Application of Weighted Partial Max-SAT for Post-improvement of the Multiple Traveling Salesman Problem

Advances allow SAT solvers to be used to solve problems in the industrial sector. Therefore, in this paper, we reduce the multiple traveling salesman problem to a weighted partial max-SAT, with the aim of increasing the quality of the solution at a reduced computational cost. A version of Clarke and Wright’s saving algorithm has been implemented to create the initial solution, while the 2-opt algorithm is applied to each route to improve the routes, the search space is extended by adding k nearest neighbors of each vertex so that post-improvement can be performed by the SAT solver. Benchmarks of four instances from the literature suggest a significant post-improvement in the quality of the solution up to 43.51% for a reasonable computational cost.