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Maximum Planar Subgraphs and Nice Embeddings: Practical Layout Tools
 ALGORITHMICA
, 1996
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Solving the Maximum Weight Planar Subgraph Problem by Branch and Cut
 PROCEEDINGS OF THE THIRD CONFERENCE ON INTEGER PROGRAMMING AND COMBINATORIAL OPTIMIZATION
, 1993
"... In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3 ..."
Abstract

Cited by 8 (1 self)
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In this paper we investigate the problem of identifying a planar subgraph of maximum weight of a given edge weighted graph. In the theoretical part of the paper, the polytope of all planar subgraphs of a graph G is defined and studied. All subgraphs of a graph G, which are subdivisions of K 5 or K 3;3 , turn out to define facets of this polytope. We also present computational experience with a branch and cut algorithm for the above problem. Our approach is based on an algorithm which searches for forbidden substructures in a graph that contains a subdivision of K 5 or K 3;3 . These structures give us inequalities which are used as cutting planes.
An Investigation of Genetic Algorithms for Facility Layout Problems
 University of Edinburgh
, 1995
"... The Facility Layout Problem (FLP) concerns minimising total traffic cost between facilities in a particular location under given conditions including facility size and traffic between each pair of them. Because of its NPcompleteness, many suboptimal methods, which look for reasonably good solutions ..."
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Cited by 5 (0 self)
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The Facility Layout Problem (FLP) concerns minimising total traffic cost between facilities in a particular location under given conditions including facility size and traffic between each pair of them. Because of its NPcompleteness, many suboptimal methods, which look for reasonably good solutions, have been suggested. Although many papers exist which compare the performance of these methods with each other, the work is limited in the following ways: benchmark tests were done only on FLPs consisting of identical facilities; most of the algorithms being compared relied on deterministic approaches. Genetic Algorithms (GAs), which use a stochastic approach, have been used with some success for a number of NPcomplete problems, typically finding good answers but not necessarily the best. However, a range of other approaches, from traditional operations research to simulated annealing, are possible. Moreover, a GA itself can be varied in many ways. So, in this research project, not only t...