Finding the best efficient solution for multi objective ‎programming problems based on the distance of objectives - Gebreel, Dr. Alia Youssef Gebreel (International Journal of Advanced Mathematical Sciences, 2025)
Multi-objective programming is one of the most famous branches of operations research. Several traditional and artificial methods have been ‎used to solve multi-objective problems in different fields. Most of these methods give a set of efficient solutions rather than an optimal ‎solution because the objective functions are conflicting in nature. This leads to different individual solutions, or no one solution can be ‎available for all objective functions. Therefore, they must reconcile. In such a situation, the best way is needed to find a ‎feasible solution that is optimal for all objectives. In other words, it is the best or preferred solution that is considered the closest to the ‎utopian point. Despite the variety of applied methods, there is not one universal method for solving multiobjective optimization problems. ‎Nevertheless, this paper introduces some new general mathematical models to find the best efficient solution for multi-objective programming problems. They depend on minimizing the distance of objectives from the utopian point for accurate as well as computationally fast ‎approaches. Of course, by doing so, the required solution is directly obtained. Additionally, some illustrative numerical linear and nonlinear ‎examples demonstrate the computational details. The results are compared with the existing solutions in other researches. ‎All results conclude that the proposed methods are very important for decision making and they can be used in a variety of problems having ‎multiple objectives in real life. One can say that these methods are very simple to give useful insights into practical problems. Finally, this ‎work strives to provide the best solution with stable steps, lowest time processing, flexibility, and applicability‎.