Bilevel Programming and Applications

Kalashnikov, Vyacheslav V.; Dempe, Stephan; Pérez-Valdés, Gerardo A.; Kalashnykova, Nataliya I.; Camacho‐Vallejo, José‐Fernando

doi:10.1155/2015/310301

Cited by 64 publications

(31 citation statements)

References 92 publications

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“… Optimal design of engineering problems [23,32].  Optimal exploitation in Energy sector [10,16].  Gas pricing and distribution [9].…”

Section: Bi-level Optimization Models and Their Applicationsmentioning

confidence: 99%

“…However, the bi-level solution contains not only components with decreasing flows through links, operated by buses. For example, the flow distribution through link (11)(12)(13)(14)(15)(16) increases from 0.0014 to 0.0118; link (15-16) also increase its flow from 0.0289 to 0.0393. That is why the single and bi-level optimization models have to be assessed and compared under common evaluation criterion.…”

Section: Traffic Flow Distribution According To Bi-level Optimizationmentioning

confidence: 99%

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Bi-Level Model for Public Rail Transportation under Incomplete Data

Pavlova

Stoilov

Stoilova

2017

Cybernetics and Information Technologies

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Abstract:The increase of the utilization of public rail transportations is searched in directions for redistribution of the passenger travels between rail and bus transportation. The rail transport benefits by redistribution of the transportation flows on paths, predominantly supported by rails. The redistribution of the transportation is formalized by bi-level optimization problem. The upper level optimization estimates the maximal flow, which can be transported through a transportation network, supported both by bus and rail transports. The lower level optimization gives priority to the rail transport by decreasing the costs of flow distribution, using rail transport. This bi-level optimization problem was applied for the case of optimization of the rail exploitation in Bulgaria, defining priorities in transportation of the National transport scheme.

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“… Optimal design of engineering problems [23,32].  Optimal exploitation in Energy sector [10,16].  Gas pricing and distribution [9].…”

Section: Bi-level Optimization Models and Their Applicationsmentioning

confidence: 99%

Section: Traffic Flow Distribution According To Bi-level Optimizationmentioning

confidence: 99%

Bi-Level Model for Public Rail Transportation under Incomplete Data

Pavlova

Stoilov

Stoilova

2017

Cybernetics and Information Technologies

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“…Definition 7. For a giveñ1 ∈ ( 1 ), a fuzzy vector̃ * 2 ∈ (̃1) is said to be a fuzzy optimal solution to the lower level problem (12)…”

Section: Definition Of the Fuzzy Optimal Solutionmentioning

confidence: 99%

“…In the past few decades, the bilevel programming problem has been researched from the theoretical and computational points of view [1][2][3][4][5][6] and has been successfully applied to a variety of fields, such as transport network design [7,8], principal-agent problems [9], price control [10], and electricity markets [11,12]. The bilevel programming problem is a hierarchical optimization problem with two levels.…”

Section: Introductionmentioning

confidence: 99%

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

Ren

2016

Mathematical Problems in Engineering

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This paper is concerned with a class of fully fuzzy bilevel linear programming problems where all the coefficients and decision variables of both objective functions and the constraints are fuzzy numbers. A new approach based on deviation degree measures and a ranking function method is proposed to solve these problems. We first introduce concepts of the feasible region and the fuzzy optimal solution of a fully fuzzy bilevel linear programming problem. In order to obtain a fuzzy optimal solution of the problem, we apply deviation degree measures to deal with the fuzzy constraints and use a ranking function method of fuzzy numbers to rank the upper and lower level fuzzy objective functions. Then the fully fuzzy bilevel linear programming problem can be transformed into a deterministic bilevel programming problem. Considering the overall balance between improving objective function values and decreasing allowed deviation degrees, the computational procedure for finding a fuzzy optimal solution is proposed. Finally, a numerical example is provided to illustrate the proposed approach. The results indicate that the proposed approach gives a better optimal solution in comparison with the existing method.

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“…Bi-level decisionmaking mainly is a bi-level optimization issue and mainly applies bi-level programming methods. It often appears in many decentralized management problems, and has motivated a number of researches to work on bi-level decision models [3,4], solution approaches [5,6] and applications [7,8].…”

Section: Introductionmentioning

confidence: 99%

Fuzzy Bi-level Decision-Making Techniques: A Survey

Zhang¹,

Han²,

Lu³

2016

IJCIS

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Bi-level decision-making techniques aim to deal with decentralized management problems that feature interactive decision entities distributed throughout a bi-level hierarchy. A challenge in handling bi-level decision problems is that various uncertainties naturally appear in decision-making process. Significant efforts have been devoted that fuzzy set techniques can be used to effectively deal with uncertain issues in bi-level decision-making, known as fuzzy bi-level decision-making techniques, and researchers have successfully gained experience in this area. It is thus vital that an instructive review of current trends in this area should be conducted, not only of the theoretical research but also the practical developments. This paper systematically reviews up-to-date fuzzy bi-level decisionmaking techniques, including models, approaches, algorithms and systems. It also clusters related technique developments into four main categories: basic fuzzy bi-level decision-making, fuzzy bi-level decision-making with multiple optima, fuzzy random bi-level decision-making, and the applications of bi-level decision-making techniques in different domains. By providing state-of-the-art knowledge, this survey paper will directly support researchers and practitioners in their understanding of developments in theoretical research results and applications in relation to fuzzy bi-level decision-making techniques.

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Bilevel Programming and Applications

Cited by 64 publications

References 92 publications

Bi-Level Model for Public Rail Transportation under Incomplete Data

Bi-Level Model for Public Rail Transportation under Incomplete Data

Solving the Fully Fuzzy Bilevel Linear Programming Problem through Deviation Degree Measures and a Ranking Function Method

Fuzzy Bi-level Decision-Making Techniques: A Survey

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