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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 ..."
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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.
Considering Production Uncertainty In Block Layout Design
, 1999
"... This paper presents a formulation of the facilities block layout problem which explicitly considers uncertainty in material handling costs by use of expected values and standard deviations of product forecasts. This formulation is solved using a genetic algorithm metaheuristic with a flexible ba ..."
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Cited by 2 (0 self)
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This paper presents a formulation of the facilities block layout problem which explicitly considers uncertainty in material handling costs by use of expected values and standard deviations of product forecasts. This formulation is solved using a genetic algorithm metaheuristic with a flexible bay construct of the departments and total facility area. It is shown that depending on the attitude of the decisionmaker towards uncertainty, the optimal layout can change significantly. Furthermore, designs can be optimized directly for robustness over a range of uncertainty that is prespecified by the user. Keywords  facilities, heuristics, optimisation, genetic algorithms, block layout, production uncertainty 1. Introduction Facility design problems generally involve the partition of a planar region into departments (work centers or cells) along with an aisle structure and a material handling system to link the departments. The primary objective of the design problem is to minimi...
New Facets for the Planar Subgraph Polytope ∗
"... This paper describes certain facet classes for the planar subgraph polytope. These facets are extensions of Kuratowski facets and are of the form 2x(U)+x(E(G)\U) ≤ 2U+E(G)\U  −2 where the edge set U varies and can be empty. Two of the new types of facets complete the class of extended subdivisi ..."
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This paper describes certain facet classes for the planar subgraph polytope. These facets are extensions of Kuratowski facets and are of the form 2x(U)+x(E(G)\U) ≤ 2U+E(G)\U  −2 where the edge set U varies and can be empty. Two of the new types of facets complete the class of extended subdivision facets, explored by Jünger and Mutzel. In addition, the other types of facets consist of a new class of facets for the polytope called 3star subdivisions. It is also shown that the extended and 3star subdivision facets are also equivalent to members of the class of facets with coefficients in {0,1,2} for the set covering polytope. Computational results displaying the effectiveness of the facets in a branchandcut scheme for the maximum planar subgraph problem are presented.