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GEOMETRIC PROBABILITY PROBLEMS FOR OPTIMIZATION PROCESS

机译:优化过程的几何概率问题

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Integer linear programming (ILP) deals in a systematic way with the minimization (maximization) problem of a linear function with several variables (some also of a random nature), subject to equality constraints and linear inequality and to the constraints that one or more variables have integer values. This mathematical approach is essential to address and solve a very large number of real problems, typical of in applied sciences, where there be an indivisibility of the goods to be produced or of the resources to be used. Thus there comes consequent need to represent the problem through models of linear programming with integer variables. The applications of the method concern many applications of modern society and extend from industrial analysis for the distribution of goods and the sequencing of productive activities, to economic problems aimed at the optimal management of a securities portfolio, to those of planning and optimal planning of public investments, to the problems inherent in biology, high energy physics, engineering and robotics [15]. In this paper, considering the formula of the kinematic measure of Poincaré [11] and the result of Stoka [14], we consider two generalized Laplace problems for a regular lattice. We determine the probability of intersection of two body tests, a rectangle with random position and a circle with constant radius, with the lattice represented in Figure 2.
机译:整数线性编程(ILP)以系统的方式处理具有多个变量的线性函数的最小化(最大化)问题(有些也具有随机性质),受到平等约束和线性不等式的约束,并受到一个或多个变量的约束具有整数值。这种数学方法对于解决和解决大量的实际问题至关重要,在应用科学中典型的问题,在该科学中,要生产的商品或要使用的资源是不可分割的。因此,因此需要通过整数变量的线性编程模型来表示问题。该方法的应用涉及现代社会的许多应用,并从工业分析范围扩展到商品分配和生产活动的测序,到旨在证券投资组合最佳管理的经济问题,再到计划和最佳计划的公众计划投资,用于生物学,高能物理,工程和机器人技术固有的问题[15]。在本文中,考虑了庞加莱运动学测量的公式[11]和Stoka [14]的结果,我们考虑了常规晶格的两个广义拉普拉斯问题。我们确定了两个身体测试的交点的概率,一个具有随机位置的矩形和一个恒定半径的圆,其晶格在图2中表示。

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