An Evolutionary Algorithm Based on a Hybrid Multi-Attribute Decision Making Method for the Multi-Mode Multi-Skilled Resource-Constrained Project Scheduling Problem

This paper addresses the multi-mode multi-skilled resource-constrained project scheduling problem. Activities of real world projects often require more than one skill to be accomplished. Besides, in many real-world situations, the resources are multi-skilled workforces. In presence of multi-skilled resources, it is required to determine the combination of workforces assigned to each activity. Hence, in this paper, a mixed-integer formulation called the MMSRCPSP is proposed to minimize the completion time of project. Since the MMSRCPSP is strongly NP-hard, a new genetic algorithm is developed to find optimal or near-optimal solutions in a reasonable computation time. The proposed genetic algorithm (PGA) employs two new strategies to explore the solution space in order to find diverse and high-quality individuals. Furthermore, the PGA uses a hybrid multi-attribute decision making (MADM) approach consisting of the Shannon’s entropy method and the VIKOR method to select the candidate individuals for reproduction. The effectiveness of the PGA is evaluated by conducting numerical experiments on several test instances. The outputs of the proposed algorithm is compared to the results obtained by the classical genetic algorithm, harmony search algorithm, and Neurogenetic algorithm. The results show the superiority of the PGA over the other three methods. To test the efficiency of the PGA in finding optimal solutions, the make-span of small size benchmark problems are compared to the optimal solutions obtained by the GAMS software. The outputs show that the proposed genetic algorithm has obtained optimal solutions for 70% of test problems.