Genetic algorithm based approach to bi-level linear programming

Mathieu, Richard G.; Pittard, L.; Anandalingam, G.

doi:10.1051/ro/1994280100011

Cited by 147 publications

(45 citation statements)

References 25 publications

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“…In the context of bilevel single-objective optimization problems, there exists a number of studies, including some useful reviews [3,13], test problem generators [1], and even some evolutionary algorithm (EA) studies [12,11,15,10,14]. However, there does not seem to be too many studies on bilevel multi-objective optimization.…”

Section: Classical Approachesmentioning

confidence: 99%

Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Deb¹,

Sinha²

2009

Lecture Notes in Computer Science

947

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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Section: Classical Approachesmentioning

confidence: 99%

Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Deb¹,

Sinha²

2009

Lecture Notes in Computer Science

947

1,594

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“…In the context of BLPP, a number of subjects have been presented, including some e ectual research studies [16,17], test problem generators [18], and some Evolutionary Algorithm (EA) studies [19][20][21][22][23]. Since then, a number of studies have been conducted on bilevel programming [24][25][26].…”

Section: Survey On Bi-level Programming Problemsmentioning

confidence: 99%

“…Also, some of the evolutionary algorithms for BLPPs have been used as nested strategies that solve the lower level optimization problem for upper level decision problem [20,23,[27][28][29]. Mathieu et al [20], Yin [23], and Li and Wang [30] utilized the upper level optimization problem by using an evolutionary algorithm and the lower level using a classical approach.…”

Section: Survey On Bi-level Programming Problemsmentioning

confidence: 99%

Development of a Cournot-oligopoly model for competition of multi-product supply chains under government supervision

2017

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Abstract. Globalization, increased governmental regulations, and customer demands regarding environmental issues have led the organizations to review the measures necessary for the implementation of the Green Supply Chain Management (GSCM) to improve the environmental and economical performances. The paper proposes a Cournot-oligopoly model for green supply chain management. It provides a novel approach to construct a model that maximizes government tari and pro ts of the suppliers and manufacturers in all the GSCs. The bi-level model is converted to a single-level model by replacing the second level with its Karush Kuhn Tucker (KKT) conditions and linearization techniques. Then, a Genetic Algorithm (GA) is utilized to solve the single-level model using MATLAB software. Afterwards, the obtained results are compared with optimal solutions acquired by Enumerative Method (EM) to evaluate the validity and feasibility of the proposed GA. The sensitivity analysis of this model indicates that the scal policy of the government greatly a ects the reduction of environmental pollution costs caused by industrial activities such as automobile production in a competitive market. Therefore, the amount of non-green products' taxes is directly related to the decrease of environmental pollution.

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“…ACO techniques for BLPPs are found in [93]. GAs have been used to solve BLPPs in inter alia [73,86,111,114,122]. PSO was applied to BLPPs in e.g.…”

Section: Solution Algorithms For the Blppmentioning

confidence: 99%

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

Koh

2013

Metaheuristics for Bi-Level Optimization

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Bi-level programming problems arise in situations when the decision maker has to take into account the responses of the users to his decisions. Several problems arising in engineering and economics can be cast within the bi-level programming framework. The bi-level programming model is also known as a Stackleberg or leader-follower game in which the leader chooses his variables so as to optimise his objective function, taking into account the response of the follower(s) who separately optimise their own objectives, treating the leader's decisions as exogenous. In this chapter, we present a unified framework fully consistent with the Stackleberg paradigm of bi-level programming that allows for the integration of meta-heuristic algorithms with traditional gradient based optimisation algorithms for the solution of bi-level programming problems. In particular we employ Differential Evolution as the main meta-heuristic in our proposal. We subsequently apply the proposed method (DEBLP) to a range of problems from many fields such as transportation systems management, parameter estimation and game theory. It is demonstrated that DEBLP is a robust and powerful search heuristic for this class of problems characterised by non smoothness and non convexity.

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Genetic algorithm based approach to bi-level linear programming

Cited by 147 publications

References 25 publications

Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Solving Bilevel Multi-Objective Optimization Problems Using Evolutionary Algorithms

Development of a Cournot-oligopoly model for competition of multi-product supply chains under government supervision

A Metaheuristic Framework for Bi-level Programming Problems with Multi-disciplinary Applications

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