Iterative flattening search for resource constrained scheduling

Iterative flattening search (ifs) is a meta-heuristic strategy for solving multi-capacity scheduling problems. Given an initial solution, ifs iteratively applies: (1) a relaxation-step, in which a subset of scheduling decisions are randomly retracted from the current solution; and (2) a flattening-step, in which a new solution is incrementally recomputed from this partial schedule. Whenever a better solution is found, it is retained, and, upon termination, the best solution found during the search is returned. Prior research has shown ifs to be an effective and scalable heuristic procedure for minimizing schedule makespan in multi-capacity resource settings. In this paper we experimentally investigate the impact on ifs performance of algorithmic variants of the flattening step. The variants considered are distinguished by different computational requirements and correspondingly vary in the type and depth of search performed. The analysis is centered around the idea that given a time bound to the overall optimization procedure, the ifs optimization process is driven by two different and contrasting mechanisms: the random sampling performed by iteratively applying the “relaxation/flattening” cycle and the search conducted within the constituent flattening procedure. On one hand, one might expect that efficiency of the flattening process is key: the faster the flattening procedure, the greater the number of iterations (and number of sampled solutions) for a given time bound; and hence the greater the probability of finding better quality solutions. On the other hand, the use of more accurate (and more costly) flattening procedures can increase the probability of obtaining better quality solutions even if their greater computational cost reduces the number of ifs iterations. Comparative results on well-studied benchmark problems are presented that clarify this tradeoff with respect to previously proposed flattening strategies, identify qualitative guidelines for the design of effective ifs procedures, and suggest some new directions for future work in this area.