Machine layout problem in flexible manufacturing systems
Operations Research
Methods for the one-dimensional space allocation problem
Computers and Operations Research
A new heuristic for the linear placement problem
Computers and Operations Research
Generating lower bounds for the linear arrangement problem
Discrete Applied Mathematics
A Spectral Bundle Method for Semidefinite Programming
SIAM Journal on Optimization
Semidefinite programming for discrete optimization and matrix completion problems
Discrete Applied Mathematics
A new lower bound for the single row facility layout problem
Discrete Applied Mathematics
An Exact Approach to the One-Dimensional Facility Layout Problem
Operations Research
Applying the sequence-pair representation to optimal facility layout designs
Operations Research Letters
VLSI module placement based on rectangle-packing by the sequence-pair
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
Optimization Methods & Software - GLOBAL OPTIMIZATION
Note: A polyhedral study of triplet formulation for single row facility layout problem
Discrete Applied Mathematics
Insertion based Lin-Kernighan heuristic for single row facility layout
Computers and Operations Research
A computational study and survey of methods for the single-row facility layout problem
Computational Optimization and Applications
A parallel ordering problem in facilities layout
Computers and Operations Research
A scatter search algorithm for the single row facility layout problem
Journal of Heuristics
Hi-index | 0.00 |
The facility layout problem is a global optimization problem that seeks to arrange a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. This paper is concerned with the single-row facility layout problem (SRFLP), the one-dimensional version of facility layout that is also known as the one-dimensional space allocation problem. It was recently shown that the combination of a semidefinite programming (SDP) relaxation with cutting planes is able to compute globally optimal layouts for SRFLPs with up to 30 facilities. This paper further explores the application of SDP to this problem. First, we revisit the recently proposed quadratic formulation of this problem that underlies the SDP relaxation and provide an independent proof that the feasible set of the formulation is a precise representation of the set of all permutations on n objects. This fact follows from earlier work of Murata et al., but a proof in terms of the variables and structure of the SDP construction provides interesting insights into our approach. Second, we propose a new matrix-based formulation that yields a new SDP relaxation with fewer linear constraints but still yielding high-quality global lower bounds. Using this new relaxation, we are able to compute nearly optimal solutions for instances with up to 100 facilities.