Optimizing a Bi-objective Preemptive Multi-mode Resource-Constrained Project Scheduling Problem: NSGA-II and MOICA Algorithms

The aim of a multi-mode resource-constrained project scheduling problem (MRCPSP) is to assign resource(s) with the restricted capacity to an execution mode of activities by considering relationship constraints to achieve pre-determined objective(s). These goals vary with managers or decision makers of any organization who should determine suitable objective(s) considering organization strategies. Also, we introduce the preemptive extension of the problem which allows for activity splitting. In this paper, the preemptive multi-mode resourceconstrained project scheduling problem (P-MMRCPSP) with Minimum makespan and the maximization of net present value (NPV) has been considered. Since the considered model is NP-Hard, the performance of our proposed model is evaluated by comparison with two well-known algorithms: non-dominated sorting genetic algorithm (NSGA II) and multi-objective imperialist competitive algorithm (MOICA). These metaheuristics have been compared on the basis of a computational experiment performed on a set of instances obtained from standard test problems constructed by the ProGen project generator, where, additionally, cash flows were generated randomly with the uniform distribution. Since the effectiveness of most meta-heuristic algorithms significantly depends on choosing the proper parameters. A Taguchi experimental design method (DOE) was applied to set and estimate the proper values of GAs parameters for improving their performances. The computational results show that the proposed MOICA outperforms the NSGA-II.