The dynamic multi-mode resource-constrained project scheduling problem (DMRCPSP) is of practical importance, as it requires making real-time decisions under changing project states and resource availability. Genetic Programming (GP) has been shown to effectively evolve heuristic rules for such decision-making tasks; however, the evolutionary process typically relies on a large number of simulation-based fitness evaluations, resulting in high computational cost. Surrogate models offer a promising solution to reduce evaluation cost, but their application to GP requires problem-specific phenotypic characterisation (PC) schemes of heuristic rules. There is currently a lack of suitable PC schemes for GP applied to DMRCPSP. This paper proposes a rank-based PC scheme derived from heuristic-driven ordering of eligible activity-mode pairs and activity groups in decision situations. The resulting PC vectors enable a surrogate model to estimate the fitness of unevaluated GP individuals. Based on this scheme, a surrogate-assisted GP algorithm is developed. Experimental results demonstrate that the proposed surrogate-assisted GP can identify high-quality heuristic rules consistently earlier than the state-of-the-art GP approach for DMRCPSP, while introducing only marginal computational overhead. Further analyses demonstrate that the surrogate model provides useful guidance for offspring selection, leading to improved evolutionary efficiency.

翻译：动态多模式资源受限项目调度问题（DMRCPSP）具有重要的实际意义，因为它要求在项目状态和资源可用性变化时做出实时决策。遗传规划（GP）已被证明能有效演化启发式规则以处理此类决策任务；然而，其进化过程通常依赖大量基于模拟的适应度评估，导致计算成本高昂。代理模型为降低评估成本提供了有前景的解决方案，但其在GP中的应用需要针对启发式规则的问题特定表型特征（PC）方案。目前，适用于DMRCPSP的GP尚缺乏合适的PC方案。本文提出了一种基于排名的PC方案，该方案源于决策情景中合格活动-模式对与活动组的启发式排序。由此产生的PC向量使代理模型能够估计未评估GP个体的适应度。基于该方案，本文开发了一种代理辅助GP算法。实验结果表明，所提出的代理辅助GP能够比DMRCPSP领域最先进的GP方法更早地一致识别出高质量启发式规则，同时仅引入微小的计算开销。进一步分析表明，代理模型为子代选择提供了有效指导，从而提高了进化效率。