Multiobjective bilevel optimization

Eichfelder, Gabriele

doi:10.1007/s10107-008-0259-0

Cited by 142 publications

(75 citation statements)

References 26 publications

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“…x and y, that is, in this work, we adopt the optimistic approach to consider the bilevel multiobjective programming problem [12].…”

Section: ð2:1þmentioning

confidence: 99%

“…Besides, Bonnel and Morgan [3], Zheng and Wan [25] considered a so-called semivectorial bilevel optimization problem and proposed solution methods based on penalty approach. A recent study by Eichfelder [12] suggested a refinement-based strategy in which the algorithm starts with a uniformly distributed set of points on upper level variable. The difficulty with such a technique is that if the dimension of upper level variable is high, generating a uniformly spread upper level variables and refining the resulting upper level variable will be computationally expensive.…”

Section: Introductionmentioning

confidence: 99%

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A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

Wan

2014

J. Oper. Res. Soc. China

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In this paper, a bilevel multiobjective programming problem, where the lower level is a convex parameter multiobjective program, is concerned. Using the KKT optimality conditions of the lower level problem, this kind of problem is transformed into an equivalent one-level nonsmooth multiobjective optimization problem. Then, a sequence of smooth multiobjective problems that progressively approximate the nonsmooth multiobjective problem is introduced. It is shown that the Pareto optimal solutions (stationary points) of the approximate problems converge to a Pareto optimal solution (stationary point) of the original bilevel multiobjective programming problem. Numerical results showing the viability of the smoothing approach are reported.

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“…x and y, that is, in this work, we adopt the optimistic approach to consider the bilevel multiobjective programming problem [12].…”

Section: ð2:1þmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

Wan

2014

J. Oper. Res. Soc. China

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“…Due to their complexity, most bilevel optimization problems are tackled by approaches which involve a model reformulation masking the bi-level aspect of the problem (see [5], [6], [13], [14]), or which are based on heuristics.…”

Section: B Evolutionary Approaches For Bi-level Optimizationmentioning

confidence: 99%

“…While most of the existing literature about bi-level optimization focuses on small-size linear problems (see for example [5], [6]), many real-life applications involve large-size instances and complex NP-hard problems, justifying the use of EAs. Existing EAs for bi-level optimization can be divided into two main classes.…”

Section: Introductionmentioning

confidence: 99%

CoBRA: A cooperative coevolutionary algorithm for bi-level optimization

Legillon

Liefooghe

Talbi

2012

2012 IEEE Congress on Evolutionary Computation

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International audienceThis article presents CoBRA, a new evolutionary algorithm, based on a coevolutionary scheme, to solve bi-level optimization problems. It handles population-based algorithms on each level, each one cooperating with the other to provide solutions for the overall problem. Moreover, in order to evaluate the relevance of CoBRA against more classical approaches, a new performance assessment methodology, based on rationality, is introduced. An experimental analysis is conducted on a bi-level distribution planning problem, where multiple manufacturing plants deliver items to depots, and where a distribution company controls several depots and distributes items from depots to re- tailers. The experimental results reveal signiﬁcant enhancements, particularly over the lower level, with respect to a more classical approach based on a hierarchical scheme

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“…According to Pieume et al [5], it is not easy to find efficient solution of BMPP. In [9], the authors propose to approximate the efficient set of multiobjective programming problem by the weakly efficient set and…”

Section: Introductionmentioning

confidence: 99%

Solving Quasiconcave Bilevel Programming Problem

Balme¹,

Fotso²

2017

AJOR

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In this paper, we find the solution of a quasiconcave bilevel programming problem (QCBPP). After formulating a Bilevel Multiobjective Programming Problem (BMPP), we characterize its leader objective function and its feasible set. We show some necessary and sufficient conditions to establish a convex union of set of efficient point, an efficient set at the QCBPP. Based on this result, we formulate and solve a new QCBPP. Finally, we illustrate our approach with a numerical example.

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Multiobjective bilevel optimization

Cited by 142 publications

References 26 publications

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

A Smoothing Method for Solving Bilevel Multiobjective Programming Problems

CoBRA: A cooperative coevolutionary algorithm for bi-level optimization

Solving Quasiconcave Bilevel Programming Problem

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