Solve a linear –quadratic bi-level programming problem by applying the genetic algorithm
DOI:
https://doi.org/10.31272/jae.i127.107Keywords:
the(linear-quadratic) bi-level programming, Genetic algorithmAbstract
The Linear-quadratic bi-level programming problem it is considered a collection of researchers it is an overlapping optimization problem with two levels , one is called the upper level (independent) and the other is called the lower level (dependent),each level has objective function and constraint . It is considered a scientific and practical tool helps the decision maker to reach the optimal. To obtain efficient upper bounds and lower bounds we use the (karush-kuhn-Tucker) (KKT) conditions for transforming the "BLPP" into single level problem.
The main objective of the study is Highlighting one of the methods of solving the bi-level programming problem(BLPP) it is the Genetic algorithm (GA) that is one of the research methods used to simulate what nature does in the reproduction of living things and use it to solve complex problems to reach optimal solution or the closest possible solution to the ideal solution.
After implementing the genetic algorithm and taking advantage of its properties and the content of its steps with linear-quadratic bi level programming problem,the results showed in the case of the genetic algorithm with bi-level programming (linear-quadratic)that it gave the best possible solutions and was also able to achieve optimization by increasing the value of the objective function of type (max) the largest possible results of bi-level programming in the cases of production and demand in addition to generating them for possible alternative solutions that help the decision maker to choose what is better and closer to the state of the plant and its production reality.
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