A Two-Way Parallel Slime Mold Algorithm by Flow and Distance for the Travelling Salesman Problem

In order to solve the problem of poor local optimization of the Slime Mold Algorithm (SMA) in the Travelling Salesman Problem (TSP), a Two-way Parallel Slime Mold Algorithm by Flow and Distance (TPSMA) is proposed in this paper. Firstly, the flow between each path point is calculated by the “critical pipeline and critical culture” model of SMA; then, according to the two indexes of flow and distance, the set of path points to be selected is obtained; finally, the optimization principle with a flow index is improved with two indexes of flow and distance and added random strategy. Hence, a two-way parallel optimization method is realized and the local optimal problem is solved effectively. Through the simulation of Traveling Salesman Problem Library (TSPLIB) on ulysses16, city31, eil51, gr96, and bier127, the results of TPSMA were improved by 24.56, 36.10, 41.88, 49.83, and 52.93%, respectively, compared to SMA. Furthermore, the number of path points is more and the optimization ability of TPSMA is better. At the same time, TPSMA is closer to the current optimal result than other algorithms by multiple sets of tests, and its time complexity is obviously better than others. Therefore, the superiority of TPSMA is adequately proven.