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两个变量线性问题的优化解巳可用图解法——拐点法(即极点法)求得。它对于确定满足约束条件的可行域和求出符合目标函数极大或极小值的最优解是比较直观的。由于它是一个平面问题,在平面图形中可以表达得十分清楚,它的优越性是很明显的。 关于多维变量线性问题的求优化解;目前通用的是单纯形法,也有关于运输问题的表上作业法,资源分配问题和匈牙利法(Hnugarian Method)等。就以通用的单纯形法而言,它提供一种由某一初始极点出发,顺序找到最优解的迭代计算程序和图表的表示方法也是比较繁锁的。 笔者介绍一种关于三个变量线性问题求最优解的方法,即利用拐点理论把三维问题用几何平面图形直观地表达其最优解。为使求解方法更易被接受,还以通用的单纯形法加以印证。笔者所介绍的这种方法,比较直观,比较快捷。
The optimal solution to the linear problem of two variables can be obtained by the graphical method, inflection point method (ie, the pole method). It is relatively straightforward to determine the feasible region that satisfies the constraint and find the optimal solution that meets the maximum or minimum value of the objective function. Since it is a plane problem, it can be expressed very clearly in a plane graphic. Its superiority is obvious. The optimal solution to the linear problem of multidimensional variables; the current common method is the simplex method, as well as the on-table operation method for transportation problems, the resource allocation problem, and the Hungarian method. In terms of the common simplex method, it provides a method of expressing the iterative calculation procedure and the diagram that finds the optimal solution in order from a certain initial pole. It is also cumbersome. The author introduces a method to find the optimal solution for the linear problem of three variables. That is to use the inflection point theory to express the optimal solution of the three-dimensional problem visually with a geometrical plane graphic. In order to make the solution method more acceptable, it is also confirmed by the common simplex method. This method introduced by the author is more intuitive and faster.