Unequal-area stochastic facility layout problems: solutions using improved covariance matrix adaptation evolution strategy, particle swarm optimisation, and genetic algorithm

Determining the locations of departments or machines in a shop floor is classified as a facility layout problem. This article studies unequal-area stochastic facility layout problems where the shapes of departments are fixed during the iteration of an algorithm and the product demands are stochastic with a known variance and expected value. These problems are non-deterministic polynomial-time hard and very complex, thus meta-heuristic algorithms and evolution strategies are needed to solve them. In this paper, an improved covariance matrix adaptation evolution strategy (CMA ES) was developed and its results were compared with those of two improved meta-heuristic algorithms (i.e. improved particle swarm optimisation PSO and genetic algorithm GA). In the three proposed algorithms, the swapping method and two local search techniques which altered the positions of departments were used to avoid local optima and to improve the quality of solutions for the problems. A real case and two problem instances were introduced to test the proposed algorithms. The results showed that the proposed CMA ES has found better layouts in contrast to the proposed PSO and GA.