# Comparison of the branching and determination algorithm with Taylor's method for solving bi-level nonlinear programming with a practical application.

## DOI:

https://doi.org/10.31272/jae.i133.938## Keywords:

nonlinear bi-level programming, Taylor method, selection, and branching algorithm## Abstract

** ** In this research, two methods of solving non-linear Bi-level Programming are used, they are the Beanch and Bound Algorithm and Taylor method and they are compared in terms of the value of the objective function to reach the optimal solution through the method of Simulation using Monte Carlo method and different sample sizes small and large, and the preference of the selection and branching algorithm was reached in solving the non-linear two-level programming problem because its results were better in terms of cost reduction.

** ** In this research, two methods of solving non-linear Bi-level Programming are used, they are the Beanch and Bound Algorithm and Taylor method and they are compared in terms of the value of the objective function to reach the optimal solution through the method of Simulation using Monte Carlo method and different sample sizes small and large, and the preference of the selection and branching algorithm was reached in solving the non-linear two-level programming problem because its results were better in terms of cost reduction.

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