A hybrid Honey Bees Mating Optimization algorithm for the Probabilistic Traveling Salesman Problem

The probabilistic traveling salesman problem is a variation of the classic traveling salesman problem and one of the most significant stochastic routing problems. In this paper, a new hybrid algorithmic nature inspired approach based on honey bees mating optimization (HBMO), greedy randomized adaptive search procedure (GRASP) and expanding neighborhood search strategy (ENS) is proposed for the solution of the probabilistic traveling salesman problem. The proposed algorithm has two additional main innovative features compared to other honey bees mating optimization algorithms that concern the crossover operator and the workers. The proposed algorithm is tested on a numerous benchmark problems from TSPLIB with very satisfactory results. Comparisons with the classic GRASP algorithm, the Particle Swarm Optimization (PSO) algorithm and with a Tabu Search algorithm are also presented. Also, a comparison is performed with the results of a number of implementations of the Ant Colony Optimization algorithm from the literature and in 6 out of 10 cases the proposed algorithm gives a new best solution.