High Performance Immune Clonal Algorithm for Solving Large Scale TSP

Abstract

Traveling Salesman Problem (TSP) is one of the most challenging combinatorial optimization problems. As the city number of TSP grows, the feasible solution space size increases factorially. For the small to mid-size TSP, the Lin-Kernighan (D. S. Johnson, 1990) (LK) and Lin-Kernighan Heuristic (C. Walshaw, 2001) (LKH) algorithms are very effective. However, these two algorithms are local search methods which find the best TSP tour in the k-change neighborhoods of the given initial TSP tour. Thus, they can only find a local optimal tour for TSP with complex solution space. Accordingly, the LK and LKH algorithms become very sensitive to the initial solution and often fail to find the global optimal tour within a reasonable time for solving large scale TSP. To remedy this problem, we make use of the global search ability of the immune clonal algorithm. Especially, we combine the two types of approaches (i.e. LK and immune clonal algorithm) to achieve high performance of the immune clonal algorithm, which can be run on loose-coupled computing environment for solving the large scale TSP. The immune clonal algorithm inspired by biological immune system is a type of evolutionary random search algorithms. More and more research achievements indicate that immune clonal algorithm can maintain good population diversity and strong global search capability. Under the searching framework of the immune clonal algorithm, heuristic search strategies can be conveniently employed to enhance its local search capability. Such combinations take into account both global and local search strategies, and thus can realize a good tradeoff between effectiveness and efficiency. Moreover, the parallelizability of the biological immune system ensures the immune clonal algorithm can be run on loosecoupled computing environment which is advantageous to solve massive optimization problems such as the large scale TSP. Simulation and analysis results show that the edges in the intersection set of several local optimal tours obtained by LK approach appear in the global optimal tour with high probability and the probability increases rapidly as the amount of local optimal tours increases. Using this phenomenon, an intersection set based vaccination strategy is designed in this chapter to accelerate the convergence speed of the immune clonal algorithm for TSP. In the immune clonal algorithm, vaccine is a set of genes which are estimations of the genes expected to appear in the global optimal antibody. The proposed approach in this chapter takes the intersection gene set of several memory antibodies as vaccine and injects the set