Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe ...Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.展开更多
Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morph...Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morphology information, Existing geological surface models suffer from high levels of uncertainty, which exposes oil and gas exploration and development to additional risk. In this paper, we achieve a reconstruction of the uncertainties associated with a geological surface using chance-constrained programming based on multisource data. We also quantifi ed the uncertainty of the modeling data and added a disturbance term to the objective function. Finally, we verifi ed the applicability of the method using both synthetic and real fault data. We found that the reconstructed geological models met geological rules and reduced the reconstruction uncertainty.展开更多
A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncert...A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.展开更多
An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain varia...An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.展开更多
We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers...We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers are uncertain variables. This research was studied with the assumption that customers patronize the nearest distribution center to satisfy their full demands. Within the framework of uncertainty theory, we construct the expected value model to maximize the expected profit of the new distribution center. In order to seek for the optimal solution, this model can be transformed into its deterministic form by taking advantage of the operational law of uncertain variables. Then we can use mathematical software to obtain the optimal location. In addition, a numerical example is presented to illustrate the effectiveness of the presented model.展开更多
This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sam...This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sample size for any random variable. Such approach mainly consists of sample allocation, evaluation, proliferation and mutation. The former two, depending on a lower bound estimate acquired, not only decide the sample size of random variable and the importance level of each evolving B cell, but also ensure that such B cell is evaluated with low computational cost; the third makes diverse B cells participate in evolution and suppresses the influence of noise; the last, which associates with the information on population diversity and fitness inheritance, creates diverse and high-affinity B cells. Under such approach, three similar immune algorithms are derived after selecting different mutation rules. The experiments, by comparison against two valuable genetic algorithms, have illustrated that these immune algorithms are competitive optimizers capable of effectively executing noisy compensation and searching for the desired optimal reliable solution.展开更多
The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constan...The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.展开更多
The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interva...The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.展开更多
Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling ...Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.展开更多
This paper extends Slutsky’s classic work on consumer theory to a random horizon stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertainties in future incomes and life...This paper extends Slutsky’s classic work on consumer theory to a random horizon stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertainties in future incomes and life span. Utility maximization leading to a set of ordinary wealth-dependent demand functions is performed. A dual problem is set up to derive the wealth compensated demand functions. This represents the first time that wealth-dependent ordinary demand functions and wealth compensated demand functions are obtained under these uncertainties. The corresponding Roy’s identity relationships and a set of random horizon stochastic dynamic Slutsky equations are then derived. The extension incorporates realistic characteristics in consumer theory and advances the conventional microeconomic study on consumption to a more realistic optimal control framework.展开更多
To address uncertainty as well as transient stability constraints simultaneously in the preventive control of windfarm systems, a novel three-stage optimization strategy is established in this paper. In the first stag...To address uncertainty as well as transient stability constraints simultaneously in the preventive control of windfarm systems, a novel three-stage optimization strategy is established in this paper. In the first stage, the probabilisticmulti-objective particle swarm optimization based on the point estimate method is employed to cope with thestochastic factors. The transient security region of the system is accurately ensured by the interior point methodin the second stage. Finally, the verification of the final optimal objectives and satisfied constraints are enforcedin the last stage. Furthermore, the proposed strategy is a general framework that can combine other optimizationalgorithms. The proposed methodology is tested on the modified WSCC 9-bus system and the New England 39-bussystem. The results verify the feasibility of the method.展开更多
Controlled islanding plays an essential role in preventing the blackout of power systems.Although there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable...Controlled islanding plays an essential role in preventing the blackout of power systems.Although there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable energy sources(RESs)that may cause unpredictable unbalanced power and the observabilit>T of power systems after islanding that is essential for back-up black-start measures.Therefore,a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming(MISOCCP)is proposed to address these issues.First,the uncertainty of RESs is characterized by their possibility distribution models with chance constraints,and the requirements,e.g.,system observability,for rapid back-up black-start measures are also considered.Then,a law of large numbers(LLN)based method is em-ployed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex one.Finally,case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed model.The results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.展开更多
Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form express...Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them.We then design a Monte Carlo algorithm,based on these estimators,to solve chance-constrained programs.Our numerical study shows that the algorithm works well,especially only with the gradient estimators.展开更多
在基于接收信号强度(received signal strength,RSS)的定位中,传感器量测的系统偏差及锚节点位置的不确定性会对定位结果造成严重影响。对此,提出一种面向不确定量测的鲁棒定位方法。首先,针对传感器量测有偏差及锚节点位置不确定的定...在基于接收信号强度(received signal strength,RSS)的定位中,传感器量测的系统偏差及锚节点位置的不确定性会对定位结果造成严重影响。对此,提出一种面向不确定量测的鲁棒定位方法。首先,针对传感器量测有偏差及锚节点位置不确定的定位问题,建立相应的量测模型;其次,基于经典的极大似然估计准则建立关于目标位置的估计问题;最后,对所建立的非凸位置估计问题,采用合理的近似、松弛数学手段,将其转化为凸的半正定规划问题,从而保证得到全局最优解。仿真实验表明,在不同定位场景和条件下,所提方法的定位精度相比文献中的几种定位方法均有明显的优势,最高可提升约50%,证明其能有效降低量测不确定性对定位结果的不利影响,具有良好的鲁棒性。展开更多
文摘Multiple objective stochastic linear programming is a relevant topic. As a matter of fact, many practical problems ranging from portfolio selection to water resource management may be cast into this framework. Severe limitations on objectivity are encountered in this field because of the simultaneous presence of randomness and conflicting goals. In such a turbulent environment, the mainstay of rational choice cannot hold and it is virtually impossible to provide a truly scientific foundation for an optimal decision. In this paper, we resort to the bounded rationality principle to introduce satisfying solution for multiobjective stochastic linear programming problems. These solutions that are based on the chance-constrained paradigm are characterized under the assumption of normality of involved random variables. Ways for singling out such solutions are also discussed and a numerical example provided for the sake of illustration.
基金by National Science and Technology Major Project(Grant No.2017ZX05018004004)the National Natural Science Foundation of China (No.U1562218 & 41604107).
文摘Geological surface modeling is typically based on seismic data, well data, and models of regional geology. However, structural interpretation of these data is error-prone, especially in the absence of structural morphology information, Existing geological surface models suffer from high levels of uncertainty, which exposes oil and gas exploration and development to additional risk. In this paper, we achieve a reconstruction of the uncertainties associated with a geological surface using chance-constrained programming based on multisource data. We also quantifi ed the uncertainty of the modeling data and added a disturbance term to the objective function. Finally, we verifi ed the applicability of the method using both synthetic and real fault data. We found that the reconstructed geological models met geological rules and reduced the reconstruction uncertainty.
文摘A deterministic linear programming model which optimizes the abatement of each SO2 emission source, is extended into a CCP form by introducing equations of probabilistic constrained through the incorporation of uncertainty in the source-receptor-specific transfer coefficients. Based on the calculation of SO2 and sulfate average residence time for Liuzhou City, a sulfur deposition model has been developed and the distribution of transfer coefficients have been found to be approximately log-normal. Sulfur removal minimization of the model shows that the abatement of emission sources in the city is more effective, while control cost optimization provides the lowest cost programmes for source abatement at each allowable deposition limit under varied environmental risk levels. Finally a practicable programme is recommended.
基金supported by the National Natural Science Foundation of China(71601183 71571190)
文摘An uncertain multi-objective programming problem is a special type of mathematical multi-objective programming involving uncertain variables. This type of problem is important because there are several uncertain variables in real-world problems.Therefore, research on the uncertain multi-objective programming problem is highly relevant, particularly those problems whose objective functions are correlated. In this paper, an approach that solves an uncertain multi-objective programming problem under the expected-variance value criterion is proposed. First, we define the basic framework of the approach and review concepts such as a Pareto efficient solution and expected-variance value criterion using an order relation between various uncertain variables.Second, the uncertain multi-objective problem is converted into an uncertain single-objective programming problem via a linear weighted method or ideal point method. Then the problem is transformed into a deterministic single objective programming problem under the expected-variance value criterion. Third, four lemmas and two theorems are proved to illustrate that the optimal solution of the deterministic single-objective programming problem is an efficient solution to the original uncertainty problem. Finally, two numerical examples are presented to validate the effectiveness of the proposed approach.
文摘We employ uncertain programming to investigate the competitive logistics distribution center location problem in uncertain environment, in which the demands of customers and the setup costs of new distribution centers are uncertain variables. This research was studied with the assumption that customers patronize the nearest distribution center to satisfy their full demands. Within the framework of uncertainty theory, we construct the expected value model to maximize the expected profit of the new distribution center. In order to seek for the optimal solution, this model can be transformed into its deterministic form by taking advantage of the operational law of uncertain variables. Then we can use mathematical software to obtain the optimal location. In addition, a numerical example is presented to illustrate the effectiveness of the presented model.
基金supported in part by National Natural Science Foundation of China(Nos.61563009 and 61065010)Doctoral Fund of Ministry of Education of China(No.20125201110003)
文摘This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sample size for any random variable. Such approach mainly consists of sample allocation, evaluation, proliferation and mutation. The former two, depending on a lower bound estimate acquired, not only decide the sample size of random variable and the importance level of each evolving B cell, but also ensure that such B cell is evaluated with low computational cost; the third makes diverse B cells participate in evolution and suppresses the influence of noise; the last, which associates with the information on population diversity and fitness inheritance, creates diverse and high-affinity B cells. Under such approach, three similar immune algorithms are derived after selecting different mutation rules. The experiments, by comparison against two valuable genetic algorithms, have illustrated that these immune algorithms are competitive optimizers capable of effectively executing noisy compensation and searching for the desired optimal reliable solution.
文摘The purpose of this paper is to combine the estimation of output price risk and positive mathematical programming (PMP). It reconciles the risk programming presented by Freund with a consistent estimate of the constant absolute risk aversion (CARA) coefficient. It extends the PMP approach to calibration of realized production outputs and observed input prices. The results of this specification include 1) uniqueness of the calibrating solution, 2) elimination of the tautological calibration constraints typical of the original PMP procedure, 3) equivalence between a phase I calibrating solution and a solution obtained by combining phase I and phase II of the traditional PMP procedure. In this extended PMP framework, the cost function specification involves output quantities and input prices—contrary to the myopic cost function of the traditional PMP approach. This extension allows for a phase III calibrating model that replaces the usual linear technology with relations corresponding to Shephard lemma (in the primal constraints) and the marginal cost function (in the dual constraints). An empirical example with a sample of farms producing four crops illustrates the novel procedure.
文摘The uncertain multi-attribute decision-making problems because of the information about attribute weights being known partly, and the decision maker＇s preference information on alternatives taking the form of interval numbers complementary to the judgment matrix, are investigated. First, the decision-making information, based on the subjective uncertain complementary preference matrix on alternatives is made uniform by using a translation function, and then an objective programming model is established. The attribute weights are obtained by solving the model, thus the overall values of the alternatives are gained by using the additive weighting method. Second, the alternatives are ranked, by using the continuous ordered weighted averaging （C-OWA） operator. A new approach to the uncertain multi-attribute decision-making problems, with uncertain preference information on alternatives is proposed. It is characterized by simple operations and can be easily implemented on a computer. Finally, a practical example is illustrated to show the feasibility and availability of the developed method.
文摘Project scheduling problem is mainly to determine the schedule of allocating resources in order to balance the total cost and the completion time. This paper chiefly uses chance theory to introduce project scheduling problem with uncertain variables. First, two types of single-objective programming models with uncertain variables as uncertain chance-constrained model and uncertain maximization chance-constrained model are established to meet different management requirements, then they are extended to multi-objective programming model with uncertain variables.
文摘This paper extends Slutsky’s classic work on consumer theory to a random horizon stochastic dynamic framework in which the consumer has an inter-temporal planning horizon with uncertainties in future incomes and life span. Utility maximization leading to a set of ordinary wealth-dependent demand functions is performed. A dual problem is set up to derive the wealth compensated demand functions. This represents the first time that wealth-dependent ordinary demand functions and wealth compensated demand functions are obtained under these uncertainties. The corresponding Roy’s identity relationships and a set of random horizon stochastic dynamic Slutsky equations are then derived. The extension incorporates realistic characteristics in consumer theory and advances the conventional microeconomic study on consumption to a more realistic optimal control framework.
文摘To address uncertainty as well as transient stability constraints simultaneously in the preventive control of windfarm systems, a novel three-stage optimization strategy is established in this paper. In the first stage, the probabilisticmulti-objective particle swarm optimization based on the point estimate method is employed to cope with thestochastic factors. The transient security region of the system is accurately ensured by the interior point methodin the second stage. Finally, the verification of the final optimal objectives and satisfied constraints are enforcedin the last stage. Furthermore, the proposed strategy is a general framework that can combine other optimizationalgorithms. The proposed methodology is tested on the modified WSCC 9-bus system and the New England 39-bussystem. The results verify the feasibility of the method.
基金the National Natural Science Foundation of China(No.51777185)National Key R&D Program of China(No.2016YFB0900100)Zhejiang University Academic Award for Outstanding Doctoral Candidates.
文摘Controlled islanding plays an essential role in preventing the blackout of power systems.Although there are several studies on this topic in the past,no enough attention is paid to the uncertainty brought by renewable energy sources(RESs)that may cause unpredictable unbalanced power and the observabilit>T of power systems after islanding that is essential for back-up black-start measures.Therefore,a novel controlled islanding model based on mixed-integer second-order cone and chance-constrained programming(MISOCCP)is proposed to address these issues.First,the uncertainty of RESs is characterized by their possibility distribution models with chance constraints,and the requirements,e.g.,system observability,for rapid back-up black-start measures are also considered.Then,a law of large numbers(LLN)based method is em-ployed for converting the chance constraints into deterministic ones and reformulating the non-convex model into convex one.Finally,case studies on the revised IEEE 39-bus and 118-bus power systems as well as the comparisons among different models are given to demonstrate the effectiveness of the proposed model.The results show that the proposed model can result in less unbalanced power and better observability after islanding compared with other models.
基金the Hong Kong Research Grants Council(No.GRF 613213)。
文摘Joint probability function refers to the probability function that requires multiple conditions to satisfy simultaneously.It appears naturally in chanceconstrained programs.In this paper,we derive closed-form expressions of the gradient and Hessian of joint probability functions and develop Monte Carlo estimators of them.We then design a Monte Carlo algorithm,based on these estimators,to solve chance-constrained programs.Our numerical study shows that the algorithm works well,especially only with the gradient estimators.
文摘在基于接收信号强度(received signal strength,RSS)的定位中,传感器量测的系统偏差及锚节点位置的不确定性会对定位结果造成严重影响。对此,提出一种面向不确定量测的鲁棒定位方法。首先,针对传感器量测有偏差及锚节点位置不确定的定位问题,建立相应的量测模型;其次,基于经典的极大似然估计准则建立关于目标位置的估计问题;最后,对所建立的非凸位置估计问题,采用合理的近似、松弛数学手段,将其转化为凸的半正定规划问题,从而保证得到全局最优解。仿真实验表明,在不同定位场景和条件下,所提方法的定位精度相比文献中的几种定位方法均有明显的优势,最高可提升约50%,证明其能有效降低量测不确定性对定位结果的不利影响,具有良好的鲁棒性。
