Contact shape optimization: a bilevel programming approach

“…The equilibrium condition in many optimal shape design problems appears in the form of variational inequalities which require the overall problem to formulated as a two level task. For optimal design applications the readers may refer to [84], [47], [22], [94], [95]. 5) Defense applications: Bilevel optimization has a number of applications in the defense sector [31], for example attacker-defender Stackelberg games [86], [35], [138], [126], [9], [132], [133].…”

Section: Applicationsmentioning

confidence: 99%

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

Sinha

Malo

Deb

2018

IEEE Trans. Evol. Computat.

680

296

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Bilevel optimization is defined as a mathematical program, where an optimization problem contains another optimization problem as a constraint. These problems have received significant attention from the mathematical programming community. Only limited work exists on bilevel problems using evolutionary computation techniques; however, recently there has been an increasing interest due to the proliferation of practical applications and the potential of evolutionary algorithms in tackling these problems. This paper provides a comprehensive review on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary. A number of potential application problems are also discussed. To offer the readers insights on the prominent developments in the field of bilevel optimization, we have performed an automated textanalysis of an extended list of papers published on bilevel optimization to date. This paper should motivate evolutionary computation researchers to pay more attention to this practical yet challenging area.

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“…The traditional methods employed to solve these problems include penalty functions ([1]), the Karush-Kuhn-Tucker method ( [6,19]) and branch-and-bound procedures [5]. Relevant literature related to bi-level programming models is presented in ( [14,12,20]).…”

Section: Doi: 1014736/kyb-2016-2-0258mentioning

confidence: 99%

An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

Trejo¹,

Clempner²,

Poznyak³

2016

Kybernetika

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Contact shape optimization: a bilevel programming approach

Cited by 70 publications

References 10 publications

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

Annotated Bibliography on Bilevel Programming and Mathematical Programs with Equilibrium Constraints

A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications

An optimal strong equilibrium solution for cooperative multi-leader-follower Stackelberg Markov chains games

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