Multi-objective Particle Swarm Optimization For The Unequal-area Facility Layout Problem

With n objects and a bounded space provided with given shape and size,the layout problem is to research how best to palace these objects into the bounded space without overlaps,so as to satisfy with some given objectives.Under the background of the layout planning of workshop equipment in enterprise production,the unequal-area static facility layout problem(SFLP)and the unequal-equal dynamic facility layout problem(DFLP)are studied.The facility layout problem(FLP)belongs to a kind of NP hard problem.It not only solves combinatorial explosion problems in mathematics,but also aims at complex engineering system problems.This kind of problem is difficult to obtain the optimal solution by the certainty algorithm.However,because of its importance in the manufacturing industry,it is important to find the optimal layout or approximate optimal layout.The specific studies of this paper are as follows:(1)The improved method of multi-objective particle swarm optimization(MOPSO)algorithm for SFLP is studied.First,a mathematical optimization model is established,and then an improved multi-objective particle swarm optimization(MOPSO)algorithm is proposed to solve the SFLP.To improve the effectiveness of the MOPSO,we propose a modified objective space division method which goverms the neighborhood topology and the local best swarm used to assess the fitness of a solution and choose the global leader particle which is a main issue in the MOPSO.Second,we put forward a heuristic configuration mutation operation and subsequent local search to satisfy the non-overlapping constraint which is a key difficulty in solving the SFLP.Combining these strategies with MOPSO,a multi-objective particle swarm optimization algorithm based on objective space division(MOPSO-OSD)is proposed.Two groups of typical instances from the literature are tested.The experimental results show that the proposed MOPSO-OSD algorithm is an effeetive method for solving the SFLP.(2)A multi-objective particle swarm optimization(MOPSO)algorithm for DFLP is studied.First,a mathematical optimization model for DFLP is established,then,the definition of the solution in the MOPSO-OSD algorithm has been redefined.According to the characteristics of the dynamic facility layout problem,some strategies in MOPSO-OSD are needed to be modified.The definition of the solution in the MOPSO-OSD algorithm has been redefined.Considering the multi-stage characteristics of the dynamic layout problem and improving the diversity of the solutions,a unit handling cost strategy is defined to update the positions of facilities in all periods.Two groups of instances are used to analyze the performance of the proposed algorithm MOPSO-OSD.The instances are classical DFLP and practical DhFLP,respectively.The experimental results illustrate that the proposed models are effective and the MOPSO-OSD algorithms are practical methods for solving DFLP compared with other algorithms.