Abstract: Time and cost are two important indicators in project scheduling, and the robustness of the schedule is the key issue for ensuring the smooth execution of the project under uncertainty. This paper involves the multi-objective project scheduling optimization problem under uncertainty, arranging the start time of activities in order to optimize time, cost and robustness simultaneously. Based on this purpose, we construct the multi-objective optimization model for the problem, analyze the trade-off relationships among the objectives through dividing the model into three sub-models, design non-dominated sorting genetic algorithm to solve the problem, apply the elitism strategy and the trade-off relationships optimization strategy among sub-models to optimize the algorithm, and perform algorithm testing and sensitivity analysis of instance parameters. Finally, the proposed model and algorithm are illustrated through a practical case, with the non-dominated set founded, and the sensitivity analysis of this case further validates the trade-off relationships in the sub-models. An effective utilization strategy of resources is presented in the end. The research of this paper can provide quantitative decision support for multi-objective project scheduling.

Key words: project scheduling, optimization model, genetic algorithm, uncertain environment, multi-objective trade-off

摘要： 项目调度中的时间和费用是两个重要的指标,而在不确定环境下进度计划的鲁棒性则是保证项目平稳实施的关键。本文研究不确定环境下的多目标项目调度优化问题,以优化项目的工期、鲁棒值和成本为目标安排各活动的开始时间。基于此,作者构建多目标项目调度优化模型,将模型分解为三个子模型分析目标间的权衡关系,然后设计非劣排序遗传算法进行求解,应用精英保留策略和基于子模型权衡关系的优化策略优化算法,进行算法测试和算例参数敏感性分析。最后,应用上述方法研究一个项目实例,计算得到非劣解集,实例的敏感性分析结果进一步验证了三个目标间的权衡关系,据此提出资源的有效利用策略。本文的研究可以为多目标项目调度制定进度计划提供定量化决策支持。

关键词: 项目调度, 优化模型, 遗传算法, 不确定环境, 多目标权衡