Abstract: Along with the resource in resource-constrained project scheduling problem being extended to flexible resource with capability difference, a mix-integer programming model is established for Project Scheduling Problem constrained by Flexible Resource with Capability Difference（PSPFRCD）, which is a practical extension of traditional Resource-Constrained Project Scheduling Problem（RCPSP）. To solve the model, an adapted particle swarm optimization algorithm based on activity list is presented. In decode process of Particle Swarm Optimization（PSO）, a flexible resource assignment algorithm based on priority rule is proposed, and Modified Serial Schedule Generation Scheme（MSSGS）, Modified Parallel Schedule Generation Scheme（MPSGS）, algorithm framework and selective particle update methods are discussed in detail. Comprehensive computational experiments are performed on adapted standard project sets in PSPLIB. Experimental results verify feasibility and effectiveness of algorithm. Results also show that PSO algorithm which uses MSSGS and fittest resource priority rule has high solution quality.

Key words: flexible resource, capability difference, resource-constrained, project scheduling problem, Particle Swarm Optimization（PSO）, priority rule

摘要： 在资源受限项目调度问题中，将可再生资源进一步拓展为具有能力差异的柔性资源，建立考虑能力差异的柔性资源受限项目调度问题模型，该模型是对传统资源约束项目调度问题（RCPSP）更接近实际的拓展。为了求解该模型，提出一种基于活动序列表示的粒子群算法，在粒子解码过程中运用了基于优先规则的柔性资源-能力分配算法，在此基础上详细介绍了改进的串行调度生成方案与改进的并行调度生成方案、算法框架、选择性粒子更新方法。通过在改造的项目调度测试问题集上进行数值实验，证明了算法的可行性和有效性，其中使用改进串行调度生成方案与最匹配资源优先规则的粒子群算法具有较好的求解性能。

关键词: 柔性资源, 能力差异, 资源受限, 项目调度问题, 粒子群算法, 优先原则