Improved covariance matrix evolution strategy algorithm for stochastic dynamic unequal area facility layouts in an open area

Abstract

Facility layout problems deal with layout of facilities, machines, cells, or departments in a shop floor. This research has formulated unequal area stochastic dynamic facility layout problems in an open or wall-less area in order to minimize the upper bound of the sum of the material handling costs, and the sum of the shifting costs in the whole time planning horizon. In addition, the areas and shapes of departments are fixed during the iteration of an algorithm and throughout the time horizon. In unequal area stochastic dynamic facility layout problems, there are several periods for the material flow among departments or product demand such that the material flow among departments or product demand is not stable in each period. In other words, the product demand is stochastic with a known expected value and standard deviation in each period. In this research, a new mixed integer nonlinear programming mathematical model was proposed for solving this type of problems. Particularly, they are non-deterministic polynomial-time hard and very complex, and exact methods could not solve them within a reasonable computational time. Therefore, meta-heuristic algorithms and evolution strategies are needed to solve them. In this research, a modified covariance matrix adaptation evolution strategy algorithm was developed and the results were compared with two improved meta-heuristic algorithms (improved particle swarm optimization and modified genetic algorithm). These two meta-heuristic algorithms were developed and used to justify the efficiency of the proposed evolution strategy algorithm. The proposed algorithms applied four methods, which are (1) department swapping method, (2) local search method 1, (3) period swapping method, and (4) local search method 2, to prevent local optima and improve the quality of solutions for the problems. The proposed algorithms and the proposed mathematical model were validated using manual and graphical inspection methods, respectively. The trial and error method was applied to set the respective parametric values of the proposed algorithms in order to achieve better layouts. A real case and a theoretical problem were introduced to test the proposed algorithms. The results showed that the proposed covariance matrix adaptation evolution strategy has found better solutions in contrast to the proposed particle swarm optimization and genetic algorithm.