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基于分布式鲁棒优化的应急救援系统选址模型和算法研究
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《基于分布式鲁棒优化的应急救援系统选址模型和算法研究》属于清华大学优秀博士学位论文丛书。
高效的应急救援系统对于降低生命和财产损失具有重...
高效的应急救援系统对于降低生命和财产损失具有重要意义,选址决策作为战略规划,具有长期的影响力。《基于分布式鲁棒优化的应急救援系统选址模型和算法研究》考虑了应急救援过程中可能存在的中断风险、需求波动,以及其他潜在的多重不确定性,采用分布式鲁棒优化方法决策应急设施选址和物资储备方式,改善了救援过程中的资金不足、救援质量下降等问题,利用理论性质对模型进行有效近似,提出了外逼近、分支剪界等算法加速求解效率。研究结果显示,本书的模型较为全面地刻画了实际应急系统,显著提升了传统算法的运算速度,同时有效兼顾了实际救援过程中的效率和公平。
本书可供管理科学与工程学、工业工程、交通运输工程、物流工程及物流管理方向的高年级本科生、研究生及相关领域科研人员参考。
刘康琳,工学博士,北京交通大学交通运输学院物流工程系讲师,主要研究方向为供应链网络优化、人道主义物流、随机和鲁棒优化。本科毕业于北京师范大学;博士毕业于清华大学工业工程系,获北京市优秀毕业生、清华大学优秀学位论文、国家奖学金等荣誉,曾赴美国密歇根大学访问。研究成果被权威期刊EJOR、TRB、IISE Transaction、IJPR接收,并担任IJOC、CIE、IJPR等国际期刊审稿人。
第1 章 引言 11.1 研究背景及意义 11.2 研究内容及方法 31.3 研究框架及本书结构 7第2 章 文献综述 92.1 选址问题及其在应急救援系统中的应用 92.2 考虑需求不确定性的应急系统选址问题 112.3 考虑中断风险的应急系统选址问题 122.4 考虑需求和供给不确定性的应急系统选址问题 152.5 分布式鲁棒优化及机会约束 172.5.1 分布式鲁棒优化 172.5.2 机会约束 192.6 本章小结 20第3 章 考虑需求不确定性的救助站选址问题 213.1 问题描述与建模 213.2 模型近似 233.2.1 目标函数 243.2.2 机会约束 263.3 模型RP-SOCP 的理论性质 323.4 求解方法 343.4.1 改进的参数迭代算法 343.4.2 求解模型RP-1 的外逼近算法 363.5 数值实验 393.5.1 性能分析 393.5.2 灵敏度分析 433.5.3 拓扑结构分析 443.5.4 稳定性验证 463.5.5 DRM 在实证数据集中的表现 493.6 本章小结 50第4 章 在Wasserstein 模糊集内考虑中断风险的选址问题 524.1 问题描述 524.2 问题重构 564.2.1 的重构模型 574.2.2 全幺模矩阵 614.2.3 两阶段模型的整体重构 654.3 理论坏情况分布 684.3.1 存在性证明 694.3.2 具体分布形式 714.4 求解方法 734.4.1 基于坏情况分布的分支剪界算法 734.4.2 基于列和约束生成的分支剪界算法 754.5 数值实验 774.5.1 算法性能分析 774.5.2 Wasserstein 球的半径选择 804.5.3 样本外表现 834.5.4 鲁棒模型的成本-收益分析 864.6 本章小结 87第5 章 考虑需求不确定性和中断风险的救助点选址问题 895.1 问题描述与建模 895.2 模型近似 925.2.1 需求满足约束(5-1b) 的近似 925.2.2 覆盖范围约束(5-1c) 的近似 945.2.3 模型P1 的整体近似 975.3 求解算法 975.3.1 迭代的OA 算法 975.3.2 基于分支剪界的OA 算法 1025.4 数值实验 1035.4.1 算法性能分析 1035.4.2 灵敏度分析 1075.4.3 模型效果对比 1095.4.4 鲁棒模型的成本-收益分析 1125.4.5 实证数据中的表现 1135.5 本章小结 115第6 章 总结与展望 1176.1 研究结论 1176.2 研究展望 120附录A 外逼近算法简介 121A.1 OA 主问题 121A.2 OA 子问题 122附录B 基于场景的随机规划问题 123B.1 第3 章中基于场景的救助站选址问题 123B.2 第4 章中基于场景的可中断设施选址问题 124B.3 第5 章中基于场景的随机设施选址问题 124附录C 实证数据详情 126参考文献 129在学期间发表的学术论文与研究成果 142致谢 144
本书的编辑出版恰逢新冠疫情世界范围依然流行、天气导致的郑州大雨刚刚结束之时,这些事件中的应急救援活动给人们留下了深刻印象。本书针对应急救援设施的选址决策开展理论研究和案例分析,正好迎合了当前热点,反映了研究工作的重要价值。非常感谢清华大学和清华大学出版社的支持,使作者的博士学位论文研究工作能够入选“清华大学优秀博士学位论文丛书”项目。本人也非常荣幸为本书作序。应急救援在现代社会发展中扮演着越来越重要的角色。它用来减少由于自然灾害(例如天气、地震、疫情等)或者人为因素(恐怖袭击、核泄漏等)给人类社会经济系统造成的巨大生命和财产损失。应急救援服务包括灾害发生前、灾害发生时和灾害发生后三个阶段。灾前决策能显著提高救援过程中的救援效率、缩短响应时间、降低救援成本。因此,针对灾前决策的研究得到了学术界的广泛关注。本书作者针对灾害发生前的应急救援设施选址这一战略性决策开展研究。特别是考虑了救援过程中来自需求端和供给端的不确定因素,采用分布鲁棒优化方法对它们进行数学建模,进而分别针对三类重要的救援设施选址问题开展了理论研究和实证分析,包括考虑需求不确定性的救助站选址问题、在 Wasserstein模糊集内考虑供给中断风险的选址问题、综合考虑需求端和供给端的不确定性的救助站选址问题。研究工作结合问题特征、数据可得性,以及模型易计算性的要求,对问题进行了数学建模研究;通过分析模型结构特征,开发了高效的算法。模型和算法在以实际案例数据为基础的数值分析中表现出优秀的性能;通过算例分析,探索了相应的应急救援设施选址决策中的若干管理规律。本书的研究应用分布鲁棒优化方法,在应急救援设施选址领域的建模和算法研究中具有较强的学术创新性,体现了研究工作的学术理论价值。同时,通过案例分析,展示了模型和算法在实际场景中的应用和效果,为不确定环境中应急救援系统的设施选址决策提供了一套可行的优化决策工具,反映出研究工作的应用价值。当前,在新冠疫情世界范围的大流行、天气导致的郑州大雨等事件中,应急救援系统在降低灾害的影响方面起到了重要的作用,也使人们愈发认识到规划建设有效的应急救援系统对于经济社会正常运行的重要意义。本书的工作综合应用了数据驱动的决策理论、优化技术和数据科学方法,对应急救援系统的选址决策进行了开创性的学术研究工作,表明这些方法在应急救援决策中的有效性,为进一步开展本领域深入的理论研究,探索了一条可行的研究技术路线;此外,研究成果的案例研究也预示了定量的科学优化决策方法可以为决策者高效地提供实际可用的解决方案,为提升应急救援系统的决策质量和效率提供有效的工具,从而进一步提升我国应急救援系统在面临突发应急事件时的应对效率和效果。
张智海 2021年8月 6日于北京
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