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A Trust Region Algorithm for Solving bilevel programming problems

Acta Mathematicae Applicatae Sinica 2013年第3期29卷 491-498页

作者： Guo-shan LIU Shi-qin XU Ji-ye HAN School of Business Renmin University of China Academy of Mathematics and Systems Science Chinese Academy of Sciences

In this paper, we present a new trust region algorithm for a nonlinear bilevel programming problem by solving a series of its linear or quadratic approximation subproblems. For the nonlinear bilevel programming problem in which the lower level programming problem is a strongly convex programming problem with linear constraints, we show that each accumulation point of the iterative sequence produced by this algorithm is a stationary point of the bilevel programming problem.

关键词： bilevel programming problem trust region algorithm global convergence mathematical program with equilibrium constraints stationary point

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A genetic algorithm for solving linear integer bilevel programming problems 14

A genetic algorithm for solving linear integer bilevel progr...

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14th International Conference on Computational Intelligence and Security (CIS)

作者： Liu Yuhui Li Hecheng Chen Huafei Qinghai Normal Univ Sch Comp Sci & Technol Xining 810008 Qinghai Peoples R China Qinghai Normal Univ Sch Math & Stat Xining 810008 Qinghai Peoples R China Sichuan Univ Sci & Engn Sch Math & Stat Zigong 643000 Peoples R China

ISBN: (纸本)9781728101699

This manuscript discusses a class of linear integer bilevel programming problems, in which the objective functions and the constraints are linear. A genetic algorithm based on gradient information guidance is proposed for this kind of problems. First of all, for each fixed upper-level variable x, it is proved that the optimal solution y to the lower level integer programming problem can be obtained by solving associated relaxed problems, and then a simplified branch and bound approach is used to solve the follower-level programming problems. In addition, a crossover operator based on gradient information guidance is designed, and the descendant individual is produced in the negative gradient direction of the upper-level function. The simulation results illustrate that the proposed algorithm is efficient and robust.

关键词： bilevel programming problem genetic algorithm integer programming gradient information optimal solutions

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Solving bilevel programming problems Using a Neural Network Approach and Its Application to Power System Environment

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SICE Journal of Control, Measurement, and System Integration 2011年第6期4卷 387-393页

作者： Shamshul Bahar Yaakob Junzo Watada Graduate School of Information Production and Systems Waseda University

In this paper, a hybrid neural network approach to solve mixed integer quadratic bilevel programming problems is proposed. bilevel programming problems arise when one optimization problem, the upper problem, is constrained by another optimization, the lower problem. The mixed integer quadratic bilevel programming problem is transformed into a double-layered neural network. The combination of a genetic algorithm (GA) and a meta-controlled Boltzmann machine (BM) enables us to formulate a hybrid neural network approach to solving bilevel programming problems. The GA is used to generate the feasible partial solutions of the upper level and to provide the parameters for the lower level. The meta-controlled BM is employed to cope with the lower level problem. The lower level solution is transmitted to the upper level. This procedure enables us to obtain the whole upper level solution. The iterative processes can converge on the complete solution of this problem to generate an optimal one. The proposed method leads the mixed integer quadratic bilevel programming problem to a global optimal solution. Finally, a numerical example is used to illustrate the application of the method in a power system environment, which shows that the algorithm is feasible and advantageous.

关键词： Boltzmann machine meta-controlled Boltzmann machine bilevel programming problem mixed-integer quadratic problem

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Integrating link-based discrete credit charging scheme into discrete network design problem

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EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2019年第1期272卷 176-187页

作者： Wang, Guangmin Gao, Ziyou Xu, Meng China Univ Geosci Sch Econ & Management Wuhan 430074 Hubei Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China Beijing Jiaotong Univ State Key Lab Rail Traff Control & Safety Beijing 100044 Peoples R China

In this paper, we present an optimization model for integrating link-based discrete credit charging scheme into the discrete network design problem, to improve the transport performance from the perspectives of both transport network planning and travel demand management. The proposed model is a mixed-integer nonlinear bilevel programming problem, which includes an upper level problem for the transport authority and a lower level problem for the network users. The lower level sub-model is the traffic network user equilibrium (UE) formulation for a given network design strategy determined by the upper level problem. The network user at the lower level tries to minimize his/her own generalized travel cost (including both the travel time and the value of the credit charged for using the link) by choosing his/her route. While the transport authority at the upper level tries to find the optimal number of lanes and credit charging level with their locations to minimize the total system travel time (or maximize the transportation system performance). A genetic algorithm is used to solve the proposed mixed-integer nonlinear bilevel programming problem. Numerical experiments show the efficiency of the proposed model for traffic congestion mitigation, reveal that interaction effects across the tradable credit scheme and the discrete network design problem which amplify their individual effects. Moreover, the integrated model can achieve better performance than the sequential decision problems. (C) 2018 Elsevier B.V. All rights reserved.

关键词： Transportation Discrete network design problem (DNDP) bilevel programming problem Tradable credit scheme (TCS)

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Fuzzy Relation bilevel Optimization Model in the Wireless Communication Station System

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IEEE ACCESS 2020年 8卷 60811-60823页

作者： Qiu, Jianjun Xue, Huanbin Li, Guanrong Yang, Xiaopeng Lingnan Normal Univ Sch Math & Stat Zhanjiang 524048 Peoples R China Hanshan Normal Univ Sch Math & Stat Chaozhou 521041 Peoples R China

In order to minimize the intensity of electromagnetic radiation, as well as the operation cost of the base stations in a wireless communication station system, we construct a bilevel programming problem with max-product fuzzy relation inequalities constraint. We first investigate the first level programming problem based on the concept of minimal solution matrix. The complete optimal solution set of the first level problem, as a union of a finite number of closed intervals, is a non-convex infinite set in some cases. Hence the second level programming is a nonlinear optimization problem with non-convex feasible domain. For solving the second level programming, we convert it into a discrete optimization problem, in which the constraint is the set of all minimum max-norm matrix solutions. Furthermore, the discrete optimization problem is equivalently converted into a 0-1 integer programming problem, which could be solved by the famous branch-and-bound technique. Numerical examples are given to illustrate the feasibility and efficiency of our proposed algorithm. In addition, the bilevel programming problem is further generalized and discussed considering a wider range of managerial requirements.

关键词： Fuzzy relation inequality bilevel programming problem max-product composition nonlinear optimization minimum max-norm matrix solution

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Joint link-based credit charging and road capacity improvement in continuous network design problem

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TRANSPORTATION RESEARCH PART A-POLICY AND PRACTICE 2014年 67卷 1-14页

作者： Wang, Guangmin Gao, Ziyou Xu, Meng Sun, Huijun China Univ Geosci Sch Econ & Management Wuhan 430074 Peoples R China Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China

In this paper, we will discuss the urban road network improvement problem from both supply and demand sides, and propose a bilevel programming model considering joint optimal link-based tradable credit charging scheme and road capacity improvement. The upper level decision-maker tries to minimize the total system travel time under a budget constraint by optimizing both link-based credit charging and road capacity improvement, whilst at the lower level considering the users' route choice behavior through the generalized travel time including the travel time and the converted time from the value of credit charging for using the link. Therefore, this proposed model integrates the improvement of the urban road network according to improving the road capacity with the given budget constraint and decreasing the travel demand with the tradable credit scheme. After presenting a relaxation algorithm, the numerical experiments on the nine node network are illustrated. Analysis shows that the proposed model is efficient in mitigating traffic congestion according to the less total system travel time than the other ways compared in this paper. The tradable credit scheme offers the better combination of cost-effectiveness, administrative flexibility and distributional fairness comparing with congestion pricing. Moreover, this tradable credit scheme is revenue neutral. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Continuous network design problem (CNDP) bilevel programming problem Relaxation algorithm Tradable credit scheme

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Worst-case traffic assignment model for mixed traffic flow of human-driven vehicles and connected and autonomous vehicles by factoring in the uncertain link capacity

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TRANSPORTATION RESEARCH PART C-EMERGING TECHNOLOGIES 2022年 140卷

作者： Wang, Jian Wang, Wei Ren, Gang Yang, Min Southeast Univ Jiangsu Prov Collaborat Innovat Ctr Modern Urban T Sch Transportat Jiangsu Key Lab Urban ITS Nanjing 211189 Peoples R China

Connected and autonomous vehicles (CAVs) can form platoons to reduce the time headway and improve the link capacity. However, in a mixed traffic flow environment where both human driven vehicles (HDVs) and CAVs exist, the platoon intensity is significantly impacted by the stochastic order of the HDVs and CAVs (i.e., the fleet sequence). Therefore, the link capacity involves a large uncertainty even under the same HDV and CAV flow. This uncertain link capacity can cause a large variation in network flow. In the literature, traffic assignment models for mixed traffic flows of HDVs and CAVs are developed based on expected link capacity models, in which the computed link capacity is deterministic for given HDV and CAV flows. These models ignore the impacts of uncertain link capacity on the network performance and network flow distribution, which can dramatically reduce the effectiveness of the corresponding planning strategies. To address this problem, this study proposes a worst-case mixed traffic assignment model. It aims to compute the worst network performance and corresponding equilibrium flow that may occur due to uncertain link capacity. The worst-case mixed traffic assignment is formulated as a bilevel programming problem, where the low-level problem is a variational inequality problem presented to compute the equilibrium results based on a fixed link capacity while the upper-level problem is to find the optimal input for all link capacities within their ranges to minimize the network performance. The partition-based norm relaxed method of the feasible direction solution algorithm is proposed to solve the bilevel worst-case mixed traffic assignment problem. A numerical application shows that the uncertain link capacity has drastic effects on the network flows and network performance, and the proposed algorithm can effectively and efficiently solve the bilevel worst-case mixed traffic assignment problem to compute the worst-case network equilibrium flows and netw

关键词： Connected and autonomous vehicles Mixed traffic assignment model bilevel programming problem Sensitivity analysis

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bilevel approach for optimal location and contract pricing of distributed generation in radial distribution systems using mixed-integer linear programming

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IET GENERATION TRANSMISSION & DISTRIBUTION 2013年第7期7卷 724-734页

作者： Rider, Marcos J. Lopez-Lezama, Jesus Maria Contreras, Javier Padilha-Feltrin, Antonio UNESP Univ Estadual Paulista Fac Engn Ilha Solteira Dept Engn Eletr Sao Paulo Brazil Univ Antioquia Efficient Energy Management Res Grp GIMEL Dept Elect Engn Medellin Colombia Univ Castilla La Mancha ETS Ingenieros Ind E-13071 Ciudad Real Spain

In this study, a novel approach for the optimal location and contract pricing of distributed generation (DG) is presented. Such an approach is designed for a market environment in which the distribution company (DisCo) can buy energy either from the wholesale energy market or from the DG units within its network. The location and contract pricing of DG is determined by the interaction between the DisCo and the owner of the distributed generators. The DisCo intends to minimise the payments incurred in meeting the expected demand, whereas the owner of the DG intends to maximise the profits obtained from the energy sold to the DisCo. This two-agent relationship is modelled in a bilevel scheme. The upper-level optimisation is for determining the allocation and contract prices of the DG units, whereas the lower-level optimisation is for modelling the reaction of the DisCo. The bilevel programming problem is turned into an equivalent single-level mixed-integer linear optimisation problem using duality properties, which is then solved using commercially available software. Results show the robustness and efficiency of the proposed model compared with other existing models. As regards to contract pricing, the proposed approach allowed to find better solutions than those reported in previous works.

关键词： distributed power generation duality (mathematics) integer programming linear programming power distribution economics pricing 34-node test-distribution system duality properties equivalent single-level mixed-integer linear optimisation problem lower-level optimisation upper-level optimisation two-agent relationship bilevel programming problem DisCo distribution company market environment radial distribution systems DG distributed generation contract pricing optimal location

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bilevel programming for generating discrete representations in multiobjective optimization

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MATHEMATICAL programming 2018年第2期169卷 585-604页

作者： Kirlik, Gokhan Sayin, Serpil Univ Maryland Med Syst Enterprise Data & Analyt Linthicum MD 21090 USA Koc Univ Coll Adm Sci & Econ TR-34450 Istanbul Turkey

The solution to a multiobjective optimization problem consists of the nondominated set that portrays all relevant trade-off information. The ultimate goal is to identify a Decision Maker's most preferred solution without generating the entire set of nondominated solutions. We propose a bilevel programming formulation that can be used to this end. The bilevel program is capable of delivering an efficient solution that maps into a given set, provided that one exits. If the Decision Maker's preferences are known a priori, they can be used to specify the given set. Alternatively, we propose a method to obtain a representation of the nondominated set when the Decision Maker's preferences are not available. This requires a thorough search of the outcome space. The search can be facilitated by a partitioning scheme similar to the ones used in global optimization. Since the bilevel programming formulation either finds a nondominated solution in a given partition element or determines that there is none, a representation with a specified coverage error level can be found in a finite number of iterations. While building a discrete representation, the algorithm also generates an approximation of the nondominated set within the specified error factor. We illustrate the algorithm on the multiobjective linear programming problem.

关键词： Multiobjective optimization Decision Maker Representation Nondominated set Coverage error bilevel programming problem

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Necessary Optimality Conditions for Multiobjective bilevel Programs

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MATHEMATICS OF OPERATIONS RESEARCH 2011年第1期36卷 165-184页

作者： Ye, Jane J. Univ Victoria Dept Math & Stat Victoria BC V8W 3R4 Canada

The multiobjective bilevel program is a sequence of two optimization problems, with the upper-level problem being multiobjective and the constraint region of the upper level problem being determined implicitly by the solution set to the lower-level problem. In the case where the Karush-Kuhn-Tucker (KKT) condition is necessary and sufficient for global optimality of all lower-level problems near the optimal solution, we present various optimality conditions by replacing the lower-level problem with its KKT conditions. For the general multiobjective bilevel problem, we derive necessary optimality conditions by considering a combined problem, with both the value function and the KKT condition of the lower-level problem involved in the constraints. Most results of this paper are new, even for the case of a single-objective bilevel program, the case of a mathematical program with complementarity constraints, and the case of a multiobjective optimization problem.

关键词： multiobjective optimization preference necessary optimality condition partial calmness constraint qualification nonsmooth analysis value function bilevel programming problem

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