, Volume 17, Issue 6, pp 637-658,
Open Access This content is freely available online to anyone, anywhere at any time.
Date: 11 Nov 2010

Matching based very large-scale neighborhoods for parallel machine scheduling

Abstract

In this paper we study very large-scale neighborhoods for the minimum total weighted completion time problem on parallel machines, which is known to be strongly \(\mathcal{NP}\) -hard. We develop two different ideas leading to very large-scale neighborhoods in which the best improving neighbor can be determined by calculating a weighted matching. The first neighborhood is introduced in a general fashion using combined operations of a basic neighborhood. Several examples for basic neighborhoods are given. The second approach is based on a partitioning of the job sets on the machines and a reassignment of them. In a computational study we evaluate the possibilities and the limitations of the presented very large-scale neighborhoods.

T. Brueggemann was supported by the Netherlands Organization for Scientific Research (NWO) grant 613.000.225 (Local Search with Exponential Neighborhoods).
J.L. Hurink was supported by BSIK grant 03018 (BRICKS: Basic Research in Informatics for Creating the Knowledge Society).