An Improved Hybrid Method for the Multi-Mode Resource-Constrained Project Scheduling Problem

This paper presents an improved harmony search metaheuristic for the multi-mode resource-constrained project scheduling problem (MRCPSP). The hybrid metaheuristic presented is an improved version of the forbidden set oriented “Sounds of Silence” harmony search metaheuristic. In the original approach a simple but efficient "rule of thumb" was applied to eliminate the hidden resource conflicts. The result of the applied rule will be a resource-feasible solution set, in which every movable activity can be shifted without affecting the resource feasibility. It is well-known, that the crucial point of the conflict repairing model is the forbidden set computation. In the improved algorithm to decrease the time requirement of the forbidden set computation and speed up the problem solving process, a fast and efficient pre-processing step was inserted before the forbidden set computation which frequently reduces the solution time dramatically. The essence of the pre-processing step is very simple: In a cyclically repairable process, the incompatible activity pairs (triplets) are selected which have exactly one conflict repairing relation and is inserted into the relations. The process is terminated when the relation set will be empty. In order to illustrate the essence and viability of the improved algorithm, we present computational results for the J30MM set from PSPLIB benchmark set.