A problem evolution algorithm with linear programming for the dynamic facility layout problem—A general layout formulation - Xiao, Yiyong; Xie, Yue; Kulturel-Konak, Sadan; Konak, Abdullah (Computers & operations research, 2017)
•The problem evolution algorithm (PEA) is developed to solve the Facility Layout Problem (FLP).•The PEA-LP works very well in solving various FLP benchmark problems.•A polyhedral inner-approximation is proposed for the nonlinear department area constraints.•Two symmetry-breaking constraints are introduced to increase the algorithmic efficiency.•Relayout of department blocks in the context of the dynamic FLP was considered. Facility layout problems (FLPs) are quite common and important in many industries. This paper presents a mixed integer linear programming (MILP) model for the dynamic facility layout problem, which is a generalization of several special cases of FLPs studied in recent years. A new evolutionary meta-heuristic framework, named as the problem evolution algorithm (PEA), is developed as a general solution approach for FLPs. Computational experiments show that the PEA combined with the linear programming (LP), called PEA-LP in short, performs well in various types of FLPs. In addition, a new polyhedral inner-approximation method is proposed based on secant lines for the linearization of the non-linear constraint for department area requirements. This new method guarantees that the actual department area is always greater than or equal to the required area within a given maximum deviation error. Furthermore, two new symmetry-breaking constraints which help to improve the computational efficiency of the MILP model are also introduced. Computational experiments on several well-known problem instances from the literature are carried out to test the DFLP-FZ and the PEA-LP with promising results.