Linear bilevel programming solution by genetic algorithm

Hejazi, Seyed Reza; Memariani, Azizollah; Jahanshahloo, G. R.; Sepehri, Mohammad Mehdi

doi:10.1016/s0305-0548(01)00066-1

Cited by 161 publications

(56 citation statements)

References 18 publications

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“…An integer random number u is generated in the interval [1,l], where l is the length of the individual. For generating the new individual, the uth component is changed to 0, if it was initially 1 and to 1 if it was initially 0 [11] Step 7: Terminations, Jude the condition of the termination. When t is larger than the maximal iteration number, stop the GA and output the optimal solution.…”

Section: Methodsmentioning

confidence: 99%

“…A bi-level programming problem is formulated for a problem in which two DecisionMakers (DMs) make decisions successively. For example, in a decentralized firm, top management, an executive board, or headquarters makes a decision such as a budget of the firm and then each division determines a production plan in the full knowledge of the budget [3][4][5][6][7][8][9][10][11][12] . Also, the Stackelberg duopoly can be cited: two firms supply homogenous goods to a market.…”

Section: Introductionmentioning

confidence: 99%

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A Solution Methodology of Bi-Level Linear Programming Based on Genetic Algorithm

Osman¹,

El-Wahed²,

Shafei³

et al. 2009

J. of Mathematics and Statistics

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Problem statement:We deal with the bi-level linear programming problem. A bi-level programming problem is formulated for a problem in which two Decision-Makers (DMs) make decisions successively. Approach: In this research we studied and designs a Genetic Algorithm (GA) of Bi-Level Linear Programming Problems (BLPP) by constructing the fitness function of the upperlevel programming problems based on the definition of the feasible degree. This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the constraints in order to improve the ability of the GA to deal with the constraints. Also we designed software to solve this problem. A comparative study between proposed method and previous methods through numerical results of some examples. Finally, parametric information of the GA was introduced. Results: Results of the study showed that the proposed method is feasible and more efficient to solve (BLPP), also there exist package to solve (BLPP) problem. Conclusion: This GA avoids the use of penalty function to deal with the constraints, by changing the randomly generated initial population into an initial population satisfying the constraints in order to improve the ability of the GA to deal with the constraints.

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Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Solution Methodology of Bi-Level Linear Programming Based on Genetic Algorithm

Osman¹,

El-Wahed²,

Shafei³

et al. 2009

J. of Mathematics and Statistics

View full text Add to dashboard Cite

show abstract

“…The fuzzy programming (FP) approaches [7,19] to decentralized hierarchical decision problems have also been investigated from the point of view of potential use to different real-life decision problem like traffic control, economic system, warfare, network design, conflict resolution, and others. The GAs [9,17] as prominent tools to optimization of multiobjective decision making (MODM) problems [15,16] have also been introduced to solve BLPPs [12,18]. The GA based fuzzy goal programming (FGP) approaches [20,24] to linear as well fractional BLPPs and MLPPs have been studied by Pal et al [29,30] in the recent past.…”

Section: Introductionmentioning

confidence: 99%

Mixed 0−1 Goal Programming Approach to Interval-Valued Bilevel Programming Problems Via Bio-Inspired Computational Algorithm

Chakraborti¹,

Biswas²

2013

Computer Science &Amp; Information Technology ( CS &Amp; IT )

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This paper presents how the mixed 0-1 programming in the framework of goal programming (GP) can be used to solve interval-valued fractional bilevel programming (IVFBLP) problems by employing genetic algorithm (GA) in a hierarchical decision making system. In the model formulation of the problem, a goal achievement function for minimizing the lower-bounds of the necessary regret intervals defined for the target intervals of achieving the goals and thereby arriving at a compromise decision is constructed by using both the aspects of 'minsum ' and 'minmax' approaches in GP. In the decision process, an GA scheme is employed for execution of the problems at the two stages, target interval specification and optimal decision determination, for distribution of decision powers to the decision makers (DMs) in the order of hierarchy. A numerical example is provided to illustrate the potential use of the approach.

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“…For example, in [21] genetic algorithms are developed using GAMS [22] and MINOS, in [23] a decomposition based on global optimization approach to bilevel and quadratic programming problems is solved by GAMS/MINOS.…”

Section: Introductionmentioning

confidence: 99%

An Inexact Restoration Package for Bilevel Programming Problems

Pilotta¹,

Torres²

2012

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Bilevel programming problems are a class of optimization problems with hierarchical structure where one of the constraints is also an optimization problem. Inexact restoration methods were introduced for solving nonlinear programming problems a few years ago. They generate a sequence of, generally, infeasible iterates with intermediate iterations that consist of inexactly restored points. In this paper we present a software environment for solving bilevel programming problems using an inexact restoration technique without replacing the lower level problem by its KKT optimality conditions. With this strategy we maintain the minimization structure of the lower level problem and avoid spurious solutions. The environment is a user-friendly set of Fortran 90 modules which is easily and highly configurable. It is prepared to use two well-tested minimization solvers and different formulations in one of the minimization subproblems. We validate our implementation using a set of test problems from the literature, comparing different formulations and the use of the minimization solvers.

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Linear bilevel programming solution by genetic algorithm

Cited by 161 publications

References 18 publications

A Solution Methodology of Bi-Level Linear Programming Based on Genetic Algorithm

A Solution Methodology of Bi-Level Linear Programming Based on Genetic Algorithm

Mixed 0−1 Goal Programming Approach to Interval-Valued Bilevel Programming Problems Via Bio-Inspired Computational Algorithm

An Inexact Restoration Package for Bilevel Programming Problems

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