### Abstract

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.

Original language | English (US) |
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Pages (from-to) | 187-207 |

Number of pages | 21 |

Journal | Computers and Operations Research |

Volume | 88 |

DOIs | |

State | Published - Dec 2017 |

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### All Science Journal Classification (ASJC) codes

- Computer Science(all)
- Modeling and Simulation
- Management Science and Operations Research

### Cite this

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**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.

Research output: Contribution to journal › Article

TY - JOUR

T1 - A problem evolution algorithm with linear programming for the dynamic facility layout problem—A general layout formulation

AU - Xiao, Yiyong

AU - Xie, Yue

AU - Kulturel-Konak, Sadan

AU - Konak, Abdullah

PY - 2017/12

Y1 - 2017/12

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85023616498&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85023616498&partnerID=8YFLogxK

U2 - 10.1016/j.cor.2017.06.025

DO - 10.1016/j.cor.2017.06.025

M3 - Article

AN - SCOPUS:85023616498

VL - 88

SP - 187

EP - 207

JO - Computers and Operations Research

JF - Computers and Operations Research

SN - 0305-0548

ER -