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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.

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 thirty departments. 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.

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Ana/ytic placement methods that simultaneously minimize wire length and spread cells are receiving renewed attention from both academia and industiy In this paper we describe the implementation details of a force-directed placer: FDP. Specifically, we provide (I) a description of eficient force computation for spreading cells, (2) an illustration of numerical instability in these methods and a meam by which these instabilities are avoided, (3) spread metrics for measuring cell distribution throughout the placement region and (4) a complementary technique which aids in directly minimizing HPWL. We present results comparing our ana/ytic placer to other academic tools for both standard cell and mixed-size designs. Compared to Kraftwerk and Capo 8.7, our tool produces results with an average improvement of 9% and 3%, respectively

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