A multi-exchange neighborhood for minimum makespan machine

We propose new local search algorithms for minimum makespan machine scheduling problems, which perform multiple exchanges of jobs among machines. Inspired by the work of Thompson and Orlin (1989) 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 VRP (Thompson and Psaraftis, 1993) and of CMST (Ahuja, Orlin and Sharma, 1998). 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. The minimum makespan machine scheduling problem with identical machines 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. The obtained results are very interesting. On some families of instances, which are very hard to solve exactly, the most promising multi-exchange algorithms proved to dominate, in gap and in time, competitive benchmark heuristics.