Ant Colony Optimization for Balanced Multiple Traveling Salesmen Problem

Balanced multiple traveling salesmen problems (BMTSP) are a popular kind of combinatorial optimization problems widely existing in the real world. This problem aims to minimize the total path length of all salesmen, and at the same time minimize the longest path among all salesmen to keep the path length balance. To solve this problem effectively, this paper proposes a balance biased ant colony optimization (BACO) algorithm. Specifically, this algorithm maintains ant groups to optimize the paths of all salesmen with each ant group responsible for constructing a feasible solution and each ant in a group responsible for building the path of one salesman. To construct balanced paths for all salesmen, this paper further develops four ant selection mechanisms to construct paths, namely, Random Selection (RS), Shortest Biased Selection (SBS), Future Balance Biased Selection (FBBS) and Future Shortest Biased Selection (FSBS). Additionally, we further introduce the 2-opt local search operation to optimize the path of each salesman. Finally, extensive experiments conducted on four TSPLIB benchmark sets with different numbers of salesmen demonstrate that the proposed BACO with the four ant selection mechanisms shows much better performance than a state-of-the-art genetic algorithm (GA). In particular, among the four selection mechanisms, the FSBS strategy helps BACO achieve the best performance in solving BMSTP.