A continuous representation and chaos theory based algorithm for solving Facility Layout Problem

This paper proposes the algorithm for solving Facility Layout Problem (FLP), which is the problem of discovering the best locations of departments within the facility in order to maximize its efficiency. In FLP research, there are two choices of representation of layout candidates: discrete-representation and continuous-representation. In recent years, the continuous-representation has become the representation of choice, as it can consider all feasible solutions. Most of continuous-representation-based methods are based on Mixed-Integer-Programming (MIP) or Non Linear Programming (NLP). However, MIP-based-approach has weak searching capability in large-scale problem due to the large number of combinations of the binary variables used in the models to maintain feasibility with respect to departments overlapping. Further, NLP-based-approach has possibility to miss the searching opportunity for the optimal solution, as it can only seek one of local solutions. In order to overcome these difficulties, this paper proposes the chaos-theory-based algorithm that controls the intensification and diversification of searching capability. In numerical experiments, different sized problems from both the literature and industrial applications are tested and the solutions are compared with the solutions from other methods to show the effectiveness of the proposed algorithm.