A multi-exchange neighborhood for minimum makespan parallel machine scheduling problems

We propose new local search algorithms for minimum makespan parallel machine scheduling problems, which perform multiple exchanges of jobs among machines. Inspired by the work of Thompson and Orlin on cyclic transfer neighborhood structures, we model multiple exchanges of jobs as special disjoint cycles and paths in a suitably defined improvement graph, by extending definitions and properties introduced in the context of vehicle routing problems and of the capacitated minimum spanning tree problem. Several algorithms for searching the neighborhood are suggested. We report the results of a wide computational experimentation, on different families of benchmark instances, performed for the case of identical machines. This problem has been selected as a case study to perform a comparison among the alternative algorithms, and to discover families of instances for which the proposed neighborhood may be promising in practice. Based on the results of the experiments, we can suggest which among the many possible variants of the proposed approaches may be more promising for developing local search algorithms based on multi-exchange moves for related problems. Also, on some families of instances, which are very hard to solve exactly, the most promising multi-exchange algorithms were observed to dominate, in solution quality and in computational time, competitive benchmark heuristics.