In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy sys...In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.展开更多
Rational distribution network planning optimizes power flow distribution,reduces grid stress,enhances voltage quality,promotes renewable energy utilization,and reduces costs.This study establishes a distribution netwo...Rational distribution network planning optimizes power flow distribution,reduces grid stress,enhances voltage quality,promotes renewable energy utilization,and reduces costs.This study establishes a distribution network planning model incorporating distributed wind turbines(DWT),distributed photovoltaics(DPV),and energy storage systems(ESS).K-means++is employed to partition the distribution network based on electrical distance.Considering the spatiotemporal correlation of distributed generation(DG)outputs in the same region,a joint output model of DWT and DPV is developed using the Frank-Copula.Due to the model’s high dimensionality,multiple constraints,and mixed-integer characteristics,bilevel programming theory is utilized to structure the model.The model is solved using a mixed-integer particle swarmoptimization algorithm(MIPSO)to determine the optimal location and capacity of DG and ESS integrated into the distribution network to achieve the best economic benefits and operation quality.The proposed bilevel planning method for distribution networks is validated through simulations on the modified IEEE 33-bus system.The results demonstrate significant improvements,with the proposedmethod reducing the annual comprehensive cost by 41.65%and 13.98%,respectively,compared to scenarios without DG and ESS or with only DG integration.Furthermore,it reduces the daily average voltage deviation by 24.35%and 10.24%and daily network losses by 55.72%and 35.71%.展开更多
An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorith...An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.展开更多
The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is signifi...The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.展开更多
Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s f...Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.展开更多
Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower’s optimal reaction is not unique. However, in these existed models, the follower’s cooperation level...Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower’s optimal reaction is not unique. However, in these existed models, the follower’s cooperation level does not depend on the leader’s decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semicontinuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and non-lower semi-continuous.展开更多
A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encod...A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.展开更多
This paper proposes an optimization model for the airport ground movement problem(GMP)based on bilevel programming to address taxi conflicts on the airport ground and to improve the operating safety and efficiency.To ...This paper proposes an optimization model for the airport ground movement problem(GMP)based on bilevel programming to address taxi conflicts on the airport ground and to improve the operating safety and efficiency.To solve GMP,an iterative heuristic algorithm is designed.Instead of separately investigating each problem,this model simultaneously coordinates and optimizes the aircraft routing and scheduling.A simulation test is conducted on Nanjing Lukou International Airport(NKG)and the results show that the bilevel programming model can clearly outperform the widely used first-come-first-service(FCFS)scheduling scheme in terms of aircraft operational time under the precondition of none conflict.The research effort demonstrates that with the reduced operating cost and the improved overall efficiency,the proposed model can assist operations of the airports that are facing increasing traffic demand and working at almost maximum capacity.展开更多
Bilevel programming problems are of growing interest both from theoretical and practical points of view.In this paper,we study a pessimistic bilevel programming problem in which the set of solutions of the lower level...Bilevel programming problems are of growing interest both from theoretical and practical points of view.In this paper,we study a pessimistic bilevel programming problem in which the set of solutions of the lower level problem is discrete.We first transform such a problem into a single-level optimization problem by using the maximum-entropy techniques.We then present a maximum entropy approach for solving the pessimistic bilevel programming problem.Finally,two examples illustrate the feasibility of the proposed approach.展开更多
A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for sol...A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.展开更多
A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ...A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.展开更多
Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems(BLPPs) are the optimization problems with hierarchical structure. In steel-making prod...Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems(BLPPs) are the optimization problems with hierarchical structure. In steel-making production, the plan is not only decided by the steel-making scheduling, but also by the transportation equipment.This paper proposes a genetic algorithm to solve continuous and ingot casting scheduling problems. Based on the characteristics of the problems involved, a genetic algorithm is proposed for solving the bilevel programming problem in steel-making production. Furthermore, based on the simplex method, a new crossover operator is designed to improve the efficiency of the genetic algorithm. Finally, the convergence is analyzed. Using actual data the validity of the proposed algorithm is proved and the application results in the steel plant are analyzed.展开更多
In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem....In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.展开更多
In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with...In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition.Then,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty.We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set.Finally,we propose an algorithm for the nonlinear bilevel programming problem.The numerical results show that the algorithm is feasible and efficient.展开更多
We present a new variant of penalty method, which is different from the existing penalty methods, for solving the weak linear bilevel programming problems. We then transform it into a single-level optimization problem...We present a new variant of penalty method, which is different from the existing penalty methods, for solving the weak linear bilevel programming problems. We then transform it into a single-level optimization problem using Kuhn-Tucker optimality condition and discuss the relations between them. Finally, two examples are used to illustrate the feasibility of the proposed penalty method.展开更多
Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first（upper level） objective function being minimized over the so...Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first（upper level） objective function being minimized over the solution set mapping of the second（lower level） optimization problem. Often the upper level decision maker is risk-averse. The resulting class of problem is named weak bilevel programming problem. This paper presents a new algorithm which embeds a penalty function method into a branch and bound algorithm to deal with a weak linear bilevel programming problem. An example illustrates the feasibility of the proposed algorithm.展开更多
For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monoto...For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.展开更多
By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the o...By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.展开更多
This paper is based on a resource constrained active network project;the constraint of the local resource and the time constraint of the cooperation resource are considered simultaneously.And the respective benefit of...This paper is based on a resource constrained active network project;the constraint of the local resource and the time constraint of the cooperation resource are considered simultaneously.And the respective benefit of the manager and cooperation partners is also considered simultaneously.And a cooperation planning model based on bilevel multi-objective programming is de-signed,according to the due time and total cost.And an extended CNP based on the permitted range for resource and time requests is presented.A larger task set in scheduling cycle is on the permitting for the request of cooperation resource and time while the task manager itself may be permitted biding for tasks.As a result,the optimization space for the cooperation planning is enlarged.So not every bidding task is successfully bid by invitee,and the task manager itself takes on some bidding tasks.Finally,the genetic algorithm is given and the validity and feasibility of the model is proved by a case.展开更多
This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We ...This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented.展开更多
基金supported by the Central Government Guides Local Science and Technology Development Fund Project(2023ZY0020)Key R&D and Achievement Transformation Project in InnerMongolia Autonomous Region(2022YFHH0019)+3 种基金the Fundamental Research Funds for Inner Mongolia University of Science&Technology(2022053)Natural Science Foundation of Inner Mongolia(2022LHQN05002)National Natural Science Foundation of China(52067018)Metallurgical Engineering First-Class Discipline Construction Project in Inner Mongolia University of Science and Technology,Control Science and Engineering Quality Improvement and Cultivation Discipline Project in Inner Mongolia University of Science and Technology。
文摘In this paper,a bilevel optimization model of an integrated energy operator(IEO)–load aggregator(LA)is constructed to address the coordinate optimization challenge of multiple stakeholder island integrated energy system(IIES).The upper level represents the integrated energy operator,and the lower level is the electricity-heatgas load aggregator.Owing to the benefit conflict between the upper and lower levels of the IIES,a dynamic pricing mechanism for coordinating the interests of the upper and lower levels is proposed,combined with factors such as the carbon emissions of the IIES,as well as the lower load interruption power.The price of selling energy can be dynamically adjusted to the lower LA in the mechanism,according to the information on carbon emissions and load interruption power.Mutual benefits and win-win situations are achieved between the upper and lower multistakeholders.Finally,CPLEX is used to iteratively solve the bilevel optimization model.The optimal solution is selected according to the joint optimal discrimination mechanism.Thesimulation results indicate that the sourceload coordinate operation can reduce the upper and lower operation costs.Using the proposed pricingmechanism,the carbon emissions and load interruption power of IEO-LA are reduced by 9.78%and 70.19%,respectively,and the capture power of the carbon capture equipment is improved by 36.24%.The validity of the proposed model and method is verified.
基金This research was funded by“Chunhui Program”Collaborative Scientific Research Project of the Ministry of Education of the People’s Republic of China(Project No.HZKY20220242)the S&T Program of Hebei(Project No.225676163GH).
文摘Rational distribution network planning optimizes power flow distribution,reduces grid stress,enhances voltage quality,promotes renewable energy utilization,and reduces costs.This study establishes a distribution network planning model incorporating distributed wind turbines(DWT),distributed photovoltaics(DPV),and energy storage systems(ESS).K-means++is employed to partition the distribution network based on electrical distance.Considering the spatiotemporal correlation of distributed generation(DG)outputs in the same region,a joint output model of DWT and DPV is developed using the Frank-Copula.Due to the model’s high dimensionality,multiple constraints,and mixed-integer characteristics,bilevel programming theory is utilized to structure the model.The model is solved using a mixed-integer particle swarmoptimization algorithm(MIPSO)to determine the optimal location and capacity of DG and ESS integrated into the distribution network to achieve the best economic benefits and operation quality.The proposed bilevel planning method for distribution networks is validated through simulations on the modified IEEE 33-bus system.The results demonstrate significant improvements,with the proposedmethod reducing the annual comprehensive cost by 41.65%and 13.98%,respectively,compared to scenarios without DG and ESS or with only DG integration.Furthermore,it reduces the daily average voltage deviation by 24.35%and 10.24%and daily network losses by 55.72%and 35.71%.
基金supported by the Fundamental Research Funds for the Central Universities(K50511700004)the Natural Science Basic Research Plan in Shaanxi Province of China(2013JM1022)
文摘An integer linear bilevel programming problem is firstly transformed into a binary linear bilevel programming problem, and then converted into a single-level binary implicit programming. An orthogonal genetic algorithm is developed for solving the binary linear implicit programming problem based on the orthogonal design. The orthogonal design with the factor analysis, an experimental design method is applied to the genetic algorithm to make the algorithm more robust, statistical y sound and quickly convergent. A crossover operator formed by the orthogonal array and the factor analysis is presented. First, this crossover operator can generate a smal but representative sample of points as offspring. After al of the better genes of these offspring are selected, a best combination among these offspring is then generated. The simulation results show the effectiveness of the proposed algorithm.
基金supported by the National Science Foundation of China (70771080)Social Science Foundation of Ministry of Education (10YJC630233)
文摘The penalty function method, presented many years ago, is an important nu- merical method for the mathematical programming problems. In this article, we propose a dual-relax penalty function approach, which is significantly different from penalty func- tion approach existing for solving the bilevel programming, to solve the nonlinear bilevel programming with linear lower level problem. Our algorithm will redound to the error analysis for computing an approximate solution to the bilevel programming. The error estimate is obtained among the optimal objective function value of the dual-relax penalty problem and of the original bilevel programming problem. An example is illustrated to show the feasibility of the proposed approach.
基金supported by the National Natural Science Fundation of China (60374063)
文摘Two classes of mixed-integer nonlinear bilevel programming problems are discussed. One is that the follower＇s functions are separable with respect to the follower＇s variables, and the other is that the follower＇s functions are convex if the follower＇s variables are not restricted to integers. A genetic algorithm based on an exponential distribution is proposed for the aforementioned problems. First, for each fixed leader＇s variable x, it is proved that the optimal solution y of the follower＇s mixed-integer programming can be obtained by solving associated relaxed problems, and according to the convexity of the functions involved, a simplified branch and bound approach is given to solve the follower＇s programming for the second class of problems. Furthermore, based on an exponential distribution with a parameter λ, a new crossover operator is designed in which the best individuals are used to generate better offspring of crossover. The simulation results illustrate that the proposed algorithm is efficient and robust.
基金supported by the National Natural Science Foundationof China (70771080)the National Science Foundation of Hubei Province(20091107)Hubei Province Key Laboratory of Systems Science in Metallurgical Process (B201003)
文摘Partial cooperation models are studied for many years to solve the bilevel programming problems where the follower’s optimal reaction is not unique. However, in these existed models, the follower’s cooperation level does not depend on the leader’s decision. A new model is proposed to solve this deficiency. It is proved the feasibility of the new model when the reaction set of the lower level is lower semicontinuous. And the numerical results show that the new model has optimal solutions when the reaction set of the lower level is discrete, lower semi-continuous and non-lower semi-continuous.
基金supported by the National Natural Science Foundation of China (60873099)
文摘A quadratic bilevel programming problem is transformed into a single level complementarity slackness problem by applying Karush-Kuhn-Tucker（KKT） conditions.To cope with the complementarity constraints,a binary encoding scheme is adopted for KKT multipliers,and then the complementarity slackness problem is simplified to successive quadratic programming problems,which can be solved by many algorithms available.Based on 0-1 binary encoding,an orthogonal genetic algorithm,in which the orthogonal experimental design with both two-level orthogonal array and factor analysis is used as crossover operator,is proposed.Numerical experiments on 10 benchmark examples show that the orthogonal genetic algorithm can find global optimal solutions of quadratic bilevel programming problems with high accuracy in a small number of iterations.
基金supported by the National Natural Science Foundations of China(Nos.U1933118,U2033205)。
文摘This paper proposes an optimization model for the airport ground movement problem(GMP)based on bilevel programming to address taxi conflicts on the airport ground and to improve the operating safety and efficiency.To solve GMP,an iterative heuristic algorithm is designed.Instead of separately investigating each problem,this model simultaneously coordinates and optimizes the aircraft routing and scheduling.A simulation test is conducted on Nanjing Lukou International Airport(NKG)and the results show that the bilevel programming model can clearly outperform the widely used first-come-first-service(FCFS)scheduling scheme in terms of aircraft operational time under the precondition of none conflict.The research effort demonstrates that with the reduced operating cost and the improved overall efficiency,the proposed model can assist operations of the airports that are facing increasing traffic demand and working at almost maximum capacity.
基金Supported by the National Natural Science Foundation of China(11501233)the Key Project of Anhui Province University Excellent Youth Support Plan(gxyq ZD2016102)
文摘Bilevel programming problems are of growing interest both from theoretical and practical points of view.In this paper,we study a pessimistic bilevel programming problem in which the set of solutions of the lower level problem is discrete.We first transform such a problem into a single-level optimization problem by using the maximum-entropy techniques.We then present a maximum entropy approach for solving the pessimistic bilevel programming problem.Finally,two examples illustrate the feasibility of the proposed approach.
基金supported by the Scientific Research Fun of Sichuan Normal University (11ZDL01)the Sichuan Province Leading Academic Discipline Project (SZD0406)
文摘A new class of bilcvel generalized mixed equilibrium problems involving setvalued mappings is introduced and studied in a real Banach space. By using the auxiliary principle technique, new iterative algorithms for solving the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems involving set-valued mappings are suggested and analyzed. Existence of solutions and strong convergence of the iterative sequences generated by the algorithms are proved under quite mild conditions. The behavior of the solution set of the generalized mixed equilibrium problems and bilevel generalized mixed equilibrium problems is also discussed. These results are new and generalize some recent results in this field.
基金supported by the National Natural Science Foundation of China(70771080)the Special Fund for Basic Scientific Research of Central Colleges+2 种基金China University of Geosciences(Wuhan) (CUG090113)the Research Foundation for Outstanding Young TeachersChina University of Geosciences(Wuhan)(CUGQNW0801)
文摘A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.
基金Supported by the Educational Commission of Liaoning Province Science and Technology Research Projects(L2013237)
文摘Steel-making and continuous/ingot casting are the key processes of modern iron and steel enterprises. Bilevel programming problems(BLPPs) are the optimization problems with hierarchical structure. In steel-making production, the plan is not only decided by the steel-making scheduling, but also by the transportation equipment.This paper proposes a genetic algorithm to solve continuous and ingot casting scheduling problems. Based on the characteristics of the problems involved, a genetic algorithm is proposed for solving the bilevel programming problem in steel-making production. Furthermore, based on the simplex method, a new crossover operator is designed to improve the efficiency of the genetic algorithm. Finally, the convergence is analyzed. Using actual data the validity of the proposed algorithm is proved and the application results in the steel plant are analyzed.
文摘In this paper, a new algorithm-approximate penalty function method is designed, which can be used to solve a bilevel optimization problem with linear constrained function. In this kind of bilevel optimization problem. the evaluation of the objective function is very difficult, so that only their approximate values can be obtained. This algorithm is obtained by combining penalty function method and approximation in bilevel programming. The presented algorithm is completely different from existing methods. That convergence for this algorithm is proved.
基金Supported by the Key Project on Science and Technology of Hubei Provincial Department of Education (D20103001)
文摘In this paper,following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition,we transform the nonlinear bilevel programming problem into a normal nonlinear programming problem with the complementary slackness constraint condition.Then,we get the penalized problem of the normal nonlinear programming problem by appending the complementary slackness condition to the upper level objective with a penalty.We prove that this penalty function is exact and the penalized problem and the nonlinear bilevel programming problem have the same global optimal solution set.Finally,we propose an algorithm for the nonlinear bilevel programming problem.The numerical results show that the algorithm is feasible and efficient.
基金Supported by the National Natural Science Foundation of China(11501233)the Key Project of Anhui Province University Excellent Youth Support Plan(gxyqZD2016102)
文摘We present a new variant of penalty method, which is different from the existing penalty methods, for solving the weak linear bilevel programming problems. We then transform it into a single-level optimization problem using Kuhn-Tucker optimality condition and discuss the relations between them. Finally, two examples are used to illustrate the feasibility of the proposed penalty method.
基金Supported by the National Natural Science Foundation of China(11501233)the Natural Science Research Project of Universities of Anhui Province(KJ2018A0390)
文摘Most real-world optimization problems are hierarchical involving non-cooperative objectives. Many of these problems can be formulated in terms of the first（upper level） objective function being minimized over the solution set mapping of the second（lower level） optimization problem. Often the upper level decision maker is risk-averse. The resulting class of problem is named weak bilevel programming problem. This paper presents a new algorithm which embeds a penalty function method into a branch and bound algorithm to deal with a weak linear bilevel programming problem. An example illustrates the feasibility of the proposed algorithm.
基金Supported by the National Natural Science Foundation of China(Grant No.11171250)
文摘For a multiobjective bilevel programnfing problem （P） with an extremal-value function, its dual problem is constructed by using the Fenchel-Moreau conjugate of the functions involved. Under some convexity and monotonicity assumptions, the weak and strong duality assertions are obtained.
基金Supported by the National Natural Science Foundation of China (70371032,60574071)
文摘By applying Kuhn-Tucker condition the quadratic bilevel programming, a class of bilevel programming, is transformed into a single level programming problem, which can be simplified by some rule. So we can search the optimal solution in the feasible region, hence reduce greatly the searching space. Numerical experiments on several literature problems show that the new algorithm is both feasible and effective in practice.
基金Supported by the National Natural Science Foundation of China under Grant No.70471073the Natural Science Foundation of Jiangsu Education Department of China under Grant No.04KJB520169.
文摘This paper is based on a resource constrained active network project;the constraint of the local resource and the time constraint of the cooperation resource are considered simultaneously.And the respective benefit of the manager and cooperation partners is also considered simultaneously.And a cooperation planning model based on bilevel multi-objective programming is de-signed,according to the due time and total cost.And an extended CNP based on the permitted range for resource and time requests is presented.A larger task set in scheduling cycle is on the permitting for the request of cooperation resource and time while the task manager itself may be permitted biding for tasks.As a result,the optimization space for the cooperation planning is enlarged.So not every bidding task is successfully bid by invitee,and the task manager itself takes on some bidding tasks.Finally,the genetic algorithm is given and the validity and feasibility of the model is proved by a case.
文摘This study addresses bilevel linear multi-objective problem issues i.e the special case of bilevel linear programming problems where each decision maker has several objective functions conflicting with each other. We introduce an artificial multi-objective linear programming problem of which resolution can permit to generate the whole feasible set of the upper level decisions. Based on this result and depending if the leader can evaluate or not his preferences for his different objective functions, two approaches for obtaining Pareto- optimal solutions are presented.
