The Method of Solving for Traveling Salesman Problem Using Genetic Algorithm with Immune Adjustment Mechanism

Abstract

Genetic Algorithm (GA) is widely used to find solutions to optimization problems (Goldberg, 1989). One optimization problem using GA is Travelling Salesman problem (TSP) (Lawler et al., 1985). The disadvantages of using GA are premature convergence and poor local search capability. In order to overcome these disadvantages, evolutionary adaptation algorithms based on the working of the immune system have been devised. One such algorithm is Genetic Immune Recruitment Mechanism (GIRM) (Bersini & Varela, 1991) (Tazawa et al., 1995). By incorporating the immune recruitment test and concentrating the search for a solution in the vicinity of a high-fitness solution, GIRM improves local search capability. However, narrowing the search range risks conducting to local solutions. In contrast, Immune Algorithm (IA) (Mori et al., 1997) (Honna et al., 2005) (Matsui et al., 2006), using production of various antibodies by the immune system and its mechanism of their adjustment, primarily avoids convergence to local solutions. Its local search capability is not as good as that of GIRM, but it allows efficient searches for multiple local solutions. GIRM and IA incorporating the workings of the immune system take more computation time than GA. Thus, they must be performed with a smaller population size. To that end, the author devised an algorithm to overcome these GA’s disadvantages with the small population size. The immune system has two features, the capacity to adapt to mutations in antigen and a mechanism to balance the generation of antibodies via other antibodies, and the author developed Genetic Algorithm with Immune Adjustment Mechanism (GAIAM) incorporating these features in GA. GAIAM maintains the diversity of the population as a result of the mechanism to adjust antibodies in a group of antibodies, so it avoids narrowing of the search range. In addition, its local search capability also improved as a result of the capacity to adapt to mutations in antigen. GAIAM provides effective results even with a small population size. Using the TSP, the author compared the performance of GAIAM to that of GA, GIRM, and IA. First, an experiment was performed using eil51 from the TSPLIB. TSBLIB has benchmark data of TSP. Eil50 is one of the data in TSPLIB. Because it incorporates two features of the immune system even with a small population size, the GAIAM allows a more efficient search over the entire search range without succumbing locally. Moreover, its local search capability was found to be better than that of other techniques. Furthermore, experiments