Automatic Clustering and Multi-Directional Scheduling Scheme for Multi-Mode Scheduling Projects

In this study, a cluster-based heuristic algorithm to solve multi-mode resource constrained project scheduling problem (MMRCPSP) is presented. The MMRCPSPs are usually challenging to schedule because each activity has multiple execution modes with renewable and non-renewable resources that are categorized as an NP-hard problem. In this paper, we propose and apply three ideas to solve an MMRCPSP. Firstly, an MMRCPSP with two objectives namely, makespan and executive cost is converted into a single mode resource-constrained project scheduling problem (RCPSP) with three objectives by relaxing the non-renewable resource constraints and then defining a corresponding penalty value. In the second phase, in the light of precedence and renewable resource constraints, the new RCPSP are scheduled by calling the multi-directional scheduling schemes (multi-dss). In the end, on the basis of three objectives' value (namely makespan, cost, and penalty value), we defined a density-based fitness function for an evolutionary approach regarding the clustering methods on the new solution space. Our numerical results showed that the multi-dss with higher dimension regarding the automatic cluster-based fitness functions affected the performance of the evolutionary approach. Furthermore, the evolutionary approach based on multi-directional scheduling schemes prevents to trap into the local optimums by increasing the solutions' diversity.