摘 要
资源受限项目调度问题（RCPSP）是项目管理领域中的经典难题，其求解效率和质量对实际应用具有重要意义。本文针对动态规划算法在解决RCPSP时存在的状态空间爆炸和计算复杂度高等问题，提出了一种改进策略。研究背景源于传统动态规划方法在处理大规模问题时的局限性，以及现代工程项目对高效调度算法的需求。研究旨在通过优化状态表示、减少冗余计算和引入启发式规则，提升动态规划算法的适用性和求解效率。改进后的算法在中小规模问题上能够显著降低计算时间，同时保持较高的解质量；在大规模问题中，相较于经典动态规划和其他启发式算法，该方法展现出更强的鲁棒性和扩展性。研究结论指出，所提出的改进策略有效缓解了动态规划在RCPSP中的性能瓶颈，为复杂项目调度提供了新的解决方案。
关键词：资源受限项目调度问题；动态规划；状态压缩；启发式规则；算法改进
An Improved Strategy of Dynamic Programming Algorithm for Resource-Constrained Project Scheduling
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Abstract
Resource-limited project scheduling problem (RCPSP) is a classic problem in the field of project management, and its solving efficiency and quality are of great significance to practical application. In this paper, an improved strategy is proposed to solve the problems of state space explosion and high computational complexity in dynamic programming algorithm for RCPSP. The research background stems from the limitations of traditional dynamic programming methods in dealing with large-scale problems and the demand of modern engineering projects for efficient scheduling algorithms. The purpose of this study is to improve the applicability and efficiency of dynamic programming algorithm by optimizing state representation, reducing redundant calculation and introducing heuristic rules. The improved algorithm can significantly reduce the computation time for small and medium-sized problems while maintaining high solution quality. Compared with classical dynamic programming and other heuristic algorithms, the proposed method shows stronger robustness and expansibility in large-scale problems. It is concluded that the proposed improvement strategy effectively alleviates the performance bottleneck of dynamic programming in RCPSP and provides a new solution for complex project scheduling.
Keywords: Resource-Constrained Project Scheduling Problem；Dynamic Programming；State Compression；Heuristic Rule；Algorithm Improvement
目 录
引言 1
一、动态规划算法基础研究 1
(一)动态规划基本原理 1
(二)资源受限调度问题概述 2
(三)动态规划在调度中的应用现状 2
二、资源受限调度的挑战分析 3
(一)资源约束对调度的影响 3
(二)动态规划在复杂场景下的局限性 4
(三)当前改进策略的研究瓶颈 4
三、改进策略的设计与实现 5
(一)状态空间优化方法探讨 5
(二)转移函数的高效设计 5
(三)多目标动态规划的引入 6
四、实验验证与性能评估 7
(一)实验设计与数据准备 7
(二)改进策略的效果分析 7
(三)性能对比与优势总结 8
结论 8
参考文献 9
致谢 9
