An Ant Colony Optimization for Weighted Traveling Salesman Problem and Analysis

The traveling salesman problem (TSP) is a well-known combinatorial optimization problem. While, in classical TSP and its variants, the priority of each city is assumed as the same. The objective function neglects extra vehicle loading cost caused by practical factors when optimizing a route. However, in real-world, the priority varies from one city to another and affects the loading cost. Thus, a route without considering the effect of different priority of each city may be not reasonable enough and may lead to sub-optimal solutions. In this paper, we investigate Weighted Traveling Salesman Problem (WTSP), the cost of which concluded both distance cost and the extra loading cost when finishing a route. Considering the features of WTSP model, a Mutated Max-Min Ant System is proposed. Computational results of benchmark instances with five types of distributions are shown to prove that the M-MMAS is competitive and superior to other algorithms for most instances and that WTSP formulation is reasonable and can save more money for practical factors.