Abstract
A scheme for domain decomposition of the set partitioning problem is presented. Similar to the exploitation of special structure to improve algorithm performance, special structure can be exploited to divide the set partitioning problem into smaller subproblems. Real-world set partitioning problems from the airline industry are used to study the potential advantages of solving multiple subproblems to identify optimal solutions. The results of the study show that the decomposition is especially successful when applied to large problems that are difficult when solved using a single processor. For these cases, decomposition was able to produce smaller problems that, in the majority of cases, were far easier to solve than the original problem. Also, optimal solutions were identified in significantly less time than the time taken to solve the original problem. The results suggest that concurrent processing of subproblems should be investigated as an alternative method for solving large set partitioning problems typically encountered in real-world applications.
The set partitioning problem is well known to be computationally challenging for traditional single processor computing. Multiprocessor computing technology increases processing possibilities and therefore offers opportunities to move beyond the boundaries imposed by single processor computing. One approach to improving tractability is to divide the problem into smaller subproblems that can be solved using multiple processors. If subdivision can lead to early identification of good or optimal integer solutions, then it would be worthwhile to explore the potential of concurrent processing for mitigating the computational challenge of the set partitioning problem.
