Solving Linear Bilevel Programming Problems Using a Binary Differential Evolution

2015 ◽  
Author(s):  
Hong Li ◽  
Li Zhang
Keyword(s):  
Differential Evolution ◽  
Bilevel Programming ◽  
Linear Bilevel Programming ◽  
Bilevel Programming Problems ◽  
Binary Differential Evolution

scholarly journals An Evolutionary Algorithm Using Duality-Base-Enumerating Scheme for Interval Linear Bilevel Programming Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-8
Author(s):  
Hecheng Li ◽  
Lei Fang
Keyword(s):  
Evolutionary Algorithm ◽  
Bilevel Programming ◽  
Search Space ◽  
Linear Programs ◽  
Single Level ◽  
Linear Bilevel Programming ◽  
Interval Linear ◽  
Bilevel Programming Problems ◽  
The Right ◽  
Nonlinear Equality

Interval bilevel programming problem is hard to solve due to its hierarchical structure as well as the uncertainty of coefficients. This paper is focused on a class of interval linear bilevel programming problems, and an evolutionary algorithm based on duality bases is proposed. Firstly, the objective coefficients of the lower level and the right-hand-side vector are uniformly encoded as individuals, and the relative intervals are taken as the search space. Secondly, for each encoded individual, based on the duality theorem, the original problem is transformed into a single level program simply involving one nonlinear equality constraint. Further, by enumerating duality bases, this nonlinear equality is deleted, and the single level program is converted into several linear programs. Finally, each individual can be evaluated by solving these linear programs. The computational results of 7 examples show that the algorithm is feasible and robust.

Test problem construction for linear bilevel programming problems

1996 ◽  
Vol 8 (3) ◽  
pp. 235-243 ◽  
Author(s):  
Khosrow Moshirvaziri ◽  
Mahyar A. Amouzegar ◽  
Stephen E. Jacobsen
Keyword(s):  
Bilevel Programming ◽  
Test Problem ◽  
Problem Construction ◽  
Linear Bilevel Programming ◽  
Bilevel Programming Problems

scholarly journals A Differential Evolution with Two Mutation Strategies and a Selection Based on an Improved Constraint-Handling Technique for Bilevel Programming Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-16 ◽  
Author(s):  
Hong Li ◽  
Li Zhang
Keyword(s):  
Differential Evolution ◽  
Bilevel Programming ◽  
Differential Evolution Algorithm ◽  
Constraint Handling ◽  
Mutation Operators ◽  
Bilevel Programming Problems ◽  
Evolution Algorithm ◽  
Handling Technique ◽  
Mutation Strategies ◽  
Selection Operator

Two mutation operators are used in the differential evolution algorithm to improve the diversity of population. An improved constraint-handling technique based on a comparison mechanism is presented, and then it is combined with the selection operator in the differential evolution algorithm to fulfill constraint handling and selection simultaneously. A differential evolution with two mutation strategies and a selection based on this improved constraint-handling technique is developed to solve bilevel programming problems. The simulation results on some linear and nonlinear bilevel programming problems show the effectiveness and efficiency of the proposed algorithm.

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