A Hybrid Max–Min Ant System by Levy Flight and Opposition-Based Learning

Abstract

The max–min ant system (MMAS) is a modified ant colony optimization (ACO) algorithm. Its convergence speed is effectively improved by setting the upper and lower bounds of the pheromone and updating it in the optimal path. However, MMAS still has drawbacks, such as long search time and local extremums. In this paper, the hybrid max–min ant system (HMMAS) is proposed to deal with the shortcomings of MMAS. Employing Levy flight strategy, HMMAS can dynamically adjust the parameters to increase the diversity of solutions and expand the search range. Besides, HMMAS uses the OBL strategy to generate opposite solutions in the early stage. In this way, the convergence is accelerated. When HMMAS falls into a local extremum, the path reorganization strategy is utilized. With its help, HMMAS can redistribute the pheromone in each path and achieve global optimum. To verify the effectiveness, HMMAS is first compared with the three conventional ACO algorithms of AS, ACS, and MMAS in 20 sets of experiments. The results indicate that the average results of HMMAS in the 19 sets of TSP instances are better than the other three algorithms, and the standard deviation in the 14 sets of calculation instances is the smallest. Then, HMMAS is compared with some state-of-the-art algorithms, and the results show that HMMAS is better than other comparison algorithms, either by the minimum or the average value.