Efficient Optimization with Related Discrete Variables-- Application to the Design of Steel-Framed Buildings

这项研究的目的有两个。首先，将开发用于解决非线性优化问题的算法，其中一些变量可能具有离散值的某些组合。这些算法必须在最小化解决问题所需的分析量方面是有效的。其次，这些算法将通过将它们执行到一个通用的计算机程序中来进行测试，该程序用于为矩形钢框架建筑选择梁和柱。求解相关离散变量优化问题的方法包括：(1)执行预处理算法，生成包含可用离散值组合的约束；(2)执行标准非线性规划软件，获得连续最优；(3)执行后处理算法，在连续最优的邻域内找到离散最优。

The objective of the research is two-fold. First, algorithms will be developed for solving nonlinear optimization problems in which some of the variables may assume certain combinations of discrete values. These algorithms must be efficient in terms of minimizing the amount of analysis required to solve the problem. Second, these algorithms will be tested by implementing them into a general-purpose computer program for selecting beams and columns for rectangular steel-framed buildings. The approach for solving optimization problems with related discrete variables consists of: (1) executing a pre-processing algorithm which generates constraints enclosing the available combinations of discrete values, (2) executing standard nonlinear programming software to obtain the continuous optimun, and (3) executing a post-processing algorithm to find the discrete optimum within a neighborhood of the continuous optimum.