A differential evolution algorithm combined with linear programming for solving a closed loop facility layout problem

Abstract

Closed loop layout problem (CLLP) is an important class of design problems encountered in flexible manufacturing system. It is to determine the locations of manufacturing cells along a closed material handling loop. Existing studies on CLLPs typically ignore clearances between adjacent cells and do not optimize the dimension of the closed loop. However, separating adjacent cells with suitable clearances may achieve a better solution with lower material flow cost, and optimizing cell sequence and the dimension of closed loop simultaneously can also improve the solution quality. In this paper, a mixed integer programming formulation (MIP) is established for the CLLP. Then, based on the formulation, a hybrid approach combining an improved differential evolution algorithm and an exact approach (iDE-EA) is proposed to solve the CLLP. The iDE with a hybrid coding is utilized to optimize the dimension of closed loop and the placement sequence of cells simultaneously. The EA is to determine the exact location of each cell (i.e., the clearance between each pair of adjacent cells). iDE-EA is verified on 10 problem instances, and experiments show that iDE-EA improves upon the best-known material handling cost by 0–9.97% compared against the traditional differential evolution algorithm and three state-of-the-art approaches. In addition, using EA to further optimize clearances among cells in the solution obtained by iDE can achieve a more competitive layout in most cases.