Abstract: To consider multiple scheduling objectives of resource-constrained project scheduling problem comprehensively and to obtain a approximate nondominated solutions set of the problems efficiently, a bi-objective scheduling model with renewable resource utilization smoothness and period was developed. A genetic algorithm based on Pareto sorting and multi-objective chaos weighting was proposed, and the double linked list structure was used as chromosome encoding mechanism representing activity execution sequence and execution mode. The populations were initialized by random generation and by determination of execution modes based on activity characteristics, and the crossover and adaptive variation operations were proposed. The degree of fitness was calculated by using Pareto sorting and multi-objective chaos weighting. The strategies for reparation and punishment of infeasible solutions were also designed. Project Scheduling Problem LIBrary (PSPLIB) was used to verify the effectiveness of proposed algorithm.

Key words: resource-constrained project scheduling, multi-objective optimization, Pareto sorting, chaos weighting, genetic algorithms

摘要： 为综合考虑资源约束型项目调度问题的多个调度目标，有效获得该问题的近似非支配解集，建立了一种综合考虑可更新资源稳定性和工期的双目标项目调度模型。提出了一种基于Pareto排序和多目标混沌加权相结合的遗传算法，其中个体编码采用双链表结构，分别代表任务的执行顺序和执行模式，初始种群的生成包括随机生成和依据任务特性确定执行模式两种方式，设计了个体交叉和自适应变异算子，研究了基于Pareto排序法和基于多目标混沌加权法的个体适应度计算方法以及不可行解的修复和惩罚策略。利用项目调度问题算例库对该算法进行测试，数值测试结果验证了算法的有效性。

关键词: 资源约束型项目调度, 多目标优化, Pareto排序, 混沌加权, 遗传算法