Particle swarm optimization with expanding neighborhood topology for the permutation flowshop scheduling problem

This paper introduces a new algorithmic nature-inspired approach that uses particle swarm optimization (PSO) with different neighborhood topologies, for successfully solving one of the most computationally complex problems, the permutation flowshop scheduling problem (PFSP). The PFSP belongs to the class of combinatorial optimization problems characterized as NP-hard and, thus, heuristic and metaheuristic techniques have been used in order to find high quality solutions in reasonable computational time. The proposed algorithm for the solution of the PFSP, the PSO with expanding neighborhood topology, combines a PSO algorithm, the variable neighborhood search strategy and a path relinking strategy. As, in general, the structure of the social network affects strongly a PSO algorithm, the proposed method using an expanding neighborhood topology manages to increase the performance of the algorithm. As the algorithm starts from a small size neighborhood and by increasing (expanding) in each iteration the size of the neighborhood, it ends to a neighborhood that includes all the swarm, and it manages to take advantage of the exploration abilities of a global neighborhood structure and of the exploitation abilities of a local neighborhood structure. In order to test the effectiveness and the efficiency of the proposed method, we use a set of benchmark instances of different sizes and compare the proposed method with a number of other PSO algorithms and other algorithms from the literature.