An overview of bilevel optimization

Colson, Benoît; Marcotte, Patrice; Savard, Gilles

doi:10.1007/s10479-007-0176-2

Cited by 1,259 publications

(718 citation statements)

References 85 publications

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“…This is a generalization to the case of competing followers of the "optimistic assumption" common in the multilevel optimization literature. The simplest illustration of the assumption is in the bilevel setting where the leader has the ability to choose among alternate optima to the follower's problem (see Colson et al (2007)). Here we assume more generally that the leader can choose among the alternate pure Nash equilibria between the followers.…”

Section: Stackelberg-nash Equilibriamentioning

confidence: 99%

Rational Generating Functions and Integer Programming Games

Köppe

Ryan

Queyranne

2011

Operations Research

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We explore the computational complexity of computing pure Nash equilibria for a new class of strategic games called integer programming games with difference of piecewise linear convex payoffs. Integer programming games are games where players' action sets are integer points inside of polytopes. Using recent results from the study of short rational generating functions for encoding sets of integer points pioneered by Alexander Barvinok, we present efficient algorithms for enumerating all pure Nash equilibria, and other computations of interest, such as the pure price of anarchy, and pure threat point, when the dimension and number of "convex" linear pieces in the payoff functions are fixed. Sequential games where a leader is followed by competing followers (a Stackelberg-Nash setting) are also considered.

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Section: Stackelberg-nash Equilibriamentioning

confidence: 99%

Rational Generating Functions and Integer Programming Games

Köppe

Ryan

Queyranne

2011

Operations Research

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“…Despite the lack of theoretical results, there exists a plethora of studies related to bilevel single-objective optimization problems [1,3,12,15] in which both upper and the lower level optimization tasks involve exactly one objective each. Despite having a single objective in the lower level task, usually in such problems the lower level optimization problem has more than one optimum.…”

Section: Introductionmentioning

confidence: 99%

Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Deb¹,

Sinha²

2009

Lecture Notes in Computer Science

976

1,594

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Abstract. Bilevel optimization problems require every feasible upperlevel solution to satisfy optimality of a lower-level optimization problem. These problems commonly appear in many practical problem solving tasks including optimal control, process optimization, game-playing strategy development, transportation problems, and others. In the context of a bilevel single objective problem, there exists a number of theoretical, numerical, and evolutionary optimization results. However, there does not exist too many studies in the context of having multiple objectives in each level of a bilevel optimization problem. In this paper, we address bilevel multi-objective optimization issues and propose a viable algorithm based on evolutionary multi-objective optimization (EMO) principles. Proof-of-principle simulation results bring out the challenges in solving such problems and demonstrate the viability of the proposed EMO technique for solving such problems. This paper scratches the surface of EMO-based solution methodologies for bilevel multi-objective optimization problems and should motivate other EMO researchers to engage more into this important optimization task of practical importance.

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“…Colson published a series of representative research results to solve the solution problems of nonlinear bi-level programming models [62][63][64]. There are two types of methods to solve the bi-level programming problem: one method is to transform the bi-level programming model into a single programming model based on the optimal conditions, such as KKT conditions; the other method is to obtain the optimal solution of the lower model under a given variable value of the upper model.…”

Section: Solution Algorithmmentioning

confidence: 99%

“…There are two types of methods to solve the bi-level programming problem: one method is to transform the bi-level programming model into a single programming model based on the optimal conditions, such as KKT conditions; the other method is to obtain the optimal solution of the lower model under a given variable value of the upper model. Based on the two types of solution methods, many specific algorithms have been proposed and developed [64][65][66][67][68][69].…”

Section: Solution Algorithmmentioning

confidence: 99%

Quantifying a Financially Sustainable Strategy of Public Transport: Private Capital Investment Considering Passenger Value

et al. 2017

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Abstract:Releaving traffic congestion by developing public transport as an alternative mode of travel is a common practice all over the world. However, the increasing public transport subsidies have created a financial burden for governments. Encouragingly, private capital supplies an opportunity for public transport in sustainable finance. Previous research mainly focuses on qualitative analysis and money-for-value (MFV) analysis. In this paper, a new investment model is proposed based on the concept 'passenger value', and a bi-level programming model (BLPM) is constructed as a quantitative analysis tool. The upper target of BLPM is the total surplus (including the value of time (VOT) of passengers) of the public transport system and the upper constraint is the ticket price. The lower target of BLPM is passenger's surplus, the lower constraints are service capability and the lowest return rate of the private sector. The public transport of Jinan City, China is taken as a case to quantify the impacts of private capital investment in public transport. Results show that the proposed investment model considering passenger value is superior to the traditional one, and effective private capital investment could increase the total societal benefit of the transportation system. The proposed investment strategy satisfies economic viability and is a financially sustainability strategy. Additionally, travelers should be encouraged to use public transport through improving the service quality and passenger returns. Only in this way can the success rate of the private sector investment in public transport be improved efficiently.

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An overview of bilevel optimization

Cited by 1,259 publications

References 85 publications

Rational Generating Functions and Integer Programming Games

Rational Generating Functions and Integer Programming Games

Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Quantifying a Financially Sustainable Strategy of Public Transport: Private Capital Investment Considering Passenger Value

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