考虑共享不确定因素的应急设施最大覆盖选址模型

doi:10.12005/orms.2020.0312

运筹与管理 ›› 2020, Vol. 29 ›› Issue (12): 43-50.DOI: 10.12005/orms.2020.0312

考虑共享不确定因素的应急设施最大覆盖选址模型

于冬梅^1,2,3, 高雷阜^{2, 1}, 赵世杰^1,2

1.辽宁工程技术大学优化与决策研究所,辽宁阜新 123000;
2.辽宁工程技术大学运筹与优化研究院,辽宁阜新 123000;
3.北京航空航天大学数学科学学院,北京 100191

收稿日期:2018-11-05 出版日期:2020-12-25
作者简介:于冬梅(1986-),女,辽宁鞍山人,博士。研究方向:优化与管理决策、最优化理论、方法及应用等;高雷阜(1963-),男,辽宁阜新人,教授,博士生导师。研究方向:最优化理论与方法、数据解析与机器学习等;赵世杰(1987-),男,山东日照人,博士。研究方向:人工智能与数据挖掘、优化与管理决策等。
基金资助:
辽宁省社会科学规划基金项目(L19BGL017)

A Maximum Covering Location Model for Emergency Facility Considering Shared Uncertainties

YU Dong-mei^1,2,3, GAO Lei-fu^1,2, ZHAO Shi-jie^1,2

1. Institute of Optimization and Decision, Liaoning Technical University, Fuxin 123000, China;
2. Institute for Optimization and Decision Analytics, Liaoning Technical University, Fuxin 123000, China;
3. School of Mathematical Sciences, Beihang University, Beijing 100191, China

Received:2018-11-05 Online:2020-12-25

摘要/Abstract

摘要： 为提升应急设施的服务质量和抵御中断风险的能力,研究应急设施最大覆盖选址-分配决策问题。扩展无容量限制的固定费用的可靠性选址决策模型,建立考虑共享不确定因素的应急设施最大覆盖选址优化模型,通过在目标和约束中引入budget不确定集刻画共享不确定因素,基于Bertsimas和Sim鲁棒优化方法建立混合整数规划模型,并将非线性问题转化为易于求解的鲁棒等价模型,利用带混沌搜索策略的改进灰狼优化算法求解模型,并对不确定鲁棒水平和中断概率进行敏感性分析。最后通过案例及数据仿真结果的对比分析,验证了模型的合理性和有效性,并给出最优的选址分配布局。

关键词: 覆盖选址, 共享不确定因素, 鲁棒优化, 混沌搜索, 改进灰狼算法

Abstract: In order to improve the service quality of emergency facilities and the ability to withstand interruption risks, the maximum coverage location-allocation decision-making problem for emergency facilities is studied. The maximum covering location model for emergency facility considering shared uncertainties is developed by extending uncapacitated fix-charge location problem. The shared uncertainties are characterized by introducing budget uncertainties into both objectives and constraints. A mixed integer programming model is proposed based on Bertsimas and Sim robust method, and the nonlinear problem is transformed into a robust equivalent model which is easy to solve. The improved grey wolf optimization algorithm with chaotic search strategy is presented to solve the model,and the sensitivity analysis of robustness level and disruption probability are carried out. Finally, through the comparative analysis of case and data simulation results, we verify the rationality and effectiveness of the model and give the optimal location-allocation scheme.

Key words: coverage location, shared uncertainties, robust optimization, chaotic search, improved grey wolf algorithm

中图分类号:

于冬梅, 高雷阜, 赵世杰. 考虑共享不确定因素的应急设施最大覆盖选址模型[J]. 运筹与管理, 2020, 29(12): 43-50.

YU Dong-mei, GAO Lei-fu, ZHAO Shi-jie. A Maximum Covering Location Model for Emergency Facility Considering Shared Uncertainties[J]. Operations Research and Management Science, 2020, 29(12): 43-50.

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考虑共享不确定因素的应急设施最大覆盖选址模型

A Maximum Covering Location Model for Emergency Facility Considering Shared Uncertainties

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