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A multi-objective robust scenario-based stochastic chance constrained programming model for sustainable closed-loop agri-food supply chain

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COMPUTERS & CHEMICAL ENGINEERING 2025年 194卷

作者： Rahbari, Misagh Khamseh, Alireza Arshadi Mohammadi, Mohammad Kharazmi Univ Fac Engn Dept Ind Engn Tehran Iran

The agri-food supply chain management plays a crucial role in ensuring the interests of supply chain components and food security in society. Additionally, due to the nature of agri-food products, sustainability dimensions have always been of concern to organizations engaged in this field. The importance of the timely and quality provision of agri-food products has doubled after the global crisis. Therefore, this study focuses on optimizing and analyzing the sustainable multi-objective closed-loop supply chain network for agri-food products, with a case study on the canned food under uncertainty. Strategic and operational decisions and other features are considered to achieve more accurate results. To address the various dimensions of sustainability, the problem is considered as a four-objective one, aiming to maximize the use of available production throughput for factories, maximize job opportunities created, minimize supply chain costs, and ultimately minimize unmet demands. The carbon cap and trade mechanism is used to control greenhouse gas emissions in the supply chain network. A robust scenario-based stochastic chance constrained programming approach is employed to deal with the uncertainty, and also validation is performed using various criteria. Moreover, an augmented epsilon-constraint optimization approach is used to solve the multi-objective problem and achieve Pareto optimal solutions. Finally, sensitivity analysis is employed to prepare for potential changes in some problem parameters.

关键词： Closed-loop supply chain Scenario-based stochastic programming Agri-food supply chain chance constrained programming Sustainability Robust optimization

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A Two-Stage Joint Clearing Model for Virtual Power Plant Participating in the Flexible Ramping Product Market Based on chance-constrained programming

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JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY 2025年第3期20卷 1363-1382页

作者： Xing, Haijun Shen, Jie Cheng, Mingyang Zheng, Zhen Shi, Yiqin Luo, Jiayi Shanghai Univ Elect Power Dept Elect Engn Shanghai Peoples R China State Grid Lianyungang Power Supply Co Lianyungang Jiangsu Peoples R China State Grid Shanghai Qingpu Elect Power Supply Co Shanghai Peoples R China

With the continuous growth of high-penetration renewable energy integration, the volatility and uncertainty of wind and photovoltaic power generation pose significant challenges to the flexible operation of the power system. Existing market clearing models often struggle to efficiently handle these uncertainties and ensure sufficient ramping capacity. Therefore, the rational utilization of flexible resources and the improvement of the power system's flexible ramping capacity become essential measures to address these challenges. This paper presents a two-stage joint clearing model for the electricity energy market and the flexible ramping market using a sampling-based chance-constrained deterministic transformation method. The chance-constrained conditions are converted into mixed-integer linear constraints for solving. The diverse control capabilities of virtual power plant (VPP) are utilized to mitigate real-time market uncertainties and provide flexible ramping products, thereby enhancing the system's flexible regulation capacity and reducing operational costs. Numerical results from case studies show that the proposed model significantly reduces the total cost by approximately 0.17%, wind and photovoltaic power curtailment by 48%, and load shedding by 34% compared to existing works. Additionally, case studies at different penetration rates demonstrate the model's effectiveness and superiority in high-penetration renewable energy scenarios.

关键词： Uncertainty chance constrained programming Flexible ramping products Virtual power plant Joint market clearing

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chance constrained programming for Optimal Power Flow Under Uncertainty

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IEEE TRANSACTIONS ON POWER SYSTEMS 2011年第4期26卷 2417-2424页

作者： Zhang, Hui Li, Pu Ilmenau Univ Technol Inst Automat & Syst Engn Dept Simulat & Optimal Proc D-98684 Ilmenau Germany

Solution approaches to chance constrained programming (CCP) have been recently developed and applied in many areas for optimization under uncertainty. Due to the nonlinear model with multiple uncertain variables as well as multiple output constraints, CCP has not been directly applied to optimal power flow (OPF) under uncertainty. The objective of this paper is twofold. First, we introduce the CCP approach to OPF under uncertainty and analyze the computational complexity of the chance constrained OPF. Second, the effectiveness of implementing a back-mapping approach and a linear approximation of the nonlinear model equations to solve the formulated CCP problem is investigated. Load power uncertainties are considered as multivariate random variables with correlated normal distribution. Based on both the nonlinear and the linearized model, results of a five-bus system and the IEEE 30-bus test system are presented to demonstrate the scope of chance constrained OPF.

关键词： chance constrained programming multivariate integration optimal power flow uncertainty

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chance constrained programming Models for constrained Shortest Path Problem with Fuzzy Parameters

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JOURNAL OF MULTIPLE-VALUED LOGIC AND SOFT COMPUTING 2014年第4-6期22卷 599-618页

作者： Dursun, Pinar Bozdag, Erhan Istanbul Tech Univ Dept Ind Engn TR-34367 Istanbul Turkey

Shortest path problem is a fundamental problem in transportation networks, communication networks and optimal control. The number of studies using different tools to solve this problem in deterministic, stochastic or fuzzy environment as well as the constrained version is increasing. In this paper, two chance constrained programming models are proposed for the shortest path problem with fuzzy parameters. The first model has fuzzy constraints in addition to the classical shortest path problem. The weights of arcs which form objective function are also fuzzy in the second model. To solve the models, a hybrid algorithm consists of fuzzy simulation and genetic algorithm is developed. To demonstrate the applicability of these proposed models and algorithms, some illustrating examples are given using a sample network. From the results, we can assert that the proposed methods are promising for the real life applications of the problem.

关键词： constrained Shortest Path Problem Fuzzy Arc Weight chance constrained programming Possibility Fuzzy Simulation Genetic Algorithm

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chance constrained programming using non-Gaussian joint distribution function in design of standalone hybrid renewable energy systems

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ENERGY 2014年 66卷 677-688页

作者： Kamjoo, Azadeh Maheri, Alireza Putrus, Ghanim A. Northumbria Univ Fac Engn & Environm Newcastle Upon Tyne NE1 8ST Tyne & Wear England

Performance of a HRES (hybrid renewable energy system) is highly affected by changes in renewable resources and therefore interruptions of electricity supply may happen in such systems. In this paper, a method to determine the optimal size of HRES components is proposed, considering uncertainties in renewable resources. The method is based on CCP (chance-constrained programming) to handle the uncertainties in power produced by renewable resources. The design variables are wind turbine rotor swept area, PV (photovoltaic) panel area and number of batteries. The common approach in solving problems with CCP is based on assuming the uncertainties to follow Gaussian distribution. The analysis presented in this paper shows that this assumption may result in a conservative solution rather than an optimum. The analysis is based on comparing the results of the common approach with those obtained by using the proposed method. The performance of the proposed method in design of HRES is validated by using the Monte Carlo simulation approach. To obtain accurate results in Monte Carlo simulation, the wind speed and solar irradiance variations are modelled with known distributions as well as using time series analysis;and the best fit models are selected as the random generators in Monte Carlo simulation. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Standalone hybrid systems Hybrid wind-PV-battery Reliability chance constrained programming Design under uncertainties

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chance constrained programming models for uncertain hub covering location problems

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SOFT COMPUTING 2020年第4期24卷 2781-2791页

作者： Wang, Junbin Qin, Zhongfeng Beihang Univ Sch Econ & Management Beijing 100191 Peoples R China

Hub covering location problem is a typical strategic decision with the purpose of locating hubs and determining the assignments of other nodes to ensure the travel time is not exceeding a specific threshold. Since the parameters such as flows and travel times are difficult to be precisely obtained in advance, a feasible way is to estimate them following the experts' subjective beliefs. Hence, this paper is devoted to study hub covering location problem by using uncertain measure to characterize the subjective belief and considering the flows and travel times by uncertain variables. The uncertain hub set covering location problem is first discussed under the purpose of covering the flows entirely with the minimum setup cost of hubs. Then the uncertain hub maximal covering problem is studied by maximizing the total flow covered when the number of hubs is confirmed previously. chance constrained programming models for both problems are constructed, respectively, and their corresponding deterministic forms are derived. A hybrid intelligence algorithm named GA-VNS is proposed by combing the variable neighborhood search with the genetic algorithm. Finally, several numerical experiments are presented to indicate the efficiency of GA-VNS.

关键词： Hub covering location problem chance constrained programming Uncertain variable

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chance constrained programming Based Optimal Network Reconfiguration in Smart Grid 14

Chance Constrained Programming Based Optimal Network Reconfi...

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14th IEEE International Conference on Industrial Informatics (INDIN)

作者： Zeng, Shunqi Xu, Zhao Wen, Fushuan Lai, Loi Lei Hong Kong Polytech Univ Dept Elect Engn Hong Kong Hong Kong Peoples R China Zhejiang Univ Coll Elect Engn Hangzhou Zhejiang Peoples R China Guangdong Univ Technol Guangzhou Guangdong Peoples R China

ISBN: (纸本)9781509028702

The network reconfiguration during power system restoration after blackouts usually takes a long and complex procedure. To address the uncertainties in the restoration steps and time involved, a CCP (chance constrained programming) based method for network reconfiguration scheme optimization is proposed in this paper. The proposed method can generate the best restoration sequence to maximize the benefit of the reconfiguration scheme by taking into account the number of restarted generator-nodes and the cost of power outage saved by the load restoration accordingly. The Differential Evolution (DE) is employed to solve for the optimal solution subject to special requirements of the network reconfiguration operation. A numerical example over the New England 39-bus power system is conducted to demonstrate the effectiveness of the proposed method.

关键词： Power system restoration network reconfiguration Differential Evolution chance constrained programming

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chance constrained programming with some non-normal continuous random variables

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OPSEARCH 2020年第4期57卷 1281-1298页

作者： Mohanty, D. K. Pradhan, Avik Biswal, E. M. P. Indian Inst Technol Dept Math Kharagpur 721302 W Bengal India Gujarat Technol Univ Indrashil Inst Sci & Technol Dept Humanities & Sci Mehsana 382740 Gujarat India

Stochastic or probabilistic programming is a branch of mathematical programming that deals with some situations in which an optimal decision is desired under random uncertainty of some parameters. In this paper, we consider some chance constrained linear programming problems where the right hand side parameters of the chance-constraints follow some non-normal continuous distributions such as power function distribution, triangular distribution and trapezoidal distribution. To find the solution of the stated problems, we first convert the problems in to equivalent deterministic models. Then standard linear programming techniques are used to solve the equivalent deterministic models. Some numerical examples are presented to illustrate the methodology.

关键词： Stochastic programming chance constrained programming Power function distribution Triangular distribution Trapezoidal distribution

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Optimization of circulating cooling water systems based on chance constrained programming

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Chinese Journal of Chemical Engineering 2021年第12期34卷 167-178页

作者： Bo Liu Yufei Wang Xiao Feng State Key Laboratory of Heavy Oil Processing China University of PetroleumBeijing 102249China School of Chemical Engineering&Technology Xi’an Jiaotong UniversityXi’an 710049China

Recent research on deterministic methods for circulating cooling water systems optimization has been well developed. However, the actual operating conditions of the system are mostly variable, so the system obtained under deterministic conditions may not be stable and economical. This paper studies the optimization of circulating cooling water systems under uncertain circumstance. To improve the reliability of the system and reduce the water and energy consumption, the influence of different uncertain parameters is taken into consideration. The chance constrained programming method is used to build a model under uncertain conditions, where the confidence level indicates the degree of constraint violation. Probability distribution functions are used to describe the form of uncertain parameters. The objective is to minimize the total cost and obtain the optimal cooling network configuration *** algorithm based on Monte Carlo method is proposed, and GAMS software is used to solve the mixed integer nonlinear programming model. A case is optimized to verify the validity of the model. Compared with the deterministic optimization method, the results show that when considering the different types of uncertain parameters, a system with better economy and reliability can be obtained(total cost can be reduced at least 2%).

关键词： Circulating cooling water system Uncertainty chance constrained programming Design Optimization Simulation

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A chance constrained programming approach to transmission system expansion planning

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ELECTRIC POWER SYSTEMS RESEARCH 2005年第2-3期75卷 171-177页

作者： Yang, N Wen, FS Univ Hong Kong Dept Elect & Elect Engn Hong Kong Hong Kong Peoples R China Zhejiang Univ Dept Elect Engn Hangzhou 310027 Peoples R China

The transmission system plays a critical role in providing access to all participants in a competitive electricity market for supply and delivery of electric power. Deregulation of the power industry brings many new challenges to the transmission system optimal planning problem, such as how to handle uncertain factors concerning the locations and capacities of new power plants as well as the demand growth for the transmission system planning period studied. Although the transmission system optimal planning problem has been extensively studied, available standard optimization models and methods cannot well solve this problem for the competitive electricity market environment with many uncertain factors involved. Given this background, a new method for the optimal transmission system expansion planning based on chance constrained programming is presented in this paper with several uncertain factors such as the locations and capacities of new power plants as well as demand growth well taken into account. A stochastic optimization model is first formulated under the presumption that the locations and capacities of new power plants and future load demands could be modeled as specified probability distributions. A method is then presented for solving the optimization problem using the well-known Monte Carlo simulation method and genetic algorithm. Finally, a numerical example is served for illustrating the essential features of the developed model and method. (c) 2005 Elsevier B.V. All rights reserved.

关键词： transmission system planning uncertainties chance constrained programming Monte Carlo simulation genetic algorithm

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