Differential evolution for bilevel programming

Angelo, Jaqueline S.; Krempser, Eduardo; Barbosa, Hélio J. C.

doi:10.1109/cec.2013.6557606

Cited by 77 publications

(34 citation statements)

References 40 publications

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“…Due to the lack of space, the description of the problems is omitted (they are all available in [4], except for problem 19, available in [9]). …”

Section: Test Problemsmentioning

confidence: 99%

“…In the BlDE method [4], for each x fixed, a DE method was performed to obtain the y values. However, this process required a large number of lower level function evaluations.…”

Section: De Assisted By a Surrogate Modelmentioning

confidence: 99%

“…In this paper, a simple similarity-based surrogate model, and a different stopping criterion are applied to the BlDE algorithm, previously proposed in [4], in order to reduce the number of upper and lower level function evaluations. The method uses two nested Differential Evolution algorithms, each one responsible for optimizing one level of the problem.…”

Section: Introductionmentioning

confidence: 99%

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Differential Evolution assisted by a surrogate model for bilevel programming problems

Angelo

Krempser²,

Barbosa

2014

2014 IEEE Congress on Evolutionary Computation (CEC)

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Bilevel programming is used to model decentralized problems involving two levels of decision makers that are hierarchically related. Those problems, which arise in many practical applications, are recognized to be challenging. This paper reports a Differential Evolution (DE) method assisted by a surrogate model to solve bilevel programming problems (BLPs). The method proposed is an extension of a previous one, BlDE, developed by the authors, where two DE methods are used to generate and evolve the upper and the lower level variables. Here, the use of a similarity-based surrogate model, and a different stopping criteria, are proposed in order to reduce the number of function evaluations on both levels of the problem. The numerical results show a significant reduction in the number of function evaluations in the lower level of the problem, as well as some improvement in the upper level.

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“…Due to the lack of space, the description of the problems is omitted (they are all available in [4], except for problem 19, available in [9]). …”

Section: Test Problemsmentioning

confidence: 99%

“…In the BlDE method [4], for each x fixed, a DE method was performed to obtain the y values. However, this process required a large number of lower level function evaluations.…”

Section: De Assisted By a Surrogate Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Differential Evolution assisted by a surrogate model for bilevel programming problems

Angelo

Krempser²,

Barbosa

2014

2014 IEEE Congress on Evolutionary Computation (CEC)

Self Cite

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show abstract

“…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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“…Meta-heuristic approaches have greater ability to overcome many challenges of the BLP problems. Genetic algorithm [16], ant colony optimization algorithm [5], di erential evolution [17], Particle Swarm Optimization (PSO) [10], and coevolutionary approaches [18] are some meta-heuristic approaches introduced to solve the BLP problems.…”

Section: Introductionmentioning

confidence: 99%

Bi-level programming for supplier selection under quantity discount policy

2017

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Abstract. This paper proposes two models to formulate a Supplier Selection Problem (SSP) in a single-buyer, multi-supplier two-echelon supply chain network. The model coordinates order allocation and supplier selection problems under all-unit quantity discount policy. In this way, bi-level programming is employed to obtain two models: 1) The model with buyer as a leader; 2) The model with vendor as a leader. The resulted nonlinear bi-level programming problems are hard to solve. Therefore, Particle Swarm Optimization (PSO) algorithm is used to deal with the complexity of the model and makes it solvable. Numerical results show that the proposed model is e cient for SSP in compliance with order allocation decision making.

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Differential evolution for bilevel programming

Cited by 77 publications

References 40 publications

Differential Evolution assisted by a surrogate model for bilevel programming problems

Differential Evolution assisted by a surrogate model for bilevel programming problems

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

Bi-level programming for supplier selection under quantity discount policy

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