Ant colony optimization with shortest distance biased dispatch for visiting constrained multiple traveling salesmen problem

Abstract

The visiting constrained multiple traveling salesmen problem (VCMTSP) aims to minimize the total traveling cost of all salesmen by taking the accessibility of cities to salesmen into consideration. To solve this challenging problem, this paper devises a shortest distance biased dispatch (SDBD) scheme based on the accessibility of cities and a pheromone diffusion strategy for ant colony optimization (ACO). Specifically, this algorithm maintains a population of ant teams to construct feasible solutions. Each team maintains multiple ants with each ant responsible for constructing the route of one salesman to generate a feasible solution. During the solution construction of an ant team, the multiple ants construct the routes of all salesmen city by city in parallel based on the devised dispatch scheme. To further improve the solution quality, the 2-opt local search operation is integrated to further optimize the routes of all salesmen. Experiments conducted on several VCMTSP instances generated from the TSPLIB benchmark set demonstrate the effectiveness of the proposed algorithm.