Journal of Heuristics

, Volume 17, Issue 6, pp 637-658

Open Access This content is freely available online to anyone, anywhere at any time.

Matching based very large-scale neighborhoods for parallel machine scheduling

  • Tobias BrueggemannAffiliated withDepartment of Applied Mathematics, University of Twente
  • , Johann L. HurinkAffiliated withDepartment of Applied Mathematics, University of Twente Email author 


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.


Scheduling Parallel machines Total weighted completion time Very large-scale neighborhoods Local search