Single Objective Mayfly Algorithm with Balancing Parameter for Multiple Traveling Salesman Problem

The Multiple Travelling Salesman Problem (MTSP) is a challenging combinatorial problem that involves multiple salesman visiting a set of cities, each exactly once, starting and ending at the same depot. The aim is to determine the optimal route with minimal cost and node cuts for each salesman while ensuring that at least one salesman visits each city. As the problem is NP-Hard, a single-objective metaheuristic algorithm, called the Mayfly Algorithm, inspired by the collective behavior of mayflies, is employed to solve the problem using the TSPlib95 test data. Since the Mayfly Algorithm employs a single fitness function, a balancing parameter is added to perform multiobjective optimization. Three balancing parameters in the optimization process: SumRoute represents the total cost of all salesmen travelling, StdRoute balances each salesman cost, and StdNodes balances the number of nodes for each salesman. The values of these parameters are determined based on the results of various tests, as they significantly impact the MTSP optimization process. With the appropriate parameter values, the single-objective Mayfly Algorithm can produce optimal solutions and avoid premature convergence. Overall, the Mayfly Algorithm shows promise as a practical approach to solving the MTSP problem. Using multiobjective optimization with balancing parameters enables the algorithm to achieve optimal results and avoid convergence issues. The TSPlib95 dataset provides a robust testing ground for evaluating the algorithm’s effectiveness, demonstrating its ability to solve MTSP effectively with multiple salesman.