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11999 Very large-scale neighborhoods with performance guarantees for minimizing makespan on parallel machines

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Brueggemann, T. and Hurink, J.L. and Vredeveld, T. and Woeginger, G.J. (2008) Very large-scale neighborhoods with performance guarantees for minimizing makespan on parallel machines. In: 5th International Workshop on Approximation and Online Algorithms, October 11-12, 2007, Eilat, Israel. pp. 41-54. Lecture Notes in Computer Science 4927. Springer Verlag. ISSN 0302-9743 ISBN 978-3-540-77917-9

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Official URL: http://dx.doi.org/10.1007/978-3-540-77918-6_4

Abstract

We study the problem of minimizing the makespan on $m$ parallel machines. We introduce a very large-scale neighborhood of exponential size (in the number of machines) that is based on a matching in a complete graph. The idea is to partition for every machine the set of assigned jobs into two sets by some fixed rule and then to reassign these $2m$ parts such that every machine gets exactly two parts. The split neighborhood consists of all possible reassignments of the parts and a best neighbor can be calculated in ${\cal O}(m \log m)$ by determining a perfect matching with minimum maximal edge weight. We examine local optima in the split neighborhood and in combined neighborhoods consisting of the split and other known neighborhoods and derive performance guarantees for these local optima.

Item Type:	Conference or Workshop Paper (Full Paper, Talk)
Research Group:	EWI-DMMP: Discrete Mathematics and Mathematical Programming
Research Program:	CTIT-IE&ICT: Industrial Engineering and ICT
Research Project:	BRICKS/IS3: Decision Support Systems for Logistic Networks and Supply Chain Optimization
ID Code:	11999
Status:	Published
Deposited On:	13 February 2008
Refereed:	Yes
International:	Yes
More Information:	statistics metis

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Very Large-Scale Neighborhoods with Performance Guarantees for Minimizing Makespan on Parallel Machines (deposited 23 November 2006)
- Very large-scale neighborhoods with performance guarantees for minimizing makespan on parallel machines (deposited 13 February 2008)
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