Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems

Bi-level programming problem (BLPP) is an optimization problem consists of two interconnected hierarchical optimization problems. Solving BLPP is one of the hardest tasks facing the optimization community. This paper proposes a modified genetic algorithm and a chaotic search to solve BLPP. Firstly,...

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Bibliographic Details
Published in:Symmetry (Basel) Vol. 12; no. 5; p. 767
Main Authors: Abo-Elnaga, Yousria, Nasr, Sarah
Format: Journal Article
Language:English
Published: Basel MDPI AG 01.05.2020
Subjects:
Applied research
Chaos theory
Convergence
Decision making
Evolutionary algorithms
Genetic algorithms
Mathematical programming
Optimization
Optimization theory
Searching
Egypt
ISSN:2073-8994, 2073-8994
Online Access:Get full text
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Summary:Bi-level programming problem (BLPP) is an optimization problem consists of two interconnected hierarchical optimization problems. Solving BLPP is one of the hardest tasks facing the optimization community. This paper proposes a modified genetic algorithm and a chaotic search to solve BLPP. Firstly, the proposed algorithm solves the upper-level problem using a modified genetic algorithm. The genetic algorithm has modified with a new selection technique. The new selection technique helps the upper-level decision-maker to take an appropriate decision in anticipation of a lower level’s reaction. It distinguishes the proposed algorithm with a very small number of solving the lower-level problem, enhances the algorithm performance and fasts convergence to the solution. Secondly, a local search based on chaos theory has applied around the modified genetic algorithm solution. Chaotic local search enables the algorithm to escape from local solutions and increase convergence to the global solution. The proposed algorithm has evaluated on forty different test problems to show the proposed algorithm effectiveness. The results have analyzed to illustrate the new selection technique effect and the chaotic search effect on the algorithm performance. A comparison between the proposed algorithm results and other state-of-the-art algorithms results has introduced to show the proposed algorithm superiority.
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ISSN:2073-8994
2073-8994
DOI:10.3390/sym12050767