Resource constrained project scheduling is critical in logistic and planning operations across a range of industries. An interesting heuristic for solving this problem is the Rollout-Justification (RJ) procedure. This procedure, which has conceptual similarities with dynamic programming, incrementally builds a solution by identifying the next activity to schedule based on the projections made using a guiding priority rule (heuristic) coupled with forward-backward local search. A critical component that affects the performance of RJ procedure is the guiding priority rule (or a set of rules). In this study, instead of using existing rules from literature, we aim to evolve new priority rules using genetic programming, and systematically investigate their use with the RJ procedure. Apart from evolving new rules, we also investigate new ways of integrating/utilizing the rules within RJ procedure. To this end we consider the use of both forward and backward scheduling, independent and cohesive ensemble rule approaches, limited and unlimited number of function evaluations, among others. We use data from the project scheduling library (PSPLib) to train and test the evolved rules and their integration with RJ. A comprehensive set of numerical experiments are performed to benchmark the rules evolved using the proposed approach against a range of existing rules. The results demonstrate the competence and potential of the proposed approach, both in terms of accuracy and complexity.

资源受限的项目调度对于各行业的物流和规划运营至关重要。解决此问题的一个有趣的启发式方法是 Rollout-Justification (RJ) 过程。该过程与动态规划在概念上相似，通过使用引导优先级规则（启发式）与前向后向本地搜索相结合的预测来确定要安排的下一个活动，从而逐步构建解决方案。影响 RJ 程序性能的一个关键组成部分是指导优先级规则（或一组规则）。在本研究中，我们的目标不是使用文献中的现有规则，而是使用遗传编程制定新的优先级规则，并系统地研究它们在 RJ 程序中的使用。除了制定新规则外，我们还研究在 RJ 程序中集成/利用规则的新方法。为此，我们考虑使用前向和后向调度、独立和内聚的集成规则方法、有限和无限数量的函数评估等。我们使用项目调度库 (PSPLib) 中的数据来训练和测试演化规则及其与 RJ 的集成。进行了一组全面的数值实验，以根据一系列现有规则对使用所提出的方法演化出的规则进行基准测试。结果证明了所提出的方法在准确性和复杂性方面的能力和潜力。