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A simulation-based bi-level multi-objective programming model for watershed water quality management under interval and stochastic uncertainties

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JOURNAL OF ENVIRONMENTAL MANAGEMENT 2019年 245卷 418-431页

作者： Rong, Qiangqiang Cai, Yanpeng Su, Meirong Yue, Wencong Yang, Zhifeng Dang, Zhi Dongguan Univ Technol Res Ctr Ecoenvironm Engn Dongguan 523808 Peoples R China Guangdong Univ Technol Inst Environm & Ecol Engn Guangzhou 510006 Guangdong Peoples R China South China Univ Technol Sch Environm & Energy Guangzhou 510006 Guangdong Peoples R China

A simulation-based interval stochastic bi-level multi-objective programming (SISBLMOP) model was proposed in this research, through integrating the global nutrient export from watersheds model, interval parameter programming and stochastic chance-constrained programming into a general bi-level multi-objective programming framework. The SISBLMOP model can handle multiple uncertainties expressed as discrete intervals and probability density functions in both the simulation and optimization processes. System complexities, including the hierarchy structure of upper- and lower-level decision makers, can also be addressed in the model. The proposed model is applied to a real-world case study of the Xinfengjiang Reservoir Watershed in South China to identify the satisfactory implementation levels of multiple best management practices (BMPs). The model results show that multiple BMP schemes for water quality management can be obtained under different upper- and lower level decision-making and risk-violation scenarios, reflecting the cooperation and gaming results of the two-level decision makers. Consequently, the corresponding BMP implementation costs are acceptable to both the upper and lower-level decision makers. The model is widely applicable and can be effectively used for water quality management under multiple uncertainties and complexities.

关键词： Water quality management bi-level multi-objective programming Interval parameter programming Chance-constrained programming Nutrient export from watersheds

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Optimal river basin water resources allocation considering multiple water sources joint scheduling: A bi-level multi-objective programming with copula-based interval-bistochastic information

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COMPUTERS & INDUSTRIAL ENGINEERING 2024年 194卷

作者： Tu, Yan Lu, Yongzheng Xie, Yutong Lev, Benjamin Wuhan Univ Technol Sch Safety Sci & Emergency Management Wuhan 430070 Peoples R China Drexel Univ LeBow Coll Business Decis Sci Dept Philadelphia PA 19104 USA

The uncertainty of hydrological variables and socio-economic parameters presents new challenges for river basin water resources allocation (RBWRA). Motivated by the pressing need for more efficient and ecofriendly RBWRA solutions, a bi-level multi-objective interval-bistochastic programming (BLMOIBSP) model is proposed. The model aims to achieve optimal balance among efficiency, eco-friendliness and equity, collectively called "3E"in this paper. The basin authority, serving as the leader in RBWRA, prioritizes efficiency and eco-friendliness, aiming to maximize economic benefit and minimize total environmental pollutants. Conversely, the sub-areas, as followers, focus more on benefits, striving to maximize total benefits. Taking into account the needs of each stakeholder in the bi-level structure actually facilitates equity goals in RBWRA. Additionally, based on the joint scheduling of multiple water sources, the model considers dual stochastic hydrological variables and multiple uncertain parameters. The copula function captures the dependence between hydrological stochastic variables. Meanwhile, water demand is set as an interval parameter to address uncertainty, handled by an interval two-stage stochastic programming (ITSP) method. Fusing with a chaotic Aquila Optimizer (CAO) algorithm, a bi-level interactive approach based on satisfactory degree (SD) is employed to solve the model and ensure equity in RBWRA. Furthermore, the case of the Dongjiang River Basin in Guangdong Province, China, is presented in conjunction with a multi-scenario analysis to validate the practicality and effectiveness of the proposed model and its associated problem-solving methods. The results indicate that the proposed model effectively ensures the "3E"objectives of RBWRA. Besides that, ITSP has been demonstrated to reduce the risks associated with the uncertainty in actual water allocation in RBWRA. The proposed bi-level model balances the levels better than a single-level model. When s

关键词： River basin water resources allocation multiple water sources bi-level multi-objective programming Copula Interval two-stage stochastic programming Chaotic Aquila Optimizer

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An export coefficient based inexact fuzzy bi-level multi-objective programming model for the management of agricultural nonpoint source pollution under uncertainty

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JOURNAL OF HYDROLOGY 2018年 557卷 713-725页

作者： Cai, Yanpeng Rong, Qiangqiang Yang, Zhifeng Yue, Wencong Tan, Qian Beijing Normal Univ Sch Environm State Key Lab Water Environm Simulat Beijing 100875 Peoples R China Beijing Normal Univ Sch Environm Beijing Engn Res Ctr Watershed Environm Restorat Beijing 100875 Peoples R China Univ Regina Inst Energy Environm & Sustainable Communities 120 2 Res Dr Regina SK S4S 7H9 Canada Dongguatt Univ Technol Res Ctr Ecoenvironm Engn Dongguan 523808 Peoples R China China Agr Univ Coll Water Resources & Civil Engn Beijing 100083 Peoples R China

In this research, an export coefficient based inexact fuzzy bi-level multi-objective programming (EC-IFBLMOP) model was developed through integrating export coefficient model (ECM), interval parameter programming (IPP) and fuzzy parameter programming (FPP) within a bi-level multi-objective programming framework. The proposed EC-IFBLMOP model can effectively deal with the multiple uncertainties expressed as discrete intervals and fuzzy membership functions. Also, the complexities in agricultural systems, such as the cooperation and gaming relationship between the decision makers at different levels, can be fully considered in the model. The developed model was then applied to identify the optimal land use patterns and BMP implementing levels for agricultural nonpoint source (NPS) pollution management in a subcatchment in the upper stream watershed of the Miyun Reservoir in north China. The results of the model showed that the desired optimal land use patterns and implementing levels of best management of practices (BMPs) would be obtained. It is the gaming result between the upper- and lower-level decision makers, when the allowable discharge amounts of NPS pollutants were limited. Moreover, results corresponding to different decision scenarios could provide a set of decision alternatives for the upper- and lower-level decision makers to identify the most appropriate management strategy. The model has a good applicability and can be effectively utilized for agricultural NPS pollution management. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Agricultural nonpoint source pollution bi-level multi-objective programming Intervals Fuzzy sets Export coefficient model Optimization management

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A bi-level multi-objective programming on Data Envelopment Analysis by Penalty Approach

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International Journal of Applied and Computational Mathematics 2022年第3期8卷 1-9页

作者： Pishgouy, Ali Reza Hamidi, Farhad Saljooghi, Faranak Hosseinzadeh Department of Mathematics University of Sistan and Baluchestan Zahedan Iran

The aim of this paper is to evaluate the structure of a bi-level system, which consists of multiple leaders at the first level and multiple followers at the second. We integrate the bi-level programming and Data Envelopment Analysis with multiple leaders and followers. The proposed model differs from the existing bi-level Data Envelopment Analysis models in that we use a penalty function for evaluating the cost efficiency instead of the Kuhn–Tucker conditions. So, we first explain the bi-level linear multi-objective programming problem and then utilize an exact penalty method to evaluate the cost efficiencies of decision-making units with multiple leaders and followers. One of the features of our proposed method is that it reduces the number of nonlinear constraints and increases the computational speed compared to existing computational methods. Finally, to demonstrate the efficiency of our method, we provide a numerical example. © 2022, The Author(s), under exclusive licence to Springer Nature India Private Limited.

关键词： bi-level multi-objective programming Cost efficiency Data envelopment analysis Decision-making units Supply chain

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A dual-randomness bi-level interval multi-objective programming model for regional water resources management

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JOURNAL OF CONTAMINANT HYDROLOGY 2021年 241卷 103816-103816页

作者： Xiao, Jun Cai, Yanpeng He, Yanhu Xie, Yulei Yang, Zhifeng Guangdong Univ Technol Inst Environm & Ecol Engn Guangdong Prov Key Lab Water Qual Improvement & E Waihuan West Rd 100 Guangzhou 510006 Peoples R China Southern Marine Sci & Engn Guangdong Lab Guangzho Guangzhou 511458 Peoples R China

In this research, a dual-randomness bi-level interval multi-objective programming (DR-biMP) model was developed for supporting water resources management among multiple water sectors under complexities and uncertainties. Techniques of bi-level multi-objective programming (BMOP), double-sided stochastic chance constrained programming (DSCCP), and interval parameter programming (IPP) were incorporated into an integrated modeling framework to achieve comprehensive consideration of the complexities and uncertainties of water resources management systems. The DR-biMP model can not only effectively deal with the interactive effects between multiple decision-makers in complex water management systems through the bi-level hierarchical strategies, but also can characterize the multiple uncertainties information expressed as interval format and probability density functions. It could thus improve upon the existing bi-level multi-objective programming through addressing discrete interval parameters and dual-randomness problems in optimization processes simultaneously. Then, the developed model was applied to a real-world case to optimally allocate water resources among three different water sectors in five sub-regions in the Dongjiang River basin, south China. The results of the model include determining values, interval values, and stochastic distribution information, which can assist bi-level decision-makers to plan future resources effectively to some extent. After comparing the variations of results, it is found that an increasing probability level can lead to higher system benefits, which is increased from [20,786.00, 26,425.92] x 10(8) CNY to [22,290.84, 27,492.57] x 10(8) CNY, while the Gini value is reduced from [0.365, 0.446] to [0.345, 0.405]. A set of increased probability levels gives rise to the lower-level objectives. Furthermore, the advantages of the DR-biMP model were highlighted by comparing with the other models originated from the developed model. The compa

关键词： Water resources management Complexities and uncertainties bi-level multi-objective programming Double-sided stochastic chance-constrained programming Interval parameter programming

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Analyzing water resources with sector characteristics in Fujian Province utilizing S2-DR-biMCCP model integrated with the Gini coefficient

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JOURNAL OF CLEANER PRODUCTION 2025年 490卷

作者： Bai, Ruolin Jin, Lei Fan, Yurui Zhang, Xi Yin, Ruoyu Wei, Yi Xiamen Univ Technol Coll Environm Sci & Engn Xiamen 361024 Fujian Peoples R China Brunel Univ London Dept Civil & Environm Engn Uxbridge UB8 3PH Middx England

Water resource challenges faced by region encompass the entire spectrum of resource development and utilization, including resource stress and imbalances among diverse social users. To address these challenges, an innovative S2-DR-biMCCP model incorporating the Gini coefficient was developed. This approach presents a linearized formulation and a comprehensive set of incremental solutions for reconciling interval issues in bi-level multi-objective programming models. The S2-DR-biMCCP model was applied to address water scarcity and uneven water resource programming for three distinct water-use sectors within an urban agglomeration comprising nine cities. The findings indicate that as the risk of breaching system constraints escalates, the validity of the model resulted in an increase in the system benefit from [2075.95, 8148.68] x 109 Chinese Yuan (CNY) to [2457.03, 9979.98] x 109 CNY. Simultaneously, water equity in the system gradually increases, resulting in a decrease in the Gini coefficient from [0.1618, 0.2338] to [0.0948, 0.2383]. The model predicted a gradual increase in livestock water allocation under varying circumstances, ultimately reaching a projected total water supply of 2.63 x 109 m3 in 2030. The conclusion was obtained that Fujian Province should further optimize the spatial layout and production structure of animal husbandry to enhance the competitiveness of animal husbandry. Finally, a comparative analysis demonstrated that the S2-DR-biMCCP model effectively balanced the perspectives of multiple decision-makers across different levels. It considered the overall system benefits and equity, integrated the uncertainty factors. Stochastic uncertainty expressed as intervals and probability distributions is carefully handled, significantly improving the ability to handle uncertainty in fuzzy optimization problems, and offered the flexibility to adjust risks related to violating system constraints. This capability, along with multi-scenario analyses, can

关键词： bi-level multi-objective programming Double-sided stochastic chance-constrained Urban agglomerations Water resources allocation Gini coefficient

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Optimal trade-off of integrated river basin water resources allocation considering water market: A bi-level multi-objective model with conditional value-at-risk constraints

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COMPUTERS & INDUSTRIAL ENGINEERING 2022年 169卷

作者： Tu, Yan Shi, Hongwei Zhou, Xiaoyang Lev, Benjamin Wuhan Univ Technol Sch Safety Sci & Emergency Management Wuhan 430070 Peoples R China Xi An Jiao Tong Univ Sch Management Xian 710049 Shaanxi Peoples R China Chinese Acad Sci Acad Math & Syst Sci Beijing 100190 Peoples R China Drexel Univ LeBow Coll Business Decis Sci Dept Philadelphia PA 19104 USA

The predictable water shortage crisis is intensifying due to frequent extreme weather caused by climate change and human activities. Motivated by urgent practical needs of more scientific and balanced river basin water resources allocation (RBWRA) schemes, a comprehensive bi-level multi-objective programming (BLMOP) model for RBWRA considering uncertain risks and water market is constructed in this paper, which pursues the ob-jectives of environmental protection, equality, and economic development. River basin authority, as the leader of RBWRA, is committed to reducing pollutants while introducing Gini coefficient to maintain the equality of economic development between sub-areas. Meanwhile, the sub-areas (i.e., followers) are dedicated to improving the economic benefit. In addition, the water market is introduced as water redistribution mechanism and its effect is probed into in detail. Moreover, conditional value-at-risk (CVaR) constraints are integrated into the model to control the economic loss caused by the risks of uncertain water availability. To solve the BLMOP model, a novel bi-level interaction based adaptive global equilibrium optimization (bi-aGEO) approach is pro-posed, which can obtain the best equilibrium solution that satisfies all decision-making participants. Further-more, the proposed model and approach are applied to the Hanjiang River Basin in central China to elaborate on their feasibility and effectiveness. Results show that the proposed model is effective in ensuring the sustain-ability, equality and efficiency of RBWRA. The introduction of water market is shown to be able to improve water efficiency and promote water conservation and CVaR constraints play a significant role in controlling economic risks. Finally, some managerial suggestions are provided for different RBWRA participants for more scientific and effective integrated water resources management (IWRM).

关键词： Integrated water resources management River basin water resources allocation CVaR Water market bi-level multi-objective programming

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An inexact bi-level multi-objective modeling approach for managing agricultural water-food-carbon-land-ecology-nutrition nexus in an arid area

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JOURNAL OF HYDROLOGY 2023年第1期621卷

作者： Chen, Junxu Wu, Hui Zhang, Chenglong Guo, Ping Huo, Zailin China Agr Univ Coll Water Resource & Civil Engn Beijing 100083 Peoples R China China Agr Univ Ctr Agr Water Res China Tsinghuadong St 17 Beijing 100083 Peoples R China

multiple subsystems such as water, food, land, carbon, ecology, and nutrition are closely intertwined, and the resulting complexity and uncertainty pose challenges to water resource management. This study proposes an optimization framework from a novel water-food-carbon-land -ecology-nutrition (WONDER) nexus perspective for the integrated management of agricultural and ecological water resources. Firstly, the irrigation priority ranking of decision-making units (DMU) is obtained based on the remote sensing indices from the Google Earth Engine (GEE) platform. Secondly, the ecological satisfaction degree, which aggregates carbon sink satisfaction degree and ecological water demand satisfaction degree, is proposed to characterize the degree of achieving the pre-given ecological objectives. Then, the above two indicators (i.e., the irrigation priority ranking and the ecological satisfaction degree) are integrated with a fuzzy-interval credibility-constrained bi-level multi -objec-tive programming model to realize: (1) reconciling conflicts in food nutrition, food security, economic devel-opment, and ecological conservation;(2) making trade-offs among the positions and preferences of different decision-makers;(3) dealing with the dual uncertainties of fuzzy-interval parameters;(4) obtaining optimal agricultural and ecological water allocation schemes. The applicability of the model is verified by taking Hon-gyashan Irrigation District of Minqin County as an example. The results show that: (1) the irrigation priority ranking for the DMUs is: DMU 10 > DMU 9 > DMU 4 > DMU 5 > DMU 1 > DMU 11 > DMU 6 > DMU 8 > DMU 7 > DMU 2 > DMU 3;(2) the ratio of agricultural to ecological water allocation in the irrigation district is about 3:1, which is consistent with the water use characteristics of this area;(3) the total water allocation during the whole growth period for different crops is mainly determined by planting area, and the ranking of the water allocation is: sunflower > mai

关键词： Water-food-carbon-land-ecology-nutrition nexus GEE Irrigation priority Fuzzy-interval sets bi-level multi-objective programming Optimal water resources allocation

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