多目标线性规划模型的模糊数学解法

One Solution of Multi-Objective Linear Programming Model with Fuzzy Mathematics

多目标线性规划是优化问题的一种,是大学生数学建模中经常考核的知识点.它的解要求各子目标函数都要同时达到较优的值,造成模型求解比较困难.文章给出一种基于模糊数学规划的求解方法,通过引进伸缩因子,将各子目标模糊化,从而把多目标规划问题转化为单目标问题,利用Matlab、Lingo等数学工具软件便可容易求得其模糊最优解.最后用一个实例说明了求解过程,该方法简单易行,适合在建模竞赛时采用.

Multi-objective linear programming is one of the optimal problems, which has often been used in the China Un- dergraduate Mathematical Contest in Modeling. It requires all the objective functions to achieve comparatively optimum value at the same time, so it makes the solving of the problem more difficultly. By using the flexible indexes and let every sub-object fuzzing, a solution of the problem based on the fuzzy mathematical programming is proposed. Using the method, we can turn the multi-objective problem into a single objective problem, and get the optimal solution easily with the software tools such as, Mat- Lab, Lingo, etc. Finally, one example is given to illuminate how to get the fuzzy optimal solution, which shows that the method is very simple and suitable for using in modeling contest.