Multi-objective project scheduling has attracted wide attention for approximately two decades. However, most of the existing research has focused on the double-objective project scheduling problem, while literature on project scheduling problems with more than two objectives is rather scarce. In this paper, the typical multi-mode resource-constrained project scheduling problem is extended to a new triple-objective multi-mode project scheduling problem (TOMPSP) with the objectives of minimizing the project duration, minimizing the resource investment and maximizing the robustness of the schedule. To solve the presented triple-objective problem, we resort to the latest version of the multi-objective genetic algorithm, the non-dominated sorting genetic algorithm III (NSGA-III). In the decoding process of the NSGA-III, a modified SSGS (serial schedule generation scheme), in which resource constraints are relaxed, is suggested by considering the delays of activities. Although the NSGA-III shows excellent performance in numerous multi-objective optimization problems with more than two objectives, it has a potential disadvantage in that it occasionally cannot find the intercept during the adaptive normalization process, and thus, the population cannot be normalized as expected. Since a case without an intercept is impossible in the NSGA-II, we adopt the NSGA-II normalization process rather than that of NSGA-III. The standard instances in PSPLib are modified to serve as the instances of the TOMPSP, and a computational experiment is conducted to test the algorithms. The results show that the presented algorithm not only greatly simplifies the implementation of the NSGA-III but also significantly improves the execution efficiency and calculation quality.

多目标项目计划已吸引了大约二十年的广泛关注。然而，现有的大多数研究都集中在双目标项目调度问题上，而关于具有两个以上目标的项目调度问题的文献却很少。本文将典型的多模式资源受限项目调度问题扩展为新的三目标多模式项目调度问题（TOMPSP），其目的是最小化项目工期，最小化资源投资并最大程度地增强项目的鲁棒性。日程安排。为了解决提出的三目标问题，我们求助于最新版本的多目标遗传算法，即非支配排序遗传算法III（NSGA-III）。在NSGA-III的解码过程中，通过考虑活动的延迟，提出了一种修改后的SSGS（序列计划生成方案），其中资源约束得到了缓解。尽管NSGA-III在许多具有两个以上目标的多目标优化问题中表现出卓越的性能，但它具有潜在的缺点，即在自适应归一化过程中偶尔找不到截距，因此无法按预期对总体进行归一化。由于在NSGA-II中不可能没有拦截的情况，因此我们采用NSGA-II规范化过程，而不是NSGA-III。修改了PSPLib中的标准实例以用作TOMPSP的实例，并进行了计算实验以测试算法。