离散变量的分级优化方法及其应用

在工程优化设计中,绝大多数实际问题的设计变量往往限定取离散值,为了求得问题的真正最优解,就必须采用离散变量的优化方法进行求解.本文根据离散变量数学规划的特性,提出了一种分级优化搜索算法.这种方法的基本思想是在约束集合内,寻求一可行的离散初始点,然后在该点的邻域内,进行分级寻优搜索,以求得一个改进的新离散点,随之,以该点作为初始点,重复执行分级寻优搜索过程,直至求得问题的最优解.通过对工程实例的计算,证明本文所提出的新方法具有快速、简便的特点,能有效地应用各种工程优化设计问题.

A Discrete Nonlinear Stepping Optimization Method and Its Application

Most of the practical design variables should always be discrete quantity within engineering optimization design problems. To obtain the true optimization solution, a discrete optimization method must be used. In this paper, a new method called step optimization search method is presented to solve the discrete quantity mathematic programming problems. The basic idea of this method is to find out an initial feasible point and then to search the optimum point step by step in the neighbouring region of this point so as to obtain an improved new discrete point. Respectively, the new point can be taken as initial one, and the whole process can be carried out once more until the optimum solution of the problem is obtained.Some results of numerical examples of practical problems show that this new method can solve problems quickly and simply and can be applied in a lot of engineering design problems.