论文标题
一种自适应方法，用于解决多级多目标线性编程问题
An adaptive method to solve multilevel multiobjective linear programming problems
论文作者
论文摘要
本文是对先前工作的后续措施，在该工作中，我们定义并生成了多级多目标线性编程问题（ML-MOLPP）的所有可能妥协的集合。在本文中，我们介绍了一种新算法来求解ML-molpp，其中嵌套了线性编程的自适应方法。首先，我们首先生成所有可能的妥协的集合（所有非主导解决方案的集合）。之后，开发了基于线性编程的自适应方法的算法，以选择所实现的所有可能折衷方案的最佳妥协。此方法将使我们能够将初始多级问题转换为具有有限变量的ML-molpp。然后，应用自适应方法，该方法是解决分辨率过程中涉及的所有多目标线性编程问题最有效的方法，而不是单纯形方法（应注意，自适应方法比单纯形方法更有效）。最后，用数字示例仔细检查并说明了所有施工阶段。
This paper is a follow-up to a previous work where we defined and generated the set of all possible compromises of multilevel multiobjective linear programming problems (ML-MOLPP). In this paper, we introduce a new algorithm to solve ML-MOLPP in which the adaptive method of linear programming is nested. First, we start by generating the set of all possible compromises (set of all non-dominated solutions). After that, an algorithm based on the adaptive method of linear programming is developed to select the best compromise among all the possible compromises achieved. This method will allow us to transform the initial multilevel problem into an ML-MOLPP with bounded variables. Then, apply the adaptive method which is the most efficient to solve all the multiobjective linear programming problems involved in the resolution process instead of the simplex method (It should be noted that the adaptive method is more efficient than the simplex method). Finally, all the construction stages are carefully checked and illustrated with a numerical example.
