Discrete pigeon-inspired optimization algorithm with Metropolis acceptance criterion for large-scale traveling salesman problem

Abstract Pigeon-inspired optimization (PIO) algorithm, which is a newly proposed swarm intelligence algorithm, has been mainly applied to continuous optimization problems. In this paper, a discrete PIO (DPIO) algorithm, which uses the Metropolis acceptance criterion of simulated annealing algorithm, is proposed for Traveling Salesman Problems (TSPs). A new map and compass operator with comprehensive learning ability is designed to enhance DPIO's exploration ability. A new landmark operator, which has cooperative learning ability and can learn from the heuristic information of TSP instance, is designed to improve DPIO's exploitation ability. Aim to enhance its ability to escape from premature convergence, the Metropolis acceptance criterion is used to decide whether to accept newly produced solutions. Systematic experiments were performed to analyze the behaviours of the map and compass operator and the landmark operator. The performance of DPIO algorithm was tested on 33 large-scale TSP instances from TSPLIB with city number from 1000 to 85900. Simulation results show that the proposed algorithm is effective and is competitive with most other state-of-the-art meta-heuristic algorithms.