An exact penalty on bilevel programs with linear vector optimization lower level

Ankhili, Z.; Mansouri, Abdelatif

doi:10.1016/j.ejor.2008.06.026

Cited by 64 publications

(42 citation statements)

References 18 publications

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“…The optimistic formulation assumes that the follower accepts any efficient solution to the lower level problem. Other methods based on penalty functions were further proposed by Ankhili and Mansouri [23], Zheng and Wan [24], Zheng et al [25] and Ren and Wang [26] for the SVBP with multi-objective linear programming (MOLP) problems in the lower level. Calvete and Galé [27] also focused on bilevel problems with lower level MOLP problems.…”

Section: Semivectorial Bilevel Programmingmentioning

confidence: 99%

A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing

Alves

Antunes

2018

Computers & Operations Research

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Presently, residential electricity consumers are, in general, charged at flat or dual time-of-use tariffs along the day, which are defined by the retailer for long periods (e.g., one year). These pricing schemes do not convey price signals reflecting generation costs and grid conditions. Hence, consumers lack the incentives to engage in different consumption patterns using the flexibility they generally have in the operation of some end-use loads. Dynamic tariffs, i.e. energy prices varying possibly with significant magnitude in short periods of time, are expected to become an applicable pricing scheme in smart grids. In this setting, home energy management systems can play an important role to help end-users optimizing the usage of appliances to minimize energy costs without compromising comfort. This can be advantageous also from the perspective of grid management.A semivectorial bilevel programming approach is developed to model the interaction between electricity retailers and consumers in order to optimize electricity time-of-use retail pricing. The aim is to support the retailer in finding good decisions for the prices. The retailer (upper level decision maker) establishes dynamic time-of-use electricity prices to maximize profits. The consumer (lower level decision maker) responds by selecting, under that price setting, a load scheduling decision leading to a nondominated solution balancing his objectives of minimizing the electricity bill (cost dimension) and minimizing the dissatisfaction in face of his preferences and requirements (comfort dimension).The lower level optimization problem is formulated as a bi-objective mixed-integer linear programming problem. A hybrid approach is proposed, which consists of a genetic algorithm for the upper level problem and an exact solver to solve surrogate scalar problems at the lower level. A case study is presented and discussed.

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Section: Semivectorial Bilevel Programmingmentioning

confidence: 99%

A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing

Alves

Antunes

2018

Computers & Operations Research

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“…3 School of Mathematics and Statistics, Southwest University, Chongqing, 400715, China. 4 School of Economics and Management, China University of Geosciences, Wuhan, 430074, China.…”

Section: Necessary Optimality Conditions Using the Bilevel Optimal Vamentioning

confidence: 99%

Optimality conditions for pessimistic semivectorial bilevel programming problems

et al. 2014

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In this paper, a class of pessimistic semivectorial bilevel programming problems is investigated. By using the scalarization method, we transform the pessimistic semivectorial bilevel programming problem into a scalar objective optimization problem with inequality constraints. Furthermore, we derive a generalized minimax optimization problem using the maximization bilevel optimal value function, of which the sensitivity analysis is constructed via the lower-level value function approach. Using the generalized differentiation calculus of Mordukhovich, the first-order necessary optimality conditions are established in the smooth setting. As an application, we take the optimality conditions of the bilevel programming problems with multiobjective lower level problem when the lower level multiobjective optimization problem is linear with respect to the lower-level variables. MSC: 90C26; 90C30; 90C31; 90C46

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“…Then, an exact penalized function approach is proposed and some numerical results are reported; subsequently, following the outline in [9] and regarding the lower level objective weights as the upper level decision variables, L v and W a n [10] propose another exact penalty function approach. For the linear BMPP, where the leader has single objective and the follower has multiple objectives, A n k h i l i and M a n s o u r i [11] take the margin function of the lower level problem as the penalty term, and construct the corresponding penalized problem. Then, an exact penalty function algorithm is proposed for the above BMPP.…”

Section: Introductionmentioning

confidence: 99%

Particle Swarm Optimization Based on Smoothing Approach for Solving a Class of Bi-Level Multiobjective Programming Problem

2017

Cybernetics and Information Technologies

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An exact penalty on bilevel programs with linear vector optimization lower level

Cited by 64 publications

References 18 publications

A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing

A semivectorial bilevel programming approach to optimize electricity dynamic time-of-use retail pricing

Optimality conditions for pessimistic semivectorial bilevel programming problems

Particle Swarm Optimization Based on Smoothing Approach for Solving a Class of Bi-Level Multiobjective Programming Problem

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