Parallel simulated annealing on a message-passing multi-computer

The purpose of this project was to develop an efficient multi-computer implementation of the simulated annealing approximation algorithm (SA). This algorithm has recently been proven successful in attacking large and complex multi-criteria combinatorial optimization problems. However, large problems still require significant amounts of time, so there is a need to develop implementations that will run efficiently on the massively parallel multi-computers that are appearing on the market. Previous parallel annealing implementations have been primarily aimed at shared-memory machines, since the most straightforward algorithms require that all processors have access to the data structures defining the model. Shared-memory machines appear to be limited in their degree of parallelism, so message-passing implementations must be developed to take full advantage of the increasing power of multi-computers. This dissertation will develop and evaluate new multi-computer annealing algorithms. The focus of the first part of this research is on the parallel move simulated annealing approach (PMSA). With this method each processor starts with an identical copy of the configuration being optimized. All processors then simultaneously make one or several moves each on their own copies of the configuration. After such a cycle, individual copies of the configuration are combined to produce one or more new configurations. Then the next cycle of moves begins. The analysis of PMSA indicates that results improve as we decrease the number of processors working on a configuration and thus increase the number of results from which to select at the conclusion. This leads to the development of the adaptive multiple independent runs (MIR) implementation. The MIR method simply distributes copies of independent sequential annealing runs over all available processors. The inverse power law convergence of sequential annealing allows us to further subdivide the runs on each processor into multiple short runs, improving the run-time and yielding more solutions from which to choose. During its initial phase, the MIR algorithm estimates the starting and stopping temperatures and the total run length. The use of multiple runs permits these estimates to be further improved, and suggests a scheme for determining a suitable cooling schedule. The MIR approach performs at least as well as the other parallel approaches that we have studied, and requires no prior knowledge of the target problem, no parallelization of sequential code, and no painstaking fine-tuning of the annealing parameters. The MIR approach thus provides a flexible general-purpose annealing package suitable for large multi-computers; furthermore, this approach should also provide an effective method for sequential machines.