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A Modified Artificial Immune Algorithm for Solving Single-Objective Bi-level Optimization Problems

A.M. Hagras, N.A. Elhefnawy, M.M. El-Sherbiny, M.M. Hadhoud


The Bi-level programming problem (BLPP) is considered to be NP-hard problem. This article introduces an efficient approach based on modified Artificial Immune System (AIS) to solve nonlinear BLPP, handling by Karush-Kuhn–Tucker conditions to convert nonlinear BLPP to the single objective problem and exterior penalty function to convert it to unconstrained one, and then it is solved by modified AIS. In this approach crossover, hamming distance and new adaptive mutation are used to focus your search for affinity with high degree, while ensuring the diversity of antibodies, avoiding premature convergence and also to escape from local optima. Finally, simulation results will be presented for seven test problems and compare them with other algorithms to illustrate the efficiency and accuracy of the proposed algorithm.


Non-linear bi-level programming problem, Evolutionary algorithms, Artificial Immune system, Karush-Kuhn–Tucker conditions, Exterior penalty.

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