A global optimization method for nonlinear bilevel programming problems

Many real life problems can be stated as a continuous minimax optimization problem. Well-known applications to engineering, finance, optics and other fields demonstrate the importance of having reliable methods to tackle continuous minimax problems. In this paper a new approach to the solution of continuous minimax problems over reals is introduced, using tools based on modal intervals. Continuous minimax problems, and global optimization as a particular case, are stated as the computation of semantic extensions of continuous functions, one of the key concepts of modal intervals. Modal intervals techniques allow to compute, in a guaranteed way, such semantic extensions by means of an efficient algorithm. Several examples illustrate the behavior of the algorithms in unconstrained and constrained minimax problems.

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“…If all the inclusions are true, the cell (U j , V k ) belongs to the partition named Π (1) . If any of the inclusions…”

Section: Solution For the Constrained Minimax Problemmentioning

confidence: 99%

“…Minimax and optimization problems with constraints are well known in engineering and some algorithms have been developed for the continuous case [1,[4][5][6]15,18,23]. Many situations of practical importance can be described by means of mathematical models defining minimax values of certain functions.…”

Section: Introductionmentioning

confidence: 99%

Continuous minimax optimization using modal intervals

Saínz

Herrero

Armengol

et al. 2008

Journal of Mathematical Analysis and Applications

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“…Therefore, many researchers are devoted to develop the algorithms for BLP and propose many efficient algorithms. Traditional methods commonly used to handle BLP include Karus-Kuhn-Tucker approach [23][24][25][26], Branch-and-bound method [27], and penalty function approach [28][29][30][31]. Despite a significant progress made in traditional optimization towards solving BLPPs, the properties such as differentiation and continuity are necessary for these algorithms.…”

Section: Introductionmentioning

confidence: 99%

The Backpropagation Artificial Neural Network Based on Elite Particle Swam Optimization Algorithm for Stochastic Linear Bilevel Programming Problem

Zhang

2018

Mathematical Problems in Engineering

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For a class of stochastic linear bilevel programming problem, we firstly transform it into a deterministic linear bilevel covariance programming problem. Then, the deterministic bilevel covariance programming problem is solved by backpropagation artificial neural network based on elite particle swam optimization algorithm (BPANN-PSO). Finally, we perform the simulation experiments and the results show that the computational efficiency of the proposed algorithm has a potential upside compared with the classical algorithm.

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“…Even so, many researchers are devoted to develop the algorithms for solving BLP and propose many efficient algorithms. To date a few algorithms exist to solve BLP, and they can be classified into four types: Karus-Kuhn-Tucker approach (KKT) [2,3,16,17], Branch-and-bound method [6], penalty function approach [1,23,31,38] and descent approach [18,37]. The properties such as differentiation and continuity are necessary when proposing the traditional algorithms.…”

Section: Introductionmentioning

confidence: 99%

A cooperative coevolution PSO technique for complex bilevel programming problems and application to watershed water trading decision making problems

Zhang¹,

Chen²,

Chen³

2017

J. Nonlinear Sci. Appl.

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The complex bilevel programming problem (CBLP) in this paper mainly refers to the optimistic BLP in which the highdimensional decision variables at both levels. A cooperative coevolutionary particle swarm optimization (CCPSO) is proposed for solving the (CBLP), in which the evolutionary paradigm can efficiently prevent the premature convergence of the swarm. Furthermore, the stagnation detection strategy in our algorithm can further accelerate the convergence speed. Finally, we use the test problems from the reference and practical example about watershed water trading decision-making problem to measure and evaluate the proposed algorithm. The presented results indicate that the proposed algorithm can effectively solve the complex bilevel programming problems. c 2017 All rights reserved.Keywords: Complex bilevel programming, cooperative coevolutionary particle swarm optimization, watershed water trading decision making problems, elite strategy. 2010 MSC: 65K10, 90C25.

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A global optimization method for nonlinear bilevel programming problems

Cited by 47 publications

References 19 publications

Continuous minimax optimization using modal intervals

Continuous minimax optimization using modal intervals

The Backpropagation Artificial Neural Network Based on Elite Particle Swam Optimization Algorithm for Stochastic Linear Bilevel Programming Problem

A cooperative coevolution PSO technique for complex bilevel programming problems and application to watershed water trading decision making problems

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