Configuration space evolutionary algorithm for multi-objective unequal-area facility layout problems with flexible bays

Abstract

Facility layout problem (FLP) which deals with the layout of facilities within a given plant floor is an NP-hard combinatorial optimization problem. This paper studies multi-objective unequal-area facility layout problems (UA-FLPs) with the flexible bay structure (FBS), whose objectives refer to the material handling cost, the closeness relationship, the distance requirement and the aspect ratio of facilities. In recent years, some successes have been achieved by multi-objective evolutionary algorithms (MOEAs) for solving various kinds of optimization problems with multiple conflicting objectives. However, traditional MOEAs face a great challenge in the convergence and diversity of solutions for UA-FLPs. In this paper, a novel MOEA called the configuration space evolutionary (CSE) algorithm is developed to solve the UA-FLPs with multiple objectives. We consider a mating pool called a configuration (solution) bank in the CSE, and use evolutionary operations (selection, novel crossover and mutation) to produce new configurations of the pool. By introducing a measure of the radius dspace of the configuration bank, whose value is gradually reduced to narrow the search space, the convergence of solutions in the CSE is controlled. A method of the nearest and farthest candidate solution based on objective function normalization is combined with the fast non-dominated sorting to choose the Pareto-optimal solutions, which is good for the algorithm to keep diversity of the obtained solutions. The main contributions of this study lie in the use of a mechanism of evolution of population in the algorithm based on a configuration bank, and the use of a selection strategy based on the nearest and farthest candidate solution method, in order to improve the convergence and diversity of solutions. Experiments are carried out on eight different representative instances and performance metrics from the literature. Compared with the existing MOEAs, the CSE is able to find the better results and show better performance. The numerical experiments confirm the effectiveness of the CSE for solving multi-objective UA-FLPs.