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 u...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 simultaneously.An 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%).展开更多
The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in futu...The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in future low carbon societies.However,uncertainties from renewable energy and load variability threaten system safety and economy.Conventional chance-constrained programming(CCP)ensures reliable operation by limiting risk.However,increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks.To address this,this paper proposes a risk-adjustable chance-constrained goal programming(RACCGP)model,integrating CCP and goal programming to balance risk and cost based on system risk assessment.An intelligent nonlinear goal programming method based on the state transition algorithm(STA)is developed,along with an improved discretized step transformation,to handle model nonlinearity and enhance computational efficiency.Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP,and the solution method outperforms average sample sampling in efficiency and solution quality.展开更多
Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In ...Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.展开更多
A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Ar...A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.展开更多
Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWL...Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.展开更多
Optimization under uncertainty is a challenging topic of practical importance in the Process Systems Engineering.Since the solution of an optimization problem generally exhibits high sensitivity to the parameter varia...Optimization under uncertainty is a challenging topic of practical importance in the Process Systems Engineering.Since the solution of an optimization problem generally exhibits high sensitivity to the parameter variations, the deterministic model which neglects the parametric uncertainties is not suitable for practical applications. This paper provides an overview of the key contributions and recent advances in the field of process optimization under uncertainty over the past ten years and discusses their advantages and limitations thoroughly. The discussion is focused on three specific research areas, namely robust optimization, stochastic programming and chance constrained programming, based on which a systematic analysis of their applications, developments and future directions are presented. It shows that the more recent trend has been to integrate different optimization methods to leverage their respective superiority and compensate for their drawbacks. Moreover, data-driven optimization, which combines mathematical programming methods and machine learning algorithms, has become an emerging and competitive tool to handle optimization problems in the presence of uncertainty based on massive historical data.展开更多
We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as se...We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.展开更多
In this paper we study a Class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Str...In this paper we study a Class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.展开更多
Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a noncon...Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.展开更多
This paper proposes a novel exemplar- based method for reducing noise in computed tomography （CT） images. In the proposed method, denoising is performed on each block with the help of a given database of standard im...This paper proposes a novel exemplar- based method for reducing noise in computed tomography （CT） images. In the proposed method, denoising is performed on each block with the help of a given database of standard image blocks. For each noisy block, its denoised version is the best sparse positive linear combination of the blocks in the database. We formulate the problem as a constrained optimization problem such that the solution is the denoised block. Experimental results demonstrate the good performance of the proposed method over current state-of-the-art denoising methods, in terms of both objective and subjective evaluations.展开更多
TiO2 thin films were deposited on glass substrates by sputtering in a conventional rf magnetron sputtering system. X-ray diffraction pattern and transmission spectrum were measured. The curves of refraction index and ...TiO2 thin films were deposited on glass substrates by sputtering in a conventional rf magnetron sputtering system. X-ray diffraction pattern and transmission spectrum were measured. The curves of refraction index and extinction coefficient distributions as well as the thickness of films calculated from transmission spectrum were obtained. The optimization problem was also solved using a method based on a constrained nonlinear programming algorithm.展开更多
Public buildings present substantial demand re sponse(DR)potential,which can participate in the power sys tem operation.However,most public buildings exhibit a high degree of uncertainties due to incomplete informatio...Public buildings present substantial demand re sponse(DR)potential,which can participate in the power sys tem operation.However,most public buildings exhibit a high degree of uncertainties due to incomplete information,varying thermal parameters,and stochastic user behaviors,which hin ders incorporating the public buildings into power system oper ation.To address the problem,this paper proposes an interval DR potential evaluation method and a risk dispatch model to integrate public buildings with uncertainties into power system operation.Firstly,the DR evaluation is developed based on the equivalent thermal parameter(ETP)model,actual outdoor tem perature data,and air conditioning(AC)consumption data.To quantify the uncertainties of public buildings,the interval evalu ation is given employing the linear regression method consider ing the confidence bound.Utilizing the evaluation results,the risk dispatch model is proposed to allocate public building re serve based on the chance constrained programming(CCP).Fi nally,the proposed risk dispatch model is reformulated to a mixed-integer second-order cone programming(MISOCP)for its solution.The proposed evaluation method and the risk dis patch model are validated based on the modified IEEE 39-bus system and actual building data obtained from a southern city in China.展开更多
An optimal preventive-corrective control model for static voltage stability under multiple N-1 contingencies considering the wind power uncertainty is established in this paper.The objective is to minimize the control...An optimal preventive-corrective control model for static voltage stability under multiple N-1 contingencies considering the wind power uncertainty is established in this paper.The objective is to minimize the control variable adjustment cost including the load shedding cost of each contingency.The chance constraints of the static voltage stability margins(SvSMs)in the normal operation state and after each N-1 contingency are included.The approximate functions between the probability density functions(PDFs)of SVSMs and load shedding quantity with respect to preventive control variables are obtained to transform the expectation of load shedding quantity and the SvSM chance constraints into deterministic expressions.An approximate sequential convex quadratically constrained quadratic programming iteration method is proposed to solve the optimal control model.In each iteration,the approximate expressions and range are determined by the generated data samples.Moreover,a fast approximation calculation method of second-order matrices is proposed.By the naive Bayes classifier,the most severe N-1 contingencies are selected to replace all the contingencies to be added to the optimization model to improve the computational efficiency.Case studies on the IEEE-39 bus system and an actual provincial power grid demonstrate the effectiveness and efficiency of the proposed method.展开更多
In this paper, we discuss complex convex quadratically constrained optimization with uncertain data. Using S-Lemma, we show that the robust counterpart of complex convex quadratically constrained optimization with ell...In this paper, we discuss complex convex quadratically constrained optimization with uncertain data. Using S-Lemma, we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program. By exploring the approximate S-Lemma, we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.展开更多
We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial vari...We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.展开更多
This paper develops new semidefinite programming(SDP)relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance.The first class of ...This paper develops new semidefinite programming(SDP)relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance.The first class of problems finds two minimum norm vectors in N-dimensional real or complex Euclidean space,such that M out of 2M concave quadratic constraints are satisfied.By employing a special randomized rounding procedure,we show that the ratio between the norm of the optimal solution of this model and its SDP relaxation is upper bounded by 54πM2 in the real case and by 24√Mπin the complex case.The second class of problems finds a series of minimum norm vectors subject to a set of quadratic constraints and cardinality constraints with both binary and continuous variables.We show that in this case the approximation ratio is also bounded and independent of problem dimension for both the real and the complex cases.展开更多
In this paper a successive approximation method for solving probabilistic constrained programs is proposed. At each iteration of this method only few linear programs on a normal scale have to be solved. An error bound...In this paper a successive approximation method for solving probabilistic constrained programs is proposed. At each iteration of this method only few linear programs on a normal scale have to be solved. An error bound for the optimal value is given.展开更多
基金Financial support from the National Natural Science Foundation of China (22022816, 22078358)。
文摘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 simultaneously.An 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%).
基金Project(2022YFC2904502)supported by the National Key Research and Development Program of ChinaProject(62273357)supported by the National Natural Science Foundation of China。
文摘The electricity-hydrogen integrated energy system(EH-IES)enables synergistic operation of electricity,heat,and hydrogen subsystems,supporting renewable energy integration and efficient multi-energy utilization in future low carbon societies.However,uncertainties from renewable energy and load variability threaten system safety and economy.Conventional chance-constrained programming(CCP)ensures reliable operation by limiting risk.However,increasing source-load uncertainties that can render CCP models infeasible and exacerbate operational risks.To address this,this paper proposes a risk-adjustable chance-constrained goal programming(RACCGP)model,integrating CCP and goal programming to balance risk and cost based on system risk assessment.An intelligent nonlinear goal programming method based on the state transition algorithm(STA)is developed,along with an improved discretized step transformation,to handle model nonlinearity and enhance computational efficiency.Experimental results show that the proposed model reduces costs while controlling risk compared to traditional CCP,and the solution method outperforms average sample sampling in efficiency and solution quality.
文摘Active set method and gradient projection method are curre nt ly the main approaches for linearly constrained convex programming. Interior-po int method is one of the most effective choices for linear programming. In the p aper a predictor-corrector interior-point algorithm for linearly constrained c onvex programming under the predictor-corrector motivation was proposed. In eac h iteration, the algorithm first performs a predictor-step to reduce the dualit y gap and then a corrector-step to keep the points close to the central traject ory. Computations in the algorithm only require that the initial iterate be nonn egative while feasibility or strict feasibility is not required. It is proved th at the algorithm is equivalent to a level-1 perturbed composite Newton method. Numerical experiments on twenty-six standard test problems are made. The result s show that the proposed algorithm is stable and robust.
文摘A potential reduction algorithm is proposed for optimization of a convex function subject to linear constraints.At each step of the algorithm,a system of linear equations is solved to get a search direction and the Armijo's rule is used to determine a stepsize.It is proved that the algorithm is globally convergent.Computational results are reported.
基金supported by the National Natural Science Foundation of China(61201282)the Science and Technology on Communication Information Security Control Laboratory Foundation(9140C130304120C13064)
文摘Time-differences-of-arrival （TDOA） and gain-ratios-of- arrival （GROA） measurements are used to determine the passive source location. Based on the measurement models, the con- strained weighted least squares （CWLS） estimator is presented. Due to the nonconvex nature of the CWLS problem, it is difficult to obtain its globally optimal solution. However, according to the semidefinite relaxation, the CWLS problem can be relaxed as a convex semidefinite programming problem （SDP）, which can be solved by using modern convex optimization algorithms. Moreover, this relaxation can be proved to be tight, i.e., the SDP solves the relaxed CWLS problem, and this hence guarantees the good per- formance of the proposed method. Furthermore, this method is extended to solve the localization problem with sensor position errors. Simulation results corroborate the theoretical results and the good performance of the proposed method.
文摘Optimization under uncertainty is a challenging topic of practical importance in the Process Systems Engineering.Since the solution of an optimization problem generally exhibits high sensitivity to the parameter variations, the deterministic model which neglects the parametric uncertainties is not suitable for practical applications. This paper provides an overview of the key contributions and recent advances in the field of process optimization under uncertainty over the past ten years and discusses their advantages and limitations thoroughly. The discussion is focused on three specific research areas, namely robust optimization, stochastic programming and chance constrained programming, based on which a systematic analysis of their applications, developments and future directions are presented. It shows that the more recent trend has been to integrate different optimization methods to leverage their respective superiority and compensate for their drawbacks. Moreover, data-driven optimization, which combines mathematical programming methods and machine learning algorithms, has become an emerging and competitive tool to handle optimization problems in the presence of uncertainty based on massive historical data.
基金supported by National Natural Science Foundation of China(Grant Nos. 11001006 and 91130019/A011702)the Fund of State Key Laboratory of Software Development Environment (Grant No. SKLSDE-2011ZX-15.)
文摘We establish in this paper optimal parametric Lagrangian dual models for box constrained quadratic program based on the generalized D.C.(difference between convex) optimization approach,which can be reformulated as semidefinite programming problems.As an application,we propose new valid linear constraints for rank-one relaxation.
基金Supported by the fundamental research funds for the central universities under grant YWF-10-02-021 and by National Natural Science Foundation of China under grant 11001006 The author is very grateful to all the three anonymous referees for their constructive criticisms and useful suggestions that help to improve the paper.
文摘In this paper we study a Class of nonconvex quadratically constrained quadratic programming problems generalized from relaxations of quadratic assignment problems. We show that each problem is polynomially solved. Strong duality holds if a redundant constraint is introduced. As an application, a new lower bound is proposed for the quadratic assignment problem.
基金supported by US Army Research Office Grant(No.W911NF-04-D-0003)by the North Carolina State University Edward P.Fitts Fellowship and by National Natural Science Foundation of China(No.11171177)。
文摘Solving the quadratically constrained quadratic programming(QCQP)problem is in general NP-hard.Only a few subclasses of the QCQP problem are known to be polynomial-time solvable.Recently,the QCQP problem with a nonconvex quadratic objective function over one ball and two parallel linear constraints is proven to have an exact computable representation,which reformulates the original problem as a linear semidefinite program with additional linear and second-order cone constraints.In this paper,we provide exact computable representations for some more subclasses of the QCQP problem,in particular,the subclass with one secondorder cone constraint and two special linear constraints.
文摘This paper proposes a novel exemplar- based method for reducing noise in computed tomography （CT） images. In the proposed method, denoising is performed on each block with the help of a given database of standard image blocks. For each noisy block, its denoised version is the best sparse positive linear combination of the blocks in the database. We formulate the problem as a constrained optimization problem such that the solution is the denoised block. Experimental results demonstrate the good performance of the proposed method over current state-of-the-art denoising methods, in terms of both objective and subjective evaluations.
文摘TiO2 thin films were deposited on glass substrates by sputtering in a conventional rf magnetron sputtering system. X-ray diffraction pattern and transmission spectrum were measured. The curves of refraction index and extinction coefficient distributions as well as the thickness of films calculated from transmission spectrum were obtained. The optimization problem was also solved using a method based on a constrained nonlinear programming algorithm.
基金supported by the National Science Fund for Distinguished Young Scholars(No.52125702)the Key Science and Technology Project of China Southern Power Grid Corporation(No.090000KK52220020).
文摘Public buildings present substantial demand re sponse(DR)potential,which can participate in the power sys tem operation.However,most public buildings exhibit a high degree of uncertainties due to incomplete information,varying thermal parameters,and stochastic user behaviors,which hin ders incorporating the public buildings into power system oper ation.To address the problem,this paper proposes an interval DR potential evaluation method and a risk dispatch model to integrate public buildings with uncertainties into power system operation.Firstly,the DR evaluation is developed based on the equivalent thermal parameter(ETP)model,actual outdoor tem perature data,and air conditioning(AC)consumption data.To quantify the uncertainties of public buildings,the interval evalu ation is given employing the linear regression method consider ing the confidence bound.Utilizing the evaluation results,the risk dispatch model is proposed to allocate public building re serve based on the chance constrained programming(CCP).Fi nally,the proposed risk dispatch model is reformulated to a mixed-integer second-order cone programming(MISOCP)for its solution.The proposed evaluation method and the risk dis patch model are validated based on the modified IEEE 39-bus system and actual building data obtained from a southern city in China.
基金supported by the National Natural Science Foundation of China under Grant 51977080the Natural Science Foundation of Guangdong Province(2023A1515240075).
文摘An optimal preventive-corrective control model for static voltage stability under multiple N-1 contingencies considering the wind power uncertainty is established in this paper.The objective is to minimize the control variable adjustment cost including the load shedding cost of each contingency.The chance constraints of the static voltage stability margins(SvSMs)in the normal operation state and after each N-1 contingency are included.The approximate functions between the probability density functions(PDFs)of SVSMs and load shedding quantity with respect to preventive control variables are obtained to transform the expectation of load shedding quantity and the SvSM chance constraints into deterministic expressions.An approximate sequential convex quadratically constrained quadratic programming iteration method is proposed to solve the optimal control model.In each iteration,the approximate expressions and range are determined by the generated data samples.Moreover,a fast approximation calculation method of second-order matrices is proposed.By the naive Bayes classifier,the most severe N-1 contingencies are selected to replace all the contingencies to be added to the optimization model to improve the computational efficiency.Case studies on the IEEE-39 bus system and an actual provincial power grid demonstrate the effectiveness and efficiency of the proposed method.
基金NsF of China (Grant No.60773185,10401038)Program for Beijing Excellent Talents and NSF of China (Grant No.10571134)the Natural Science Foundation of Tianjin (Grant No.07JCYBJC05200)
文摘In this paper, we discuss complex convex quadratically constrained optimization with uncertain data. Using S-Lemma, we show that the robust counterpart of complex convex quadratically constrained optimization with ellipsoidal or intersection-of-two-ellipsoids uncertainty set leads to a complex semidefinite program. By exploring the approximate S-Lemma, we give a complex semidefinite program which approximates the NP-hard robust counterpart of complex convex quadratic optimization with intersection-of-ellipsoids uncertainty set.
文摘We propose a new method for finding the local optimal points of the constrained nonlinear programming by Ordinary Differential Equations (ODE) , and prove asymptotic stability of the singular points of partial variables in this paper. The condition of overall uniform, asymptotic stability is also given.
基金the National Natural Science Foundation of China(No.11101261).
文摘This paper develops new semidefinite programming(SDP)relaxation techniques for two classes of mixed binary quadratically constrained quadratic programs and analyzes their approximation performance.The first class of problems finds two minimum norm vectors in N-dimensional real or complex Euclidean space,such that M out of 2M concave quadratic constraints are satisfied.By employing a special randomized rounding procedure,we show that the ratio between the norm of the optimal solution of this model and its SDP relaxation is upper bounded by 54πM2 in the real case and by 24√Mπin the complex case.The second class of problems finds a series of minimum norm vectors subject to a set of quadratic constraints and cardinality constraints with both binary and continuous variables.We show that in this case the approximation ratio is also bounded and independent of problem dimension for both the real and the complex cases.
文摘In this paper a successive approximation method for solving probabilistic constrained programs is proposed. At each iteration of this method only few linear programs on a normal scale have to be solved. An error bound for the optimal value is given.
