Results 1 
3 of
3
Practical Problem Solving with Cutting Plane Algorithms in Combinatorial Optimization
, 1994
"... Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many purely comb ..."
Abstract

Cited by 20 (5 self)
 Add to MetaCart
Cutting plane algorithms have turned out to be practically successful computational tools in combinatorial optimization, in particular, when they are embedded in a branch and bound framework. Implementations of such "branch and cut" algorithms are rather complicated in comparison to many purely combinatorial algorithms. The purpose of this article is to give an introduction to cutting plane algorithms from an implementor's point of view. Special emphasis is given to control and data structures used in practically successful implementations of branch and cut algorithms. We also address the issue of parallelization. Finally, we point out that in important applications branch and cut algorithms are not only able to produce optimal solutions but also approximations to the optimum with certified good quality in moderate computation times. We close with an overview of successful practical applications in the literature.
APPROXIMATING MAXIMUM STABLE SET AND MINIMUM GRAPH COLORING PROBLEMS WITH THE POSITIVE SEMIDEFINITE RELAXATION
"... We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in m ..."
Abstract

Cited by 9 (1 self)
 Add to MetaCart
We compute approximate solutions to the maximum stable set problem and the minimum graph coloring problem using a positive semidefinite relaxation. The positive semidefinite programs are solved using an implementation of the dual scaling algorithm that takes advantage of the sparsity inherent in most graphs and the structure inherent in the problem formulation. From the solution to the relaxation, we apply a randomized algorithm to find approximate maximum stable sets and a modification of a popular heuristic to find graph colorings. We obtained high quality answers for graphs with over 1000 vertices and almost 7000 edges.
EUCLID CALMA Radio Link Frequency Assignment Project Report 2.2.1: Implementation and Testing of Polyhedral Techniques and Interior Point Methods
 Technical Annex T2.2.1 A, T.U. Eindhoven RLFAP Group and T.U. Delft RLFAP Group
, 1995
"... g all the problems of a given class, would need significant theoretical advances. Moreover the choice of an approach is frequently based on several criteria (accuracy, speed, robustness, development cost, etc ) and it is well known that multicriteria based decisions are vey difficult. Nevertheless ..."
Abstract

Cited by 2 (0 self)
 Add to MetaCart
g all the problems of a given class, would need significant theoretical advances. Moreover the choice of an approach is frequently based on several criteria (accuracy, speed, robustness, development cost, etc ) and it is well known that multicriteria based decisions are vey difficult. Nevertheless, some empirical rules based mainly on experimental results, but supported in part by theoretical analyses, should provide guidance for the decision makers in their choice of approach for any given problem type. Moreover, one of the most significant outcomes of the CALMA project will be guidance for the efficient development of each of the chosen approaches. 2 Concern 2.1 Global Objectives In this scientific and operational context, the following steps have been proposed as part of the EUCLID program (CEPA6RTP 6.4). 1. To solve a set of problems of the same type by various approaches. 2. To determine, according to the obtained results, the weakness, strengths and po