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 (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 vehicle routing problems (Thompson and Psaraftis, 1993) and of the capacitated minimum spanning tree problem (Ahuja et al., 2001). Several algorithms for searching the neighborhood are suggested.