Beating the SDP bound for the floor layout problem: A simple combinatorial idea

For many mixed-integer programming (MIP) problems, high-quality dual bounds can be obtained either through advanced formulation techniques coupled with a state-of-the-art MIP solver, or through semi-definite programming (SDP) relaxation hierarchies. In this paper, we introduce an alternative bounding approach that exploits the ‘combinatorial implosion’ effect by solving portions of the original problem and aggregating this information to obtain a global dual bound. We apply this technique to the one-dimensional and two-dimensional floor layout problems and compare it with the bounds generated by both state-of-the-art MIP solvers and by SDP relaxations. Specifically, we prove that the bounds obtained through the proposed technique are at least as good as those obtained through SDP relaxations, and present computational results that these bounds can be significantly stronger and easier to compute than these alternative strategies, particularly for very difficult problem instances.United States. National Science Foundation. Graduate Research Fellowship Program (Grant 1122374)United States. National Science Foundation. Graduate Research Fellowship Program (Grant CMMI-1351619

Global Approaches for Facility Layout and VLSI Floorplanning

This paper summarizes recent advances in the global solution of several relevant facility layout problems

Facility layout problem: Bibliometric and benchmarking analysis

Facility layout problem is related to the location of departments in a facility area, with the aim of determining the most effective configuration. Researches based on different approaches have been published in the last six decades and, to prove the effectiveness of the results obtained, several instances have been developed. This paper presents a general overview on the extant literature on facility layout problems in order to identify the main research trends and propose future research questions. Firstly, in order to give the reader an overview of the literature, a bibliometric analysis is presented. Then, a clusterization of the papers referred to the main instances reported in literature was carried out in order to create a database that can be a useful tool in the benchmarking procedure for researchers that would approach this kind of problems

Global Approaches for Facility Layout and VLSI Floorplanning

This paper summarizes recent advances in the global solution of several relevant facility layout problems

A polyhedral study of triplet formulation for single row facility layout problem

AbstractThe single row facility layout problem (SRFLP) is the problem of arranging n departments with given lengths on a straight line so as to minimize the total weighted distance between all department pairs. We present a polyhedral study of the triplet formulation of the SRFLP introduced by Amaral [A.R.S. Amaral, A new lower bound for the single row facility layout problem, Discrete Applied Mathematics 157 (1) (2009) 183–190]. For any number of departments n, we prove that the dimension of the triplet polytope is n(n−1)(n−2)/3 (this is also true for the projections of this polytope presented by Amaral). We then prove that several valid inequalities presented by Amaral for this polytope are facet-defining. These results provide theoretical support for the fact that the linear program solved over these valid inequalities gives the optimal solution for all instances studied by Amaral