Efficient local search with search space smoothing: a case study of the traveling salesman problem (TSP)

Local search is very efficient to solve combinatorial optimization problems. Due to the rugged terrain surface of the search space, it often gets stuck at a locally optimum configuration. In this paper, we give a local search method with a search space smoothing technique. It is capable of smoothing the rugged terrain surface of the search space. Any conventional heuristic search algorithm can be used in conjunction with this smoothing method. In a parameter space, by altering the shape of the objective function, the original problem instance is transformed into a series of gradually simplified problem instances with smoother terrain surfaces. Using an existing local search algorithm, an instance with the simplest terrain structure is solved first, the original problem instance with more complicated terrain structure is solved last, and the solutions of the simplified problem instances are used to guide the search of more complicated ones. A case study of using such technique to solve the traveling salesman problem (TSP) is described. We tested this method with numerous randomly generated TSP instances. We found that it has significantly improved the performance of existing heuristic search algorithms