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Abstract: We describe an improved technique for handling large numbers of cutting planes when using an interior-point method for the solution of linear or semidefinite relaxations in binary quadratic optimization. The approach does not require solving successive relaxations to optimality but chooses cuts at intermediate iterates based on indicators of inequality violation and feasibility of their slacks, which are initialized using a recently proposed warmstart technique without any additional correction steps. Computational tests on instances of max-cut suggest that this new scheme is superior to solving only the final relaxation with all relevant cuts known in advance. [ABSTRACT FROM AUTHOR]

Despite the many advantages of interior-point algorithms over active-set methods for linear optimization, one of the remaining practical challenges is their current limitation to efficiently solve series of related problems by an effective warmstarting strategy. As a remedy, in this paper we present a new infeasible-interior-point approach to quickly reoptimize an initial problem instance after data perturbations, or a new linear programming relaxation after adding cutting planes for discrete or combinatorial problems. Based on the detailed complexity analysis of the underlying algorithm, we perform a comparative analysis to coldstart initialization schemes and present encouraging computational results with iteration savings of around 50% on average for perturbations of the Netlib linear programs (LPs) and successive linear programming relaxations of max-cut and the traveling salesman problem. [ABSTRACT FROM AUTHOR]

This paper is concerned with the single-row facility layout problem (SRFLP). A globally optimal solution to the SRFLP is a linear placement of rectangular facilities with varying lengths that achieves the minimum total cost associated with the (known or projected) interactions between them. We demonstrate that the combination of a semidefinite programming relaxation with cutting planes is able to compute globally optimal layouts for large SRFLPs with up to 30 facilities. In particular, we report the globally optimal solutions for two sets of SRFLPs previously studied in the literature, some of which have remained unsolved since 1988. [ABSTRACT FROM AUTHOR]

Abstract: The facility layout problem is concerned with the arrangement of a given number of rectangular facilities so as to minimize the total cost associated with the (known or projected) interactions between them. We consider the one-dimensional space-allocation problem (ODSAP), also known as the single-row facility layout problem, which consists in finding an optimal linear placement of facilities with varying dimensions on a straight line. We construct a semidefinite programming (SDP) relaxation providing a lower bound on the optimal value of the ODSAP. To the best of our knowledge, this is the first non-trivial global lower bound for the ODSAP in the published literature. This SDP approach implicitly takes into account the natural symmetry of the problem and, unlike other algorithms in the literature, does not require the use of any explicit symmetry-breaking constraints. Furthermore, the structure of the SDP relaxation suggests a simple heuristic procedure which extracts a feasible solution to the ODSAP from the optimal matrix solution to the SDP relaxation. Computational results show that this heuristic yields a solution which is consistently within a few percentage points of the global optimal solution. [Copyright &y& Elsevier]