This study evaluates a new solution approach for the Resource-Constrained Project Scheduling with Alternative Subgraphs (RCPSP-AS) in case that complex relations (i.e. nested and linked alternatives) are considered. In the RCPSP-AS, the project activity structure is extended with alternative activity sequences. This implies that only a subset of all activities should be scheduled, which corresponds with a set of activities in the project network that model an alternative execution mode for a work package. Since only the selected activities should be scheduled, the RCPSP-AS comes down to a traditional RCPSP problem when the selection subproblem is solved. It is known that the RCPSP and, hence, its extension to the RCPSP-AS is NP-hard. Since similar scheduling and selection subproblems have already been successfully solved by satisfiability (SAT) solvers in the existing literature, we aim to test the performance of a GA-SAT approach that is derived from the literature and adjusted to be able to deal with the problem-specific constraints of the RCPSP-AS. Computational results on small- and large-scale instances (both artificial and empirical) show that the algorithm can compete with existing metaheuristic algorithms from the literature. Also, the performance is compared with an exact mathematical solver and learning behaviour is observed and analysed. This research again validates the broad applicability of SAT solvers as well as the need to search for better and more suited algorithms for the RCPSP-AS and its extensions.

中文翻译：

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使用布尔可满足性求解器解决具有替代子图的资源受限项目调度问题的遗传算法

本研究评估了在考虑复杂关系（即嵌套和链接替代方案）的情况下，具有替代子图的资源受限项目调度（RCPSP-AS）的新解决方案。在 RCPSP-AS 中，项目活动结构通过替代活动序列进行了扩展。这意味着仅应安排所有活动的子集，这对应于项目网络中为工作包建模替代执行模式的一组活动。由于只应安排选定的活动，因此当解决选择子问题时，RCPSP-AS 就归结为传统的 RCPSP 问题。众所周知，RCPSP 及其对 RCPSP-AS 的扩展是 NP 难的。由于现有文献中的可满足性 (SAT) 求解器已经成功解决了类似的调度和选择子问题，因此我们的目标是测试源自文献并经过调整以能够处理该问题的 GA-SAT 方法的性能- RCPSP-AS 的特定限制。小规模和大规模实例（人工和经验）的计算结果表明，该算法可以与文献中现有的元启发式算法竞争。此外，还将其性能与精确的数学求解器进行比较，并观察和分析学习行为。这项研究再次验证了 SAT 求解器的广泛适用性以及为 RCPSP-AS 及其扩展寻找更好、更合适算法的需要。