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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.