Hybrid Nested Partitions Method for the Traveling Salesman Problem

The nested partitions method (NPM) is a global optimization method, which can be applied to solve many large-scale discrete optimization problems. The basic procedure of this method for solving the traveling salesman problem (TSP) was introduced. Based on the analysis and determination of the strategy of the four arithmetic operators of NPM, an improved NPM was proposed. The initial most promising region was improved by weighted sampling method; The historical optimal solution of every region was recorded in a global array; the 3-opt algorithm was combined in the local search for improving the quality of solution for every subregion; the improved Lin-Kernighan algorithm was used in the search for improving the quality of solution for surrounding region. Some experimental results of TSPLIB (TSP Library) show that the proposed improved NPM can find solutions of high quality efficiently when applied to the TSP.