Nesting OpenMP in MPI to Implement a Hybrid Communication Method of Parallel Simulated Annealing on a Cluster of SMP Nodes

Concurrent computing can be applied to heuristic methods for combinatorial optimization to shorten computation time, or equivalently, to improve the solution when time is fixed. This paper presents several communication schemes for parallel simulated annealing, focusing on a combination of OpenMP nested in MPI. Strikingly, even though many publications devoted to either intensive or sparse communication methods in parallel simulated annealing exist, only a few comparisons of methods from these two distinctive families have been published; the present paper aspires to partially fill this gap. Implementation for VRPTW—a generally accepted benchmark problem—is used to illustrate the advantages of the hybrid method over others tested.