Abstract
In this article, we studied a robust resource constrained flexible project scheduling problem (RRCFPSP), in which the activity duration is an uncertain number and each activity may have multiple alternative execution routes. We represent RRCFPSP by an AND/OR network and propose a mathematical formulation. Moreover, optimal solution can be reached when the duration of each activity takes the maximum value. To employ the heuristic algorithms which specialise in solving continuous problems to solve the considered problem effectively, we develop a novel float weight optimization frame (FWOF). By combining this frame with particle swarm optimization (PSO), gravity search algorithm (GSA) and whale optimization algorithm (WOA), we propose three algorithms FPSO, FGSA and FWOA respectively. Finally, we design a series of numerical experiments, and experimental results show that the FWOF can make traditional certain heuristic algorithms solve the problems we consider effectively and accurately, especially in large-scale cases.
Highlights
Resource constrained project scheduling problem (RCPSP) is an important branch of mixed integer optimization, and is a kind of concrete description of practical problems
For resource constrained flexible project scheduling problem (RRCFPSP), it is relevant to build a float weight optimization frame FWOF such that the heuristic algorithms which aim at the linear programming problems can effectively solve the mixed integer programming problem RRCFPSP
If we let Lhg be the g−th node in level h of the selection tree, UA be the set of unselected activities, UAh denote the set of unselected activities in level h, and wli denote the weight of non-renewable resources l under activity i, where wli = 1/pmi ax, the selection strategy of activities in RC can be shown as Algorithm 1
Summary
Resource constrained project scheduling problem (RCPSP) is an important branch of mixed integer optimization, and is a kind of concrete description of practical problems. More and more variants of RCPSP are proposed, such as the multi-mode resource constrained project scheduling problem (MRCPSP), in which each activity has at least one execution mode [1]–[4]. Above situations do not study the uncertainty To solve these deterministic project scheduling problems, heuristic algorithms are employed since they are all NP-hard problems [3], [4], [10]–[24]. We consider a robust resource-constrained flexible project scheduling problem (RRCFPSP). For RRCFPSP, it is relevant to build a float weight optimization frame FWOF such that the heuristic algorithms which aim at the linear programming problems can effectively solve the mixed integer programming problem RRCFPSP. We summarize this article and put forward the prospect
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