The Resource Constrained Project Scheduling problem (RCPSP) is a complex and combinatorial optimization problem mostly relates with project management, construction industries, production planning and manufacturing domains. Although several solution methods have been proposed, no single method has been shown to be the best. Further, optimal solution of this type of problem requires different requirements of the exploration and exploitation at different stages of the optimization process. Considering these requirements, in this paper, a two-stage multi-operator differential evolution (DE) algorithm, called TS-MODE, has been developed to solve RCPSP. TS-MODE starts with the exploration stage, and based on the diversity of population and the quality of solutions, this approach dynamically place more importance on the most-suitable DE, and then repeats the same process during the exploitation phase. A complete evaluation of the components and parameters of the algorithms by a Design of Experiments technique is also presented. A number of single-mode RCPSP data sets from the project scheduling library (PSPLIB) have been considered to test the effectiveness and performance of the proposed TS-MODE against selected recent well-known state-of-the-art algorithms. Those results reveal the efficiency and competitiveness of the proposed TS-MODE approach.

资源受限项目计划问题（RCPSP）是一个复杂的组合优化问题，主要涉及项目管理，建筑行业，生产计划和制造领域。尽管已经提出了几种解决方法，但没有一种方法被证明是最好的。此外，此类问题的最佳解决方案在优化过程的不同阶段需要不同的探索和开发要求。考虑到这些要求，在本文中，开发了一种称为TS-MODE的两阶段多算子差分演化（DE）算法来解决RCPSP。TS-MODE从探索阶段开始，并基于人口的多样性和解决方案的质量，这种方法动态地将重点放在最合适的DE上，然后在开发阶段重复相同的过程。还介绍了通过实验设计技术对算法的组成部分和参数进行的完整评估。已经考虑了来自项目调度库（PSPLIB）的许多单模RCPSP数据集，以针对所选的最新知名技术进行测试所提出的TS-MODE的有效性和性能。这些结果表明了所提出的TS-MODE方法的效率和竞争力。已经考虑了来自项目调度库（PSPLIB）的许多单模RCPSP数据集，以针对所选的最新知名技术进行测试所提出的TS-MODE的有效性和性能。这些结果表明了所提出的TS-MODE方法的效率和竞争力。已经考虑了来自项目调度库（PSPLIB）的许多单模RCPSP数据集，以针对所选的最新知名技术进行测试所提出的TS-MODE的有效性和性能。这些结果表明了所提出的TS-MODE方法的效率和竞争力。