حل مسألة البرمجة ثنائية المستوى (الكسرية-الخطية)‎ بتطبيق الخوارزمية الجينية

الملخص EN

Fractional – Linear bi-level programming (FLBP) is considered an intertwining optimization problem with two levels, one of which is called the independent top level (and the other is called the lower level of the follower) and each level has its own objective function and limitations.

It is considered a scientific and practical tool that helps the decision maker to reach the ideal solution.

In order to obtain the efficiency of the maximum and the minimum, the terms of "karush-kuhn-tucker" (KKT) were used in order to convert the two-level programming to one-level and apply the genetic algorithm to it after that.

The main objective of the study is to shed light.

On one of the two-level programming solution methods, which is the Genetic Algorithm (GA), which is considered one of the research methods and is used to simulate what nature does in the reproduction of living organisms and use it to solve complex problems and reach an optimal solution or the closest possible solution to the optimal solution.

After implementing the genetic algorithm and taking advantage of its properties and content of its steps with two-level programming (fractional-linear) to calculate the monthly quantities of production and demand for the 60-ampere liquid acid battery and the data obtained from the battery production laboratory in Baghdad affiliated to the Ministry of Industry and Minerals, the results showed that the genetic algorithm gave the best solutions.

It was also able to achieve optimization by increasing the value of the target function of type (max) as much as possible from the results of bi-level programming without using the algorithm in the production and demand cases in addition to generating possible alternative solutions that help the decision maker to choose what is better and closer To the case under study and its practical reality.