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Integer programming approaches for distributionally robust chance constraints with adjustable risks

COMPUTERS & OPERATIONS RESEARCH 2025年 177卷

作者： Zhang, Yiling Univ Minnesota Ind & Syst Engn Minneapolis MN 55455 USA

We study distributionally robust chance-constrained programs (DRCCPs) with individual chance constraints under a Wasserstein ambiguity. The DRCCPs treat the risk tolerances associated with the distributionally robust chance constraints (DRCCs) as decision variables to trade off between the system cost and risk of violations by penalizing the risk tolerances in the objective function. We develop integer programming approaches for individual chance constraints with uncertainty either on the right-hand side or on the left-hand side. In particular, we derive mixed integer programming reformulations for the two types of uncertainty to determine the optimal risk tolerance for the chance constraint. Valid inequalities are derived to strengthen the formulations. We test diverse instances of diverse sizes.

关键词： Distributionally robust optimization chance-constrained programming Wasserstein metric Mixed-integer programming Adjustable risk

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Two-Stage chance-constrained Fractional programming for Sustainable Water Quality Management under Uncertainty

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JOURNAL OF WATER RESOURCES PLANNING AND MANAGEMENT 2015年第5期141卷 04014074-04014074页

作者： Zhou, X. Huang, G. H. Zhu, H. Yan, B. Univ Regina Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada North China Elect Power Univ SC Energy & Environm Res Acad Beijing 102206 Peoples R China Xiamen Univ Technol Dept Environm Engn Xiamen 361024 Peoples R China

In this study, a two-stage chance-constrained fractional programming (TCFP) method is developed for dealing with water quality management problems associated with stochastic inputs. Two-stage chance-constrained fractional programming is a hybrid of stochastic linear fractional programming (SLFP) and two-stage stochastic programming (TSP) methods. It can not only balance objectives of two aspects through converting a bi-objective problem into a ratio one but can also analyze various policy scenarios when the promised production targets are violated. For demonstrating its advantages, the proposed TCFP method is applied to a case study of water quality management where managers have to consider conflicting objectives between economic development and environmental conservation, as well as stochastic features expressed as probability distributions. The obtained solutions under different significance levels can help managers to identify desired policies under various environmental, economic, and constraint-violation conditions.

关键词： Two-stage stochastic programming Linear fractional programming chance-constrained programming Uncertainty Water quality management

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Balancing stochastic type-II assembly lines: chance-constrained mixed integer and constraint programming models

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ENGINEERING OPTIMIZATION 2020年第12期52卷 2146-2163页

作者： Pinarbasi, Mehmet Alakas, Haci Mehmet Ulukavak Mah Corum Turkey Kirikkale Univ Ind Engn Dept Yahsihan Turkey

In the literature, line balancing is mostly investigated in deterministic environments. But production systems inevitably contain stochastic situations. In this study, the stochastic type-II assembly line balancing problem (ALBP) is considered. Firstly, a chance-constrained nonlinear mixed integer programming (MIP) formulation is developed from the well-known deterministic form. Then, a new linearized stochastic model is proposed by using some transformation approaches to reduce model complexity, and the model is solved. Finally, constraint programming (CP) models for deterministic ALBPs, nonlinear chance-constrained stochastic ALBPs and linearized chance-constrained stochastic ALBPs are developed, respectively. Problems from the literature are utilized to test the effectiveness of the proposed models and the results are compared with a bidirectional heuristic algorithm. The numerical results show that the CP models are more effective and successful for solving the stochastic ALBP. Some managerial implications are also suggested for industrial environments that consistently face ALBPs.

关键词： Stochastic assembly line balancing type-II problem constraint programming mixed integer programming chance-constrained programming

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An Uncertainty-Based Random Boundary Interval Multi-Stage Stochastic programming for Water Resources Planning

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WATER RESOURCES MANAGEMENT 2023年第12期37卷 4571-4587页

作者： Raei, Mehri Hossienzad, Javad Ghorbani, Mohammad Ali Univ Tabriz Fac Agr Dept Agr Econ Tabriz Iran Univ Tabriz Fac Agr Dept Water Engn Tabriz Iran

Given the increasing population growth and rapid global economic development, the conflict between reduced available water resources and increased water demand in many countries has become a challenging issue;confirming the necessity of allocating optimal water resources to equate water conservation and environmental sustainability. Uncertainties and climate change together deteriorate the complexity of optimal allocation related to water resources used for the agricultural sector. The present study sought to design an uncertainty-based random boundary interval multi-stage stochastic programming (URBIMSP) model by integrating the Kataoka's criterion method and chance-constrained programming within a general optimization framework to control the uncertain information which exists in both constraints and goal functions. The developed model was applied to a case study of water resources allocation in the Marand basin, Iran. Then, a conjunctive water allocation system was arranged to identify the introduced model in two planning periods which were 2023 to 2025 and 2026 to 2028. The results indicated that different water allocation schemes and water shortages with varying net system benefits would be achieved under different stream flow levels and different risk scenarios. The result was significant for carrying out a comprehensive analysis of the tradeoffs between total net benefits and related risks. Finally, the findings demonstrated that improving irrigation efficiency and upgrading irrigation systems are the key strategies for farmers to achieve economic benefits while also help to mitigate environmental impacts.

关键词： chance-constrained programming Kataoka's criterion Marand basin Multi-stage stochastic programming Water resources management

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chance-constrained programming Method by Constraints Aggregation for Social Consensus Making on IT Risk Countermeasure

Chance-constrained Programming Method by Constraints Aggrega...

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IEEE International Conference on Systems, Man, and Cybernetics (SMC)

作者： Sato, Katsunori Samejima, Masaki Sasaki, Ryoichi Osaka Univ Grad Sch Informat Sci & Technol 2-1 Yamadaoka Suita Osaka Japan Tokyo Denki Univ Sch Sci & Technol Future Life Tokyo 1208551 Japan

ISBN: (纸本)9781479906529

This paper addresses the chance-constrained programming for the social consensus making on IT risk counter-measures. The sample average approximation method is a well-known method for solving the chance-constrained programming. However, the computational time is still so long that the opinion leaders can not use the solution of the chance-constrained programming in their discussion. So, we proposed the interactive chance-constrained programming method to show the solutions that are being searched to the opinion leaders. Through the preliminary experiment, we clarified the issues of sampling for the approximation and controlling the search of the solution.

关键词： chance-constrained programming

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A decomposition algorithm for distributionally robust chance-constrained programs with polyhedral ambiguity set

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OPTIMIZATION LETTERS 2025年 1-23页

作者： Pathy, Soumya Ranjan Rahimian, Hamed Clemson Univ Dept Ind Engn Clemson SC 29634 USA

In this paper, we study a distributionally robust optimization approach to chance-constrained stochastic programs to hedge against uncertainty in the distributions of the random parameters. We consider a general polyhedral ambiguity set under finite support. We develop a decomposition-based solution approach to solve the model and use mixing inequalities to develop custom feasibility cuts. In addition, probability cuts are also developed to handle the distributionally robust chance constraint. Finally, we present a numerical study to illustrate the effectiveness of the proposed decomposition-based algorithm and showcase the results for Wasserstein ambiguity set, total variation distance ambiguity set, and moment-based ambiguity set as special cases of the polyhedral ambiguity set.

关键词： Distributionally robust optimization Polyhedral ambiguity set chance-constrained programming Decomposition algorithm Cutting planes

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Robust fuzzy programming for designing a closed-loop supply chain under uncertainty and flexible constraints

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CLEANER LOGISTICS AND SUPPLY CHAIN 2025年 14卷

作者： Dehshiri, Seyyed Jalaladdin Hosseini Amiri, Maghsoud Allameh Tabatabai Univ Fac Management & Accounting Dept Ind Management Tehran Iran

Due to enacting laws and increasing awareness of environmental issues, the design of a Closed-Loop Supply Chain network (CLSC) has received attention. The design of CLSC is a strategic issue with long-term effects and faces uncertainty in the real world, which affects its performance. In the studies on CLSC, robust optimization, cognitive uncertainty, and soft constraints are not assessed simultaneously in modeling and this area is deficient. So, in this investigation, mixed-robust-possibilistic-flexible programming is proposed. This research develops CLSC problem-solving approaches under conditions of cognitive uncertainty and soft constraints and leads to the presentation of operation engineering and optimization in CLSC. The Decision Maker's (DM) risk level is measured flexibly using a credibility criterion. Also, deviation of possibilistic and constraint violations are controlled in the proposed approach. To evaluate the presented approach, a study is executed to design a paper supply chain with economic and environmental objectives. The results show that it is possible to determine the number, place of facilities, and optimal flow of products and materials between different centers. The proposed approach and multi-objective model solution method are capable of providing realistic and flexible solutions based on the trade-off between other objectives and DMs' preferences. The performance of the proposed approach was analyzed and results confirmed the developed approach compared to similar approaches for the design of CLSC.

关键词： Closed-loop supply chain chance-constrained programming Mixed-integer programming Flexible approach Possibilistic absolute deviation

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DERIVATIVE-FREE APPROACHES FOR chance-constrained PROBLEMS WITH RIGHT-HAND SIDE UNCERTAINTY

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SIAM JOURNAL ON OPTIMIZATION 2025年第1期35卷 1-27页

作者： DE Oliveira, W. Univ PSL Ctr Math Appl CMA Mines Paris Sophia Antipolis France

This work addresses (mixed-integer) joint chance-constrained optimization problems in which the only uncertain parameter corresponds to the right-hand side coefficients in an inequality system. It exploits one-dimensional marginals to construct upper and lower models for the underlying joint probability function, which need not be differentiable or satisfy generalized concavity properties. Based on these models, two optimization methods are proposed. Neither of them requires the probability function's (sub)gradients and can thus be considered derivative-free methods. The first approach iteratively enriches an upper model for the probability function within an outer approximation algorithm that is shown to compute, under mild assumptions, an approximate global solution to the nonconvex chance-constrained problem. When the problem's data is linear, the outer approximation algorithm requires solving (approximately) a mixed-integer linear programming problem per iteration. The second method works with a lower model and penalization techniques to efficiently compute points satisfying a new criticality condition. The approach, which handles only continuous variables, defines iterates as critical points of a nonlinear master program that can be handled with off-the-shelf nonlinear programming solvers. Numerical experiments on academic chance-constrained problems highlight the approach's potential and limitations.

关键词： chance-constrained programming global optimization variation analysis

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Coordination of Maintenance and Multi-Technical Flexibility Retrofits for Coal-Fired Power Plants

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IEEE TRANSACTIONS ON INDUSTRY APPLICATIONS 2024年第3期60卷 4946-4957页

作者： Ban, Mingfei Sun, Yaofei Chen, Qichao Liu, Yiqi Jiang, Haiyang Song, Wenlong Xia, Shiwei Song, Meng Liu, Hongwen Bai, Wenchao Northeast Forestry Univ Coll Comp & Control Engn Harbin 150040 Peoples R China State Grid Econ & Technol Res Inst Co Ltd Beijing 102209 Peoples R China State Grid Heilongjiang Elect Power Co Ltd Harbin 150090 Peoples R China North China Elect Power Univ State Key Lab Alternate Elect Power Syst Renewable Beijing 102206 Peoples R China Southeast Univ Sch Elect Engn Nanjing 210096 Peoples R China

Power system requires developing more flexible sources to handle the variability and stochastic of ever-increasing renewable energy. Retrofitting conventional coal-fired power plants (CPPs) is a viable and promising pathway for providing large-scale flexibility at this stage. Typical flexibility retrofit technologies mainly include reducing minimum load, improving ramping capability, and speeding up startups/shutdowns. They involve multiple subsystems of CPPs and coupled technical issues, and they have different flexibility-enhancing effects. This paper focuses on scheduling the multi-technical flexibility retrofits of CPP fleets in long-term operation to enhance the flexibility of power systems cost-effectively. It proposes performing optional flexibility retrofit within CPP maintenance periods and introduces a maintenance preference window to largely reduce the scheduling complexity. Also, it formulates the characteristics and relationship models of multiple typical flexibility retrofit options using a mixed- integer linear programming (MILP) approach. Then, a comprehensive coordination strategy of maintenance and multi-technical flexibility retrofits of CPPs is developed. Moreover, chance-constrained optimization handles the short-term uncertainty of renewable energy and loads, and linearization techniques are employed to accelerate the solution. Numerical results validate the effectiveness of the proposed methods and demonstrate the potential of flexibility retrofitting for CPPs.

关键词： chance-constrained programming coal-fired power plant flexibility retrofit maintenance scheduling

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chance-constrained optimal sizing of BESS with emergency load shedding for frequency stability

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APPLIED ENERGY 2024年 367卷

作者： Cao, Yongji Wu, Qiuwei Li, Changgang Jiao, Wenshu Tan, Jin Shandong Univ Acad Intelligent Innovat Jinan 250101 Peoples R China Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China Shandong Univ Key Lab Power Syst Intelligent Dispatch & Control Minist Educ Jinan 250061 Peoples R China Shanghai Univ Elect Power Coll Elect Engn Shanghai 200090 Peoples R China

The integration of renewable energy sources may result in more severe active power disturbances, and requires more load shedding. The battery energy storage system (BESS) characterized with high flexibility can handle such uncertain disturbances and reduce load shedding amount. This paper proposes a chance -constrained optimal sizing scheme of the BESS to coordinate with the synchronous generator and emergency load shedding (ELS) for frequency stability. First, considering the role of the synchronous generator, BESS, and ELS in frequency stability control, an extended system frequency response model is established to calculate the amount of load shedding, and the required capability of frequency regulation. Then, a multi -objective and chanceconstrained mixed integer nonlinear programming (MINLP) model is built for the BESS sizing to minimize investment cost and maximize operation profits, which considers the uncertainties of disturbances. With the utilization of the linear weighted method, max-affine function -based piecewise linearization method and Bernstein approximation, the model is reformulated into a tractable form, which is iteratively solved by the multi -cut Benders decomposition. Case studies were carried out to verify the effectiveness of the proposed scheme, showing superior performance in reducing load shedding amount and improving frequency nadir.

关键词： Battery energy storage system chance-constrained programming Emergency load shedding Frequency stability

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