Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in un...Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.展开更多
Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power sta...Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.展开更多
高比例新能源的接入对电力系统既是机遇也是挑战:新能源具有清洁低碳的环保优势,但其出力不确定性大、物理惯量低的特点也对系统的频率安全运行带来挑战。针对上述问题,提出一种考虑碳-绿证市场耦合的新能源与储能虚拟惯量-阻尼调度方...高比例新能源的接入对电力系统既是机遇也是挑战:新能源具有清洁低碳的环保优势,但其出力不确定性大、物理惯量低的特点也对系统的频率安全运行带来挑战。针对上述问题,提出一种考虑碳-绿证市场耦合的新能源与储能虚拟惯量-阻尼调度方法。首先,构建包含电力决策、碳交易市场和绿证交易市场三者耦合关系,并计及系统动态频率安全约束的虚拟惯量-阻尼调度优化模型;其次,为降低决策保守性,将不确定性约束建模为整体的联合机会约束形式;然后,采用改进的样本平均近似(modified sample average approximation, MSAA)方法对所提模型进行求解,有效规避常规样本平均近似(sample average approximation, SAA)方法中0-1指示变量导致的计算负担。在IEEE-39节点系统的仿真结果表明:与现有模型和机会约束建模方法相比,所提方法能够根据系统时变扰动需求自适应调整虚拟惯量和下垂阻尼,在满足风险概率5%的前提下,以比固定系数方法低6.03%的成本,确保系统频率偏差在0.5 Hz以内。展现出更好的经济性、低碳性和频率安全性;同时,改进的MSAA方法较传统SAA方法计算时间减少了约90%,可显著提升计算效率。展开更多
网络购物的普及与冷链技术的不断成熟,促进了生鲜电商行业的快速发展。针对生鲜电商的前置仓选址及订单履约问题,本文考虑了生鲜商品需求的不确定性及保质期特点,构建了以选址成本和订单履约成本最小化为目标的两阶段随机规划模型。提...网络购物的普及与冷链技术的不断成熟,促进了生鲜电商行业的快速发展。针对生鲜电商的前置仓选址及订单履约问题,本文考虑了生鲜商品需求的不确定性及保质期特点,构建了以选址成本和订单履约成本最小化为目标的两阶段随机规划模型。提出了一种基于样本均值近似SAA(sample average approximation)的Benders分解算法,即SBD算法(sAA-based Benders decomposition)。该算法通过拉丁超立方抽样法将原模型转化为混合整数规划的SAA近似模型,再通过Benders分解算法对该模型进行求解。最后,以一个案例验证了所提出算法的有效性。结果表明,SBD算法在求解时间与求解精度上均优于商业求解器Cplex的求解结果;所提出的两阶段随机规划方法能够有效帮助生鲜电商企业在不确定环境下降低成本,为前置仓的布局及订单履约提供决策上的支持。展开更多
This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained opti...This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.展开更多
This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative re...This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.展开更多
This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited i...This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.展开更多
基金supported by the National Natural Science Foundation of China(No.51977042)。
文摘Joint chance constraints(JCCs)can ensure the consistency and correlation of stochastic variables when participating in decision-making.Sample average approximation(SAA)is the most popular method for solving JCCs in unit commitment(UC)problems.However,the typical SAA requires large Monte Carlo(MC)samples to ensure the solution accuracy,which results in large-scale mixed-integer programming(MIP)problems.To address this problem,this paper presents the partial sample average approximation(PSAA)to deal with JCCs in UC problems in multi-area power systems with wind power.PSAA partitions the stochastic variables and historical dataset,and the historical dataset is then partitioned into non-sampled and sampled sets.When approximating the expectation of stochastic variables,PSAA replaces the big-M formulation with the cumulative distribution function of the non-sampled set,thus preventing binary variables from being introduced.Finally,PSAA can transform the chance constraints to deterministic constraints with only continuous variables,avoiding the large-scale MIP problem caused by SAA.Simulation results demonstrate that PSAA has significant advantages in solution accuracy and efficiency compared with other existing methods including traditional SAA,SAA with improved big-M,SAA with Latin hypercube sampling(LHS),and the multi-stage robust optimization methods.
基金supported in part by the National Natural Science Foundation of China under Grant No.61473066in part by the Natural Science Foundation of Hebei Province under Grant No.F2021501020+2 种基金in part by the S&T Program of Qinhuangdao under Grant No.202401A195in part by the Science Research Project of Hebei Education Department under Grant No.QN2025008in part by the Innovation Capability Improvement Plan Project of Hebei Province under Grant No.22567637H
文摘Recently,one of the main challenges facing the smart grid is insufficient computing resources and intermittent energy supply for various distributed components(such as monitoring systems for renewable energy power stations).To solve the problem,we propose an energy harvesting based task scheduling and resource management framework to provide robust and low-cost edge computing services for smart grid.First,we formulate an energy consumption minimization problem with regard to task offloading,time switching,and resource allocation for mobile devices,which can be decoupled and transformed into a typical knapsack problem.Then,solutions are derived by two different algorithms.Furthermore,we deploy renewable energy and energy storage units at edge servers to tackle intermittency and instability problems.Finally,we design an energy management algorithm based on sampling average approximation for edge computing servers to derive the optimal charging/discharging strategies,number of energy storage units,and renewable energy utilization.The simulation results show the efficiency and superiority of our proposed framework.
文摘高比例新能源的接入对电力系统既是机遇也是挑战:新能源具有清洁低碳的环保优势,但其出力不确定性大、物理惯量低的特点也对系统的频率安全运行带来挑战。针对上述问题,提出一种考虑碳-绿证市场耦合的新能源与储能虚拟惯量-阻尼调度方法。首先,构建包含电力决策、碳交易市场和绿证交易市场三者耦合关系,并计及系统动态频率安全约束的虚拟惯量-阻尼调度优化模型;其次,为降低决策保守性,将不确定性约束建模为整体的联合机会约束形式;然后,采用改进的样本平均近似(modified sample average approximation, MSAA)方法对所提模型进行求解,有效规避常规样本平均近似(sample average approximation, SAA)方法中0-1指示变量导致的计算负担。在IEEE-39节点系统的仿真结果表明:与现有模型和机会约束建模方法相比,所提方法能够根据系统时变扰动需求自适应调整虚拟惯量和下垂阻尼,在满足风险概率5%的前提下,以比固定系数方法低6.03%的成本,确保系统频率偏差在0.5 Hz以内。展现出更好的经济性、低碳性和频率安全性;同时,改进的MSAA方法较传统SAA方法计算时间减少了约90%,可显著提升计算效率。
文摘网络购物的普及与冷链技术的不断成熟,促进了生鲜电商行业的快速发展。针对生鲜电商的前置仓选址及订单履约问题,本文考虑了生鲜商品需求的不确定性及保质期特点,构建了以选址成本和订单履约成本最小化为目标的两阶段随机规划模型。提出了一种基于样本均值近似SAA(sample average approximation)的Benders分解算法,即SBD算法(sAA-based Benders decomposition)。该算法通过拉丁超立方抽样法将原模型转化为混合整数规划的SAA近似模型,再通过Benders分解算法对该模型进行求解。最后,以一个案例验证了所提出算法的有效性。结果表明,SBD算法在求解时间与求解精度上均优于商业求解器Cplex的求解结果;所提出的两阶段随机规划方法能够有效帮助生鲜电商企业在不确定环境下降低成本,为前置仓的布局及订单履约提供决策上的支持。
基金This research is partly supported by the National Natural Science Foundation of China under Grant Nos. 71171027 and 11071028, the Fundamental Research Funds for the Central Universities under Grant No. DUT11SX11, and the Key Project of the National Natural Science Foundation of China under Grant No. 71031002.
文摘This paper considers a class of stochastic variational inequality problems. As proposed by Jiang and Xu （2008）, by using the so-called regularized gap function, the authors formulate the problems as constrained optimization problems and then propose a sample average approximation method for solving the problems. Under some moderate conditions, the authors investigate the limiting behavior of the optimal values and the optimal solutions of the approximation problems. Finally, some numerical results are reported to show efficiency of the proposed method.
基金Supported by the Guangxi Natural Science Foundation (2024GXNSFBA010345)the Innovation and Entrepreneurship Training Program of Guangxi Minzu University (S202310608001)。
文摘This paper extends the quantitative stability results to a more general class of two-stage stochastic variational inequality problems(TSVIP).The existence of solutions to the TSVIP is discussed,and the quantitative relationship between the TSVIP and its distribution perturbed problem is derived.
文摘This study aims to solve a typical long-term strategic decision problem on supply chain network design with consideration to uncertain demands. Existing methods for these problems are either deterministic or limited in scale. We analyze the impact of uncertainty on demand based on actual large data from industrial companies.Deterministic equivalent model with nonanticipativity constraints, branch-and-fix coordination, sample average approximation(SAA) with Bayesian bootstrap, and Latin hypercube sampling were adopted to analyze stochastic demands. A computational study of supply chain network with front-ends in Europe and back-ends in Asia is presented to highlight the importance of stochastic factors in these problems and the efficiency of our proposed solution approach.
