Bilevel Genetic Algorithm with Clustering for Large Scale Traveling Salesman Problems

The Traveling Salesman Problem (TSP) belongs to the class of NP-hard optimization problems. Its solving procedure is complicated, especially for large scale problems. In order to solve the large scale TSPs efficiently, this paper presents a bilevel genetic algorithm with clustering (BLGAC). BLGA-C uses a clustering method to divide a large scale TSP into several subproblems, each subproblem corresponds to a cluster. K-Means clustering method is adopted in this paper. In the lower level, a genetic algorithm is used to find the shortest hamiltonian cycle for each cluster. All these clusters can be handled parallelly. Then, we need to select two nearest vertices between two clusters, and determine which edges will be deleted from the shortest hamiltonian cycle for each cluster, and which edges will be linked for combining two adjacent clusters into one. Repeat this procedure until all clusters are joined into one whole tour. Different combing sequences among clusters will result in different travelling tours, searching for the shortest is our purpose. Therefore, in the higher level, a modified genetic algorithm is designed for integral optimization with the objective of shortest the whole traveling tour. At last in this paper, we trial run a set of experiments on benchmark instances for testing the performance of the proposed BLGAC. Experimental results demonstrate its effective and efficient performance.