4,164 research outputs found

    Two-Level Rectilinear Steiner Trees

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    Given a set PP of terminals in the plane and a partition of PP into kk subsets P1,...,PkP_1, ..., P_k, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree TiT_i connecting the terminals in each set PiP_i (i=1,...,ki=1,...,k) and a top-level tree TtopT_{top} connecting the trees T1,...,TkT_1, ..., T_k. The goal is to minimize the total length of all trees. This problem arises naturally in the design of low-power physical implementations of parity functions on a computer chip. For bounded kk we present a polynomial time approximation scheme (PTAS) that is based on Arora's PTAS for rectilinear Steiner trees after lifting each partition into an extra dimension. For the general case we propose an algorithm that predetermines a connection point for each TiT_i and TtopT_{top} (i=1,...,ki=1,...,k). Then, we apply any approximation algorithm for minimum rectilinear Steiner trees in the plane to compute each TiT_i and TtopT_{top} independently. This gives us a 2.372.37-factor approximation with a running time of O(PlogP)\mathcal{O}(|P|\log|P|) suitable for fast practical computations. The approximation factor reduces to 1.631.63 by applying Arora's approximation scheme in the plane

    A multifacility location problem on median spaces

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    AbstractThis paper is concerned with the problem of locating n new facilities in the median space when there are k facilities already located. The objective is to minimize the weighted sum of distances. Necessary and sufficient conditions are established. Based on these results a polynomial algorithm is presented. The algorithm requires the solution of a sequence of minimum-cut problems. The complexity of this algorithm for median graphs and networks and for finite median spaces with ¦V¦points is O(¦V¦3 + ¦V¦ψ(n)), where ψ(n) is the complexity of the applied maximum-flow algorithm. For a simple rectilinear polygon P with N edges and equipped with the rectilinear distance the analogical algorithm requires O(N + k(logN + logk + ψ(n))) time and O(N + kψ(n)) time in the case of the vertex-restricted multifacility location problem

    A new integrated design framework for the facility layout problem

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    This thesis proposes a new integrated design framework for solving facility layout problems (FLP). The most popular existing framework, Muther\u27s Systematic Layout Planning (SLP) does not address the variety of design goals associated with facility layout problems and is highly manual and so time consuming to perform. Furthermore, the SLP framework does not help the designer select a modeling tool to use in developing design alternatives, either by defining what a requisite model would include, or explicitly suggesting ones from literature. With the advancements made in academic research and computational capabilities since the development of the SLP framework, a new framework was needed to better address varying design goals, and assist designers in the selection of appropriate models. The framework proposed here guides the designer through determination of model requirements to meet their design goals by framing the FLP in terms of Design Layers . In addition, it proposes candidate models (or methodologies) to generate analytically derived solutions for design goals such as construction of simple block layouts, or determination of input/output points and flow paths in order to create detailed block layouts. The models and methodologies proposed are shown to rapidly reach good candidate solutions to a wide range of design problems

    Computer-aided design of cellular manufacturing layout.

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    Heuristics for the dynamic facility layout problem with unequal area departments

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    The facility layout problem (FLP) is a well researched problem of finding positions of departments on a plant floor such that departments do not overlap and some objective(s) is (are) optimized. In this dissertation, the FLP with unequal area rectangular shaped departments is considered, when material flows between departments change during the planning horizon. This problem is known as the dynamic FLP. The change in material flows between pairs of departments in consecutive periods may require rearrangements of departments during the planning horizon in order to keep material handling costs low. The objective of our problem is to minimize the sum of the material handling and rearrangement costs. Because of the combinatorial structure of the problem, only small sized problems can be solved in reasonable time using exact techniques. As a result, construction and improvement heuristics are developed for the proposed problem. The construction algorithms are boundary search heuristics as well as a dual simplex method, and the improvement heuristics are tabu search and memetic heuristics with boundary search and dual simplex (linear programming model) techniques. The heuristics were tested on a generated data set as well as some instances from the literature. In summary, the memetic heuristic with the boundary search technique out-performed the other techniques with respect to solution quality
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