# Matching based very large-scale neighborhoods for parallel machine scheduling

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DOI: 10.1007/s10732-010-9149-8

- Cite this article as:
- Brueggemann, T. & Hurink, J.L. J Heuristics (2011) 17: 637. doi:10.1007/s10732-010-9149-8

## 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.