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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...
ProximityBased Adjacency Determination for Facility Layout
"... We define a new model for adjacency subgraph selection for the facility layout problem based on proximity and present some heuristics for its solution. The new model presents a more realistic representation of the problem than previous ones in that departments which are nonadjacent yet "clo ..."
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Cited by 1 (0 self)
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We define a new model for adjacency subgraph selection for the facility layout problem based on proximity and present some heuristics for its solution. The new model presents a more realistic representation of the problem than previous ones in that departments which are nonadjacent yet "close" to each other are compensated in the determination of the optimal adjacency subgraph. Empirical results comparing the heuristics with the method of Leung [17] are reported.
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.
Layout Design of a Furniture Production Line Using Formal Methods
"... This paper experiments application of different heuristic approaches to a real facility layout problem at a furniture manufacturing company. All the models are compared using AHP, where a number of parameters of interest are employed. The experiment shows that formal layout modelling approaches can ..."
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This paper experiments application of different heuristic approaches to a real facility layout problem at a furniture manufacturing company. All the models are compared using AHP, where a number of parameters of interest are employed. The experiment shows that formal layout modelling approaches can be effectively used real problems faced in industry, leading to significant improvements.
Graph Planarization
, 1998
"... . We survey graph planarization and related problems. We first describe variants and applications of graph planarization. Then we focus on algorithms. We begin by describing the branchandcut algorithm of Junger and Mutzel (1996). Then, we review work on heuristics based on planarity testing an ..."
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. We survey graph planarization and related problems. We first describe variants and applications of graph planarization. Then we focus on algorithms. We begin by describing the branchandcut algorithm of Junger and Mutzel (1996). Then, we review work on heuristics based on planarity testing and those based on twophase procedures. Finally, computational results comparing algorithms for graph planarization are presented. 1. Introduction A graph is said to be planar if it can be drawn on the plane in such a way that no two of its edges cross. Given a graph G = (V, E) with vertex set V and edge set E, the objective of graph planarization is to find a minimum cardinality subset of edges F # E such that the graph G # = (V, E \ F ), resulting from the removal of the edges in F from G, is planar. This problem is also known as the maximum planar subgraph problem. A related and simpler problem is that of finding a maximal planar subgraph, which is a planar subgraph G # = (V, E # ) ...
Graph Theoretic Based Heuristics For the Facility Layout Design Problems
"... The facility layout problem is concerned with determining the location of a number of facilities which optimizes a prescribed objective such as profit, cost, or distance. This problem arises in many applications; for example, in design of buildings and in plant layout design. The facility layout pro ..."
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The facility layout problem is concerned with determining the location of a number of facilities which optimizes a prescribed objective such as profit, cost, or distance. This problem arises in many applications; for example, in design of buildings and in plant layout design. The facility layout problem has been modeled as: a quadratic assignment problem; a quadratic set covering problem; a linear integer programming problem; a graph theoretic problem. Since this problem is NPcomplete, most approaches are heuristic in nature and based on graph theoretic concepts. Graph theoretically, when the objective is to maximize profit, the facility layout problem is to determine, in a given edge weighted graph G, a maximum weight planar subgraph. In this paper, we discuss a number of heuristics for this problem. The performance of the heuristics is established through a comparative analysis based on an extensive set of random test problems. 1. Introduction Typically the facility layout design ...