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A NONPARAMETRIC ROBUST OPTIMIZATION APPROACH FOR CHANCE-CONSTRAINED KNAPSACK PROBLEM

SIAM Journal on Optimization 2025年第2期35卷 739-766页

作者： Xu, Liang Zhang, Chao Xu, Zhou Long, Daniel Zhuoyu School of Business Administration Southwestern University of Finance and Economics Chengdu China Big Data Laboratory on Financial Security and Behavior SWUEF Laboratory of Philosophy and Social Sciences Ministry of Education Chengdu China School of Medical Informatics Chongqing Medical University Chongqing China Department of Logistics Management and Maritime Studies Hong Kong Polytechnic University Hong Kong Department of System Engineering and Engineering Management Chinese University of Hong Kong Hong Kong

A chance-constrained knapsack problem (CCKP) is a knapsack problem restricted by a chance constraint, which ensures that the total capacity constraint under uncertain volume can be violated only up to a given probability threshold. CCKP is challenging to solve due to its combinatorial nature and the involvement of its chance constraint. Existing solution methods for CCKP with tractability guarantees mainly focus on two approaches: (1) a full-information approach (stochastic programming) that assumes the uncertain volume follows certain distributions, such as normal or empirical distribution;(2) a partial-information approach (robust optimization) that adopts specific statistics of the unknown distribution, such as the mean and variance. The existing full-information approach lacks robustness under limited samples due to its strong assumption;the existing partial-information approach can be further improved, as the uncertainty set or distributional ambiguity set can be ameliorated. With these concerns in mind, we propose a nonparametric robust approach for CCKP by involving a novel nonparametric statistic to form a new distributional ambiguity set. Furthermore, we develop an upper bound on the violation probability of the chance constraint under the distributional ambiguity set to approximate CCKP by a deterministic robust counterpart. In terms of solution methodology, we decompose the deterministic robust counterpart into cardinality-constrained knapsack problems, which can be efficiently solved by the proposed dynamic programming algorithm. Computational results show that our proposed solution methods produce better solutions to CCKP compared with existing approaches. © 2025 Society for Industrial and Applied Mathematics.

关键词： stochastic programming

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Pharmaceutical capacity expansion under uncertainty: Framework and models

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COMPUTERS & CHEMICAL ENGINEERING 2024年 189卷

作者： Lindahl, Simon B. Babi, Deenesh K. Sin, Gurkan Tech Univ Denmark Proc & Syst Engn Ctr PROSYS Dept Chem & Biochem Engn Soltofts Plads 228 DK-2800 Lyngby Denmark Novo Nord A S PS API Mfg Dev BIO Novo Alle 1 DK-2880 Bagsvaerd Denmark

This work presents a methodology for capacity planning under uncertainty in general multi-stage manufacturing networks. Multiple manufacturing lines are available and the production time on each line must be divided between a set of materials. The methodology generates mixed-integer linear programming models that represent capacity expansions with economy of scale costs functions and production planning details. A deterministic model is solved to create a baseline and the impact of uncertainty is investigated by sensitivity analysis and stochastic programming. The applicability of the methodology is exemplified through two case studies derived from industrial pharmaceutical manufacturing. The methodology identifies bottlenecks that limit supply and, where required, activates, and assigns capacity expansion projects for satisfying demand subject to uncertainty. The methodology determines the best use of existing resources and the location and size of capacity expansions thereby generating a portfolio of recommendations for decision making on integrated planning of capacity and production.

关键词： Capacity expansion Production planning Pharmaceutical manufacturing MILP stochastic programming

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Fast Continuous and Integer L-Shaped Heuristics Through Supervised Learning

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INFORMS JOURNAL ON COMPUTING 2024年第1期36卷 1-304, C2页

作者： Larsen, Eric Frejinger, Emma Gendron, Bernard Lodi, Andrea Univ Montreal Dept Comp Sci & Operat Res Montreal PQ H3C 3J7 Canada Univ Montreal Ctr Interuniv Rech Reseaux Entreprise Logist & Tra Montreal PQ H3C 3J7 Canada Polytech Montreal Canada Excellence Res Chair Montreal PQ H3C 3A7 Canada Cornell Tech Jacobs Technion Cornell Inst New York NY 10044 USA

We propose a methodology at the nexus of operations research and machine learning (ML) leveraging generic approximators available from ML to accelerate the solution of mixed-integer linear two-stage stochastic programs. We aim at solving problems where the second stage is demanding. Our core idea is to gain large reductions in online solution time, while incurring small reductions in first-stage solution accuracy by substituting the exact second-stage solutions with fast, yet accurate, supervised ML predictions. This upfront investment in ML would be justified when similar problems are solved repeatedly over time-for example, in transport planning related to fleet management, routing, and container yard management. Our numerical results focus on the problem class seminally addressed with the integer and continuous L-shaped cuts. Our extensive empirical analysis is grounded in standardized families of problems derived from stochastic server location (SSLP) and stochastic multi-knapsack (SMKP) problems available in the literature. The proposed method can solve the hardest instances of SSLP in less than 9% of the time it takes the state-of-the-art exact method, and in the case of SMKP, the same figure is 20%. Average optimality gaps are, in most cases, less than 0.1%.

关键词： stochastic programming machine learning integer L-shaped integer linear programming supervised learning

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Index policy for multiarmed bandit problem with dynamic risk measures

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2024年第2期312卷 627-640页

作者： Malekipirbazari, Milad Cavus, Ozlem Bilkent Univ Dept Ind Engn TR-06800 Ankara Turkey

The multiarmed bandit problem (MAB) is a classic problem in which a finite amount of resources must be allocated among competing choices with the aim of identifying a policy that maximizes the expected total reward. MAB has a wide range of applications including clinical trials, portfolio design, tuning parameters, internet advertisement, auction mechanisms, adaptive routing in networks, and project management. The classical MAB makes the strong assumption that the decision maker is risk-neutral and indifferent to the variability of the outcome. However, in many real life applications, these assumptions are not met and decision makers are risk-averse. Motivated to resolve this, we study risk-averse control of the multiarmed bandit problem in regard to the concept of dynamic coherent risk measures to determine a policy with the best risk-adjusted total discounted return. In respect of this specific setting, we present a theoretical analysis based on Whittle's retirement problem and propose a priority-index policy that reduces to the Gittins index when the level of risk-aversion converges to zero. We generalize the restart formulation of the Gittins index to effectively compute these risk-averse allocation indices. Nu-merical results exhibit the excellent performance of this heuristic approach for two well-known coherent risk measures of first-order mean-semideviation and mean-AVaR. Our experimental studies suggest that there is no guarantee that an index-based optimal policy exists for the risk-averse problem. Nonetheless, our risk-averse allocation indices can achieve optimal or near-optimal policies which in some instances are easier to interpret compared to the exact optimal policy.& COPY;2023 Elsevier B.V. All rights reserved.

关键词： stochastic programming Multiarmed bandit problem Gittins index Dynamic coherent risk measures Risk-averse control

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Optimal Planning of IDR-integrated Electricity-heat Systems Considering Techno-economic and Carbon Emission Issues

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CSEE Journal of Power and Energy Systems 2023年第6期9卷 2344-2355页

作者： Bo Zeng Yu Liu Yangfan Luo Hao Xu Luqman Ahmed the State Key Laboratory of Alternate Electrical Power System with Renewable Energy Sources North China Electric Power UniversityBeijing 102206China the State Grid Kaifeng Power Supply Company Kaifeng 475000China

This study presents an optimal electricity-heat system(EHS)planning framework to promote the accommodation of wind power while considering technical,economic and environmental *** this end,integrated demand response(IDR)is introduced as a flexibility resource to complement the inherent fluctuation of renewable energy sources and modeled by using price elasticity *** the timing transferring and energy substitution potentials are considered in the proposed IDR *** the effect of IDR into the EHS planning model,a two-stage stochastic programming model can be devised,in which the optimal EHS configuration design and associated operation control techniques are found simultaneously to minimize the system’s total economic and carbon-emission costs over the planning *** multi-scale uncertainties arising from both long-term demand growth and operation-level variability of renewables/load demands are captured collectively by using a scenario-based *** suggested planning approach is illustrated using a real EHS test case and the results show that it is effective in practical applications.

关键词： Electricity-heat system(EHS) carbon emission wind power multi-scale uncertainties stochastic programming

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How Will Dynamic Charging Tariff Affect Electric Truck Fleet Operation:A Two-Stage stochastic Model

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Journal of Shanghai Jiaotong university(Science) 2024年第6期29卷 1050-1062页

作者： DENG Jiali HU Hao DAI Lei State Key Laboratory of Ocean Engineering School of Naval ArchitectureOcean and Civil EngineeringShanghai Jiao Tong UniversityShanghai 200240China

Technical advances and sustainable development tendency accelerate the implementation of electric ***,the penetration of dynamic charging tariff policy poses a huge challenge to the cost-optimal operation of the electric truck *** this end,a two-stage stochastic electric vehicle routing model is formulated to support cost-efficient routing and charging ***,an experimental study based on a real-world distribution network is conducted to evaluate impacts of dynamic charging tariffs on logistics *** results show that the daily operation cost can reduce by 3.57%to 5.55%as the number of dynamic charging stations *** value of stochastic solution confirms the benefits of implementing stochastic programming model,which will ensure a lower operation cost in the long-term through robust route planning.

关键词： dynamic charging tariff electric vehicle routing stochastic programming

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Optimization of Local Voltage Control With Coordinating Droop Functions Under High PV Penetration

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IEEE TRANSACTIONS ON POWER SYSTEMS 2024年第5期39卷 6776-6779页

作者： Zhang, Cuo Xu, Ruipeng Yang, Linfeng Univ Sydney Sch Elect & Comp Engn Sydney NSW 2006 Australia Univ New South Wales Sch Elect Engn & Telecommun Kensington NSW 2052 Australia Guangxi Univ Guangxi Key Lab Multimedia Commun Network Technol Sch Comp & Elect Informat Nanning 530004 Peoples R China

PV power generation has significantly penetrated distribution networks, and inverter based local voltage control has been applied in practice. However, volt-var and volt-watt droop control functions are not optimized or coordinated. This letter proposes an effective optimization model for inverter based local voltage control, systematically optimizing both volt-var and volt-watt droop functions under uncertainties and adopts a new solution method. The simulation results show high efficiency of the optimized droop control functions in minimizing power losses and PV power curtailment and addressing the overvoltage issue.

关键词： Voltage control Inverters Real-time systems stochastic processes Uncertainty programming Reactive power Distribution networks local voltage control mixed integer programming stochastic programming

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Bounds for probabilistic programming with application to a blend planning problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2022年第3期297卷 964-976页

作者： Peng, Shen Maggioni, Francesca Lisser, Abdel KTH Royal Inst Technol Dept Math Optimizat & Syst Theory Lindstedtsvagen 25 SE-10044 Stockholm Sweden Univ Bergamo Dept Management Informat & Prod Engn Via Marconi 5 I-24127 Dalmine Bg Italy Univ Paris Saclay L2S Cent Supelec Bat Breguet3 Rue Joliot Curie F-91190 Gif Sur Yvette France

In this paper, we derive deterministic inner approximations for single and joint independent or dependent probabilistic constraints based on classical inequalities from probability theory such as the onesided Chebyshev inequality, Bernstein inequality, Chernoff inequality and Hoeffding inequality (see Pinter, 1989). The dependent case has been modelled via copulas. New assumptions under which the bounds based approximations are convex allowing to solve the problem efficiently are derived. When the convexity condition can not hold, an efficient sequential convex approximation approach is further proposed to solve the approximated problem. Piecewise linear and tangent approximations are also provided for Chernoff and Hoeffding inequalities allowing to reduce the computational complexity of the associated optimization problem. Extensive numerical results on a blend planning problem under uncertainty are finally provided allowing to compare the proposed bounds with the Second Order Cone (SOCP) formulation and Sample Average Approximation (SAA). (c) 2021 Elsevier B.V. All rights reserved.

关键词： stochastic programming Joint chance-constraints Bounds Copulas Blending problem

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A risk analytics model for strategic workforce planning: readiness of enlisted military personnel

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ANNALS OF OPERATIONS RESEARCH 2024年第1期338卷 513-533页

作者： MacDonald, Leo Paul, Jomon Aliyas Kennesaw State Univ Dept Econ Finance & Quantitat Anal 560 Parliament Garden Way Kennesaw GA 30144 USA

We develop a dynamic stochastic model of military workforce planning that incorporates uncertainties about personnel gains and losses across ranks. We then apply it to determine the probability of not meeting required targets as well as the resulting shortages and overages in the short, medium, and long terms along with the evaluation of policies to mitigate these risks. Our model allows decision makers to adjust recruiting and training practices to minimize the risk of not meeting target personnel levels as well as to value retention and reenlistment policies by calculating the expected marginal value of retaining additional service members. Moreover, it allows us to create a penalty function to optimize recruiting and training levels. The outcome is a tool to evaluate and ensure comprehensive force readiness.

关键词： stochastic programming Workforce planning Military Risk analysis

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Subproblem sampling vs. scenario reduction: efficacy comparison for stochastic programs in power systems applications

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ENERGY SYSTEMS-OPTIMIZATION MODELING SIMULATION AND ECONOMIC ASPECTS 2025年第1期16卷 111-139页

作者： Sakhavand, Nahal Gangammanavar, Harsha Univ Texas Arlington Dept Ind Mfg & Syst Engn Arlington TX 76010 USA Southern Methodist Univ Dept Operat Res & Engn Management Dallas TX 75275 USA

In this paper, we present a two-stage stochastic programming and simulation-based framework for tackling large-scale planning and operational problems that arise in power systems with significant renewable generation. Traditional algorithms (the L-shaped method, for example) used to solve the sample average approximation of the true problem suffer from computational difficulties when the number of scenarios or the size of the subproblem increases. To address this, we develop a cutting plane method that uses sampling internally within optimization to select only a random subset of subproblems to solve in any iteration. We analyze the convergence property of the subproblem sampling-based method and demonstrate its computational advantages on two alternative formulations of the stochastic unit commitment-economic dispatch problem. We conduct the numerical experiments on modified IEEE-30 and IEEE-118 test systems. We also present detailed steps for assessing the quality of solutions obtained from sampling-based stochastic programming methods and determining a solution to prescribe to the system operators.

关键词： stochastic programming Unit commitment Economic dispatch Sampling-based cutting-plane methods Scenario reduction

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