An Efficient Genetic Algorithm for Interval Linear Bilevel Programming Problems

2013 ◽  
Author(s):  
Hecheng Li ◽  
Lei Fang
Keyword(s):  
Genetic Algorithm ◽  
Bilevel Programming ◽  
Linear Bilevel Programming ◽  
Interval Linear ◽  
Bilevel Programming Problems

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.

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