the integration of LS methods in metaheuristic algorithms for solving single, multi, and many-objective COP with a focus on the TSP and its variants. The LS methods reviewed in this study were classified into one-way and two-way based on their mode of operation. In addition, practical suggestions were discussed and possible future directions were pointed out.