A hybrid Particle Swarm Optimization - Variable Neighborhood Search algorithm for Constrained Shortest Path problems

In this paper, a well known NP-hard problem, the Constrained Shortest Path problem, is studied. As efficient metaheuristic approaches are required for its solution, a new hybridized version of Particle Swarm Optimization algorithm with Variable Neighborhood Search is proposed for solving this significant combinatorial optimization problem. Particle Swarm Optimization (PSO) is a population-based swarm intelligence algorithm that simulates the social behavior of social organisms by using the physical movements of the particles in the swarm. A Variable Neighborhood Search (VNS) algorithm is applied in order to optimize the particles' position. In the proposed algorithm, the Particle Swarm Optimization with combined Local and Global Expanding Neighborhood Topology (PSOLGENT), a different equation for the velocities of particles is given and a novel expanding neighborhood topology is used. Another issue in the application of the VNS algorithm in the Constrained Shortest Path problem is which local search algorithms are suitable from this problem. In this paper, a number of continuous local search algorithms are used. The algorithm is tested in a number of modified instances from the TSPLIB and comparisons with classic versions of PSO and with other versions of the proposed method are performed. Also, the results of the algorithm are compared with the results of a number of metaheuristic and evolutionary algorithms. The results obtained are very satisfactory and strengthen the efficiency of the algorithm.