Multi-objective particle swarm optimization algorithm based on objective space division for the unequal-area facility layout problem

The facility layout problem (FLP) is the problem of placing facilities in a certain shop floor so that facilities do not overlap each other and are satisfied with some given objectives. Considering practical situations, this study focuses on the multi-objective unequal-area facility layout problem (UA-FLP), where the facilities have unequal-areas and fixed shapes and are placed orthogonally in the continuous shop floor. The objectives of the problem aim to optimize the material handling cost, the total adjacency value and the utilization ratio of the shop floor. The chief difficulties of this version of the FLP lie in the satisfaction of non-overlapping constraint between any two different facilities and the optimization of multiple objectives in the huge solution space. In this paper, we put forward a heuristic configuration mutation operation and subsequent local search based on the gradient method to satisfy the non-overlapping constraint, and the multi-objective particle swarm optimization (MOPSO) algorithm, which has recently proven its high effectiveness and robustness in solving multi-objective problems, to obtain a set of Pareto-optimal solutions of the problem. The novelty of the paper lies in the use of an objective space division method in the MOPSO which governs the neighborhood topology and the local best swarm used to assess the global fitness of a solution and choose the global leader particle. The proposed algorithm is tested on three sets of different UA-FLPs from the literature with the size of the problem up to 62 facilities. The numerical results show that the proposed method is effective in solving the multi-objective UA-FLP.