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Article

Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems

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Department of Basic Science, Higher Technological Institute, Tenth of Ramadam City 44629, Egypt
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Department of Basic Engineering Science, Faculty of Engineering, Shebin El-Kom, Menoufia University, Shebin El-Kom 32511, Egypt
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Author to whom correspondence should be addressed.
Symmetry 2020, 12(5), 767; https://doi.org/10.3390/sym12050767
Received: 9 March 2020 / Revised: 14 April 2020 / Accepted: 15 April 2020 / Published: 6 May 2020
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. View Full-Text
Keywords: bi-level optimization; chaos theory; evolutionary algorithms; genetic algorithm bi-level optimization; chaos theory; evolutionary algorithms; genetic algorithm
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MDPI and ACS Style

Abo-Elnaga, Y.; Nasr, S. Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems. Symmetry 2020, 12, 767. https://doi.org/10.3390/sym12050767

AMA Style

Abo-Elnaga Y, Nasr S. Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems. Symmetry. 2020; 12(5):767. https://doi.org/10.3390/sym12050767

Chicago/Turabian Style

Abo-Elnaga, Yousria, and Sarah Nasr. 2020. "Modified Evolutionary Algorithm and Chaotic Search for Bilevel Programming Problems" Symmetry 12, no. 5: 767. https://doi.org/10.3390/sym12050767

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