Journal Article10.1016/S0305-0548(01)00066-1
Linear bilevel programming solution by genetic algorithm
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TL;DR: An attempt has been made to develop an efficient approach based on genetic algorithm for solving bilevel programming problem by providing some theorems that makes the algorithm more efficient than other techniques.
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About: This article is published in Computers & Operations Research. The article was published on 01 Nov 2002. The article focuses on the topics: Bilevel optimization & Genetic algorithm.
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Citations
A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications
TL;DR: A comprehensive review on bilevel optimization from the basic principles to solution strategies is provided in this paper, where a number of potential application problems are also discussed and an automated text-analysis of an extended list of papers has been performed.
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A Review on Bilevel Optimization: From Classical to Evolutionary Approaches and Applications.
TL;DR: An automated text-analysis of an extended list of papers published on bilevel optimization from the basic principles to solution strategies; both classical and evolutionary is performed.
268
Solving discretely-constrained MPEC problems with applications in electric power markets
TL;DR: This paper presents a mathematical formulation in order to solve a Stackelberg game for a network-constrained energy market using integer programming and reformulated as mixed-integer linear program (MILP) by using disjunctive constraints and linearization.
175
A hybrid of genetic algorithm and particle swarm optimization for solving bi-level linear programming problem – A case study on supply chain model
R. J. Kuo,Y.S. Han +1 more
TL;DR: In this paper, a hybrid of GA and PSO is proposed to solve the problem of supply chain distribution problem and the performance of the proposed method is ascertained by comparing the results with GA and particle swarm optimization using four problems in the literature.
173
A new approach for solving linear bilevel problems using genetic algorithms
TL;DR: A genetic algorithm for the linear bilevel problem in which both objective functions are linear and the common constraint region is a polyhedron is developed, which aims to combine classical extreme point enumeration techniques with genetic search methods by associating chromosomes with extreme points of thepolyhedron.
166
References
A Representation and Economic Interpretation of a Two-Level Programming Problem
TL;DR: A solution procedure is developed that replaces the subproblem by its Kuhn-Tucker conditions and then further transforms it into a mixed integer quadratic programming problem by exploiting the disjunctive nature of the complementary slackness conditions.
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Two-Level Linear Programming
Wayne F. Bialas,Mark H. Karwan +1 more
TL;DR: This paper examines the special case of the two-level linear programming problem and presents geometric characterizations and algorithms to demonstrate the tractability of such problems and motivate a wider interest in their study.
583
New branch-and-bound rules for linear bilevel programming
TL;DR: In this paper, a branch-and-bound algorithm for linear bilevel programming is proposed, where necessary optimality conditions expressed in terms of tightness of the follower's constraints are used to fathom or simplify subproblems, branch and obtain penalties similar to those used in mixed-integer programming.
570
A Branch and Bound Algorithm for the Bilevel Programming Problem
Jonathan F. Bard,James T. Moore +1 more
TL;DR: An algorithm for solving the linear/quadratic case of the bilevel programming problem is reformulated as a standard mathematical program by exploiting the follower's Kuhn–Tucker conditions.
435
Computational Difficulties of Bilevel Linear Programming
Omar Ben-Ayed,Charles E. Blair +1 more
TL;DR: It is shown, using small examples, that two algorithms previously published for the Bilevel Linear Programming problem BLP may fail to find the optimal solution and thus must be considered to be heuristics.