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

Authors:
Tobias Brueggemann;Johann L. Hurink;Tjark Vredeveld;Gerhard J. Woeginger
Affiliations:
Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands;Dept. of Applied Mathematics, University of Twente, Enschede, The Netherlands;Dept. of Quantitative Economics, Maastricht University, Maastricht, The Netherlands;Dept. of Mathematics and Computer Science, Eindhoven University of Technology, Eindhoven, The Netherlands
Venue:
WAOA'07 Proceedings of the 5th international conference on Approximation and online algorithms
Year:
2007

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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 O(mlogm) 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.