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bilevel optimization problem With Random-Term-Absent Max-Product Fuzzy Relation Inequalities Constraint

IEEE TRANSACTIONS ON FUZZY SYSTEMS 2021年第11期29卷 3374-3388页

作者： Qiu, Jianjun 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

The max-product fuzzy relation inequalities have been applied to describe the quantitative relation in a wireless communication base-station system in the existing work. However, the potential line fault between a base station and a signal testing point has not been considered. In this article, we define the so-called random-term-absent max-product fuzzy relation inequalities for describing the wireless communication base-station system with a random line fault. Based on the practical application consideration, we further construct a bilevel optimization problem subject to random-term-absent max-product fuzzy relation inequalities. For solving such bilevel optimization problem, properties of the random-term-absent system, as well as the common single-level fuzzy relation programming, are investigated. At last, a detailed algorithm is developed to find the optimal solution of our proposed bilevel optimization problem.

关键词： optimization Wireless communication Programming Mathematical model Testing Streaming media Servers bilevel optimization problem fuzzy relation inequality max-product composition optimization algorithm random-term-absent (RTA) solution matrix

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On the Karush-Kuhn-Tucker reformulation of the bilevel optimization problem

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2012年第3期75卷 1202-1218页

作者： Dempe, S. Zemkoho, A. B. Tech Univ Bergakad Freiberg Inst Numer Math & Optimizat D-09596 Freiberg Germany

This paper is mainly concerned with the classical KKT reformulation and the primal KKT reformulation (also known as an optimization problem with generalized equation constraint (OPEC)) of the optimistic bilevel optimization problem. A generalization of the MFCQ to an optimization problem with operator constraint is applied to each of these reformulations, hence leading to new constraint qualifications (CQs) for the bilevel optimization problem. M- and S-type stationarity conditions tailored for the problem are derived as well. Considering the close link between the aforementioned reformulations, similarities and relationships between the corresponding CQs and optimality conditions are highlighted. In this paper, a concept of partial calmness known for the optimal value reformulation is also introduced for the primal KKT reformulation and used to recover the M-stationarity conditions. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： bilevel optimization problem KKT reformulation Set-valued mapping Basic CQ Optimality conditions

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Portfolio-Consumption Choice with Information Cost

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JOURNAL OF THE OPERATIONS RESEARCH SOCIETY OF CHINA 2025年第1期13卷 184-209页

作者： Yang, Zhou Mai, Rui-Feng Lv, Man-Ni South China Normal Univ Sch Math Sci Guangzhou 510631 Guangdong Peoples R China Wuhan Univ Econ & Management Sch Wuhan 430072 Hubei Peoples R China

This paper studies an optimal portfolio-consumption choice with information cost. In financial market, investors collect market information to understand the market parameters, make reasonable investment and consumption choice while controlling risks, and finally gain utility. Information acquisition and portfolio-consumption choice are two important steps of investment behavior, which are a whole. Nevertheless, the existing literature usually only considers the cost of information acquisition or only considers portfolio-consumption choice. In order to study the overall behavior of investors in financial market, these two issues are considered together in this paper. Firstly, based on portfolio-consumption choice model in ambiguity market, a bilevel optimization problem is established to discuss how investors should acquire information and make investment-consumption strategies to maximize their comprehensive utilities. Then, the inner stochastic game problem with constraints is simplified into finding saddle point of a function, and the value function of game problem is provided via the function value at the saddle point, so that the objective function of the outer optimization problem can be represented as a non-convex and non-concave binary function. At last, the existence condition and the range of the optimal strategy are presented, and the sensitivity analysis is studied.

关键词： Portfolio-consumption choice bilevel optimization problem Information cost Market ambiguity

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bilevel optimization problemS OF DISTRIBUTION OF INTERBUDGETARY TRANSFERS UNDER GIVEN LIMITATIONS

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CYBERNETICS AND SYSTEMS ANALYSIS 2019年第6期55卷 905-913页

作者： Sergienko, I. V. Semenova, N. V. Semenov, V. V. Natl Acad Sci Ukraine VM Glushkov Inst Cybernet Kiev Ukraine

The problems of optimal distribution of transfers within given budget limitations are formulated and analyzed. The mathematical model is presented as a bilevel linear optimization problem that contains linear problems of integer optimization at the lower level. Both optimistic and pessimistic versions of the problem are considered. Far the approximate solution of optimistic version, the algorithm of finding local solutions for parametric lower-level integer programming problems on the basis of the method of directing neighborhoods is proposed. The auxiliary integer progrannning problem with Boolean variables of a higher level is solved bused on local algorithms.

关键词： bilevel optimization problem integer optimization parametric programming Boolean variables local algorithm

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A projection-based recurrent neural network and its application in solving convex quadratic bilevel optimization problems

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NEURAL COMPUTING & APPLICATIONS 2020年第8期32卷 3887-3900页

作者： Golbabai, Ahmad Ezazipour, Soraya Iran Univ Sci & Technol Fac Math Sci Dept Appl Math POB 16846-13114 Tehran Iran

In this paper, a projection-based recurrent neural network is proposed to solve convex quadratic bilevel programming problems (CQBPP). The Karush-Kuhn-Tucker optimal conditions (KKT) of the lower level problem are used to obtain identical one-level optimization problem. A projected dynamical system which its equilibrium point coincides with the global optimal solution of the corresponding optimization problem is presented. Compared to existing models, the proposed model has the least number of variables and a simple structure with low complexity. Analytically, it is demonstrated that the state vector of the suggested neural network model is stable in the sense of Lyapunov and globally convergent to an optimal solution of CQBPP in finite time. Some numerical examples, a supply chain model and an application deals with an environmental problem are discussed in order to confirm the efficiency of the theoretical results and the performance of the model.

关键词： bilevel optimization problem Artificial neural network Dynamical systems Globally convergent

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The formulation of the optimal strategies for the electricity producers based on the particle swarm optimization algorithm

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IEEE TRANSACTIONS ON POWER SYSTEMS 2006年第4期21卷 1663-1671页

作者： Ma, Yuchao Jiang, Chuanwen Hou, Zhijian Wang, Chenming Shanghai Jiao Tong Univ Dept Elect Engn Shanghai 200030 Peoples R China

In competitive electricity markets, the producer as a market participant strives to find the optimal supply function with the objective of maximizing his/her producer surplus in the market clearing. The model of the producer surplus maximization is a bilevel mathematical programming problem within which the market clearing is taken into account. By using the deterministic approaches, it is difficult to obtain the global solution of the bilevel optimization problem, even for a single hourly market clearing. This is due to the fact that the objective function of such a problem is not concave, and there are nonlinear complementarity terms introduced by using the KKT conditions to represent the market clearing. When the bilevel optimization problem is modified to consider multiple hourly market clearings, such as to maximize the total producer surplus in one day, solving such a problem is almost intractable. A heuristic approach should be another option. For its simplicity and immunity to the local optimum, the particle swarm optimization (PSO) algorithm is employed in this paper to find the optimal supply function of the electricity producer. Based on the IEEE 30-bus test system, different simulation cases with respect to a single hourly market clearing and a daily market clearing are tested to show the efficiency and robustness of the PSO algorithm. In addition, the parameterization techniques used in formulating the optimal supply function are analyzed based on the simulation results.

关键词： bilevel optimization problem optimal supply function particle swarm optimization (PSO)

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Necessary optimality conditions for optimistic bilevel programming problems using set-valued programming

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JOURNAL OF GLOBAL optimization 2015年第4期61卷 769-788页

作者： Dempe, Stephan Pilecka, Maria Tech Univ Bergakad Freiberg Dept Math & Comp Sci D-09596 Freiberg Germany

In this paper we adapt the main results from Amahroq and Gadhi (J Glob Optim 21:435-443, 2001) for a general set-valued optimization problem to an optimistic bilevel programming problem as an optimization problem with implicitly given set-valued constraint. Since this constraint is assumed to be upper but not lower semicontinuous in the sense of Berge, we need to deal with a lower semicontinuous distance function to this mapping. In order to approximate the gradient of the distance function, we introduce a new concept for a directional convexificator. Some calculus rules for this new tool are adapted and several properties are characterized. The main result presents optimality conditions for an optimistic bilevel programming problem using a convexificator constructed with the aid of the directional convexificator.

关键词： bilevel optimization problem Convexificators Necessary optimality conditions Support function

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An agile vehicle-based dynamic user equilibrium scheme for urban traffic signal control

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IET INTELLIGENT TRANSPORT SYSTEMS 2021年第5期15卷 619-634页

作者： Liu, Wei-Li Gong, Yue-Jiao Chen, Wei-Neng Zhang, Jun Dou, Zhi South China Univ Technol Sch Comp Sci & Engn Guangzhou 510006 Peoples R China Univ Victoria Melbourne Vic Australia Henan Normal Univ Coll Comp & Informat Engn Xinxiang Henan Peoples R China Guangdong Polytech Normal Univ Sch Comp Sci Guangzhou Peoples R China

Traffic Signal Control (TSC) is a fundamental task in modern intelligent transport systems. TSC is often formulated as a bi-level optimization problem, comprised by the signal timing at the upper level and the Dynamic User Equilibrium (DUE) traffic assignment at the lower level. Since DUE is non-convex, existing methods either formulate approximation models or adopt traffic simulators. However, approximation models may oversimplify the practical situations, while traffic simulators are usually time-consuming. This paper formulates a vehicle-based DUE (vDUE) model and proposes an agile method that can simultaneously maintain the computational simplicity and the traffic dynamics for the traffic assignment. Further, an agile TSC system is built by combining the vDUE at the lower level for the traffic assignment with an adaptive differential evolution algorithm at the upper level for the signal timing optimization. To enhance the effectiveness of optimization, the TSC problem formulation is also improved to make it better characterize the practical requirements. In the experiments undertaken, comparisons of different TSC methods are carried out on both real-world and synthetic transportation networks. The experimental results validate the effectiveness of the proposed agile TSC system in various traffic situations.

关键词： Traffic engineering computing signal timing optimization adaptive differential evolution algorithm bilevel optimization problem agile vehicle-based dynamic user equilibrium scheme Optimisation techniques road traffic control agile TSC system nonconvex model vehicle-based DUE model traffic dynamics urban traffic signal control traffic situations optimisation intelligent transport systems TSC problem formulation evolutionary computation dynamic user equilibrium traffic assignment traffic simulators traffic engineering computing approximation models

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Inferring oncoenzymes in a genome-scale metabolic network for hepatocytes using bilevel optimization framework

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JOURNAL OF THE TAIWAN INSTITUTE OF CHEMICAL ENGINEERS 2018年 91卷 97-104页

作者： Wu, Wu-Hsiung Chien, Chen-Yu Wu, Yu-Hao Wu, Hsuan-Hui Lai, Jin-Mei Chang, Peter Mu-Hsin Huang, Chi-Ying F. Wang, Feng-Sheng Natl Chung Cheng Univ Dept Chem Engn 168Sec 1Univ Rd Chiayi 62102 Taiwan Natl Yang Ming Univ Inst Biopharmaceut Sci Taipei 11211 Taiwan Fu Jen Catholic Univ Dept Life Sci New Taipei City Hsien 24205 Taiwan Taipei Vet Gen Hosp Dept Oncol Taipei 11217 Taiwan Natl Yang Ming Univ Fac Med Taipei 11211 Taiwan Natl Yang Ming Univ Dept Biotechnol & Lab Sci Med Taipei 11211 Taiwan

Cancer cells exhibit unusual metabolic activity, characterized by high rates of glucose consumption and lactate production, even under aerobic conditions, as well as increased glutamine catabolism and amino acid metabolism. Based on the behaviors of metabolic reprogramming, we can infer oncogenesis from a genome-scale model of cancer cell metabolism. This study establishes a bilevel optimization formulation that integrates the genome-scale metabolic model of hepatocytes, the Warburg hypothesis, and LC/MS experimental data to detect multiple-hit enzyme deficiencies that induce metabolic reprogramming in hepatocytes. A nested hybrid differential evolution algorithm was employed to solve the bilevel optimization problem. The results predicted dopa decarboxylase (DDC) to be an influential enzyme that causes oncogenesis. A cluster analysis of the flux variations for different enzyme deficiencies obtained through a flux variability analysis showed that DDC is a dominant overexpressed enzyme, and it was classified into a group with similar trends of flux and metabolite alternations. (C) 2018 Taiwan Institute of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Oncoenzyme bilevel optimization problem Ddc gene

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Regularization-based modulation transfer function compensation for optical satellite image restoration using joint statistical model in curvelet domain

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JOURNAL OF APPLIED REMOTE SENSING 2020年第3期14卷

作者： Wong, Soo Mee Ong, Simying Chan, Chee Seng Univ Malaya Ctr Image & Signal Proc Fac Comp Sci & Informat Technol Kuala Lumpur Malaysia

The heavy-tailed properties of modulation transfer function (MTF) typically introduce noise and an aliasing effect in the MTF compensation (MTFC) effort to improve the spatial quality of optical satellite images. These degradative effects compromise the image's signal-to-noise ratio (SNR). Consequently, users must evaluate the relative importance of image sharpness versus SNR for their applications to decide whether MTFC processing is appropriate. We propose a high-fidelity MTFC method that executes an optimal trade-off between noise regularization and detail preservation in the image restoration process to address this problem. To this end, we exploit the merit of image prior characteristics in both local smoothness and nonlocal self-similarity properties of an image in a hybrid domain (viz., space spatial and frequency) to design effective regularization terms that reflect these image properties. Furthermore, we establish a simple joint statistical model in the curvelet domain to combine these two properties. To make this regularization-based MTFC method tractable and robust, we employ the multiobjective bilevel optimization approach to solve the severely ill-posed inverse problem of MTFC. We conduct extensive experiments to evaluate the proposed regularization-based MTFC method using synthetically blurred images simulated from the level 2A product of IKONOS and real satellite images with unknown blur. Quantitative measurements of image quality reveal that the proposed method produces competitive restoration results with minimum computational complexity and exhibits a good convergence property. These experimental results show that the proposed method can find a compromise between regularizing noise and preserving image fidelity. (C) 2020 Society of Photo-Optical Instrumentation Engineers (SPIE)

关键词： regularization terms modulation transfer function image priors joint statistical model spatial image quality bilevel optimization problem

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