Time-Cost-Resource Optimization of ResourceConstrained Project Scheduling Problem with Discounted Cash Flows using Multi-objective Gravitational Search Algorithm

Resource-constrained project scheduling problem (RCPSP) is the basis of scheduling problems in operations research. In order to have more realistic model, the problem is studied with objectives of time, cost and a modified objective of resource leveling with discounted cash flows and several modes of execution for activities. Since the problem is an NPhardness, various kinds of heuristic and meta-heuristic methods have been proposed by many researchers to present the more efficient solution. The gravitational search algorithm is one of meta-heuristics introduced in recent years. Due to single-objective and continuity of the decision space, this algorithm has not been used to the multi-objective discrete RCPSPs. In this paper, multi-objective gravitational search algorithm (MOGSA) is proposed for solving the given problem . The performance of the proposed MOGSA is compared with a well-known NSGA-II algorithm in terms of some indices for several small and largesized PSPLIB test problems. The results show the proposed MOGSA outperforms the NSGA-II.