Optimisation of multiple travelling salesman problem using metaheuristic methods

The problem of travelling salesmen (TSP) is a well-known task in the field of combinatorial optimisation. However, the problem of the multiple travelling salesman (mTSP), which extends the former, is a more challenging and complex combinatorial optimisation problem. This problem included addressing real-world issues where more than one salesman needed to be responsible for. This paper covered the use of heuristic approaches to tackle 180 cities and six travelling salesmen to reduce the path distances. To transform an mTSP into a TSP, a K-means clustering algorithm was used. Genetic algorithm (GA) was applied to the cluster after the clustering was done and iterated to provide the best possible value for distance following convergence. Now, with the ant colony optimisation (ACO) algorithm, every cluster was once again solved to determine the optimum distance value as a TSP. Once the two heuristic methods were applied, it became evident that due to the thorough analysis and constructive design of the algorithm, the ant colony optimisation algorithm yielded better results and more efficient tour than the genetic algorithm.