A two-phase ant colony optimization based approach for single depot multiple travelling salesman problem in Type-2 fuzzy environment

In this paper, a two-phase ant colony optimization (ACO) based approach has been presented to solve a single depot multiple travelling salesmen problem (mTSP) in Type-2 Gaussian fuzzy environment. In the single depot mTSP, a set of nodes and a set of salesmen are present, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot. In this paper, a two-phase algorithm has been devised with ACO algorithm and some features of genetic algorithm (GA) to solve the projected problem. The devised algorithm is working appropriately with single depot mTSP. Here, in the first phase, the ACO algorithm is used for creating complete paths, and after that in the second phase, the GA features are used for optimizing the paths of multiple travellers. Moreover, the travelling cost is considered as Type-2 Gaussian fuzzy in nature and is reduced to its approximate crisp value using the reduction method of critical values. Some benchmark instances from TSPLIB have been used for performance analysis of the proposed algorithm. Computated results show that the devised algorithm is a competitive one for solving mTSP. Computational results with different datasets have been presented and some sensitivity analysis has also been done for fuzzy instances.