Mixed Variable Optimization of the Number and Composition of Heat Intercepts in a Thermal Insulation System

作     者：Kokkolaras, Michael Audet, Charles Dennis, J. E., Jr. 

作者机构：Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA Ecole Polytech Montreal Dept Math & Genie Ind Montreal PQ Canada Rice Univ Dept Computat & Appl Math Houston TX USA 

出 版 物：《OPTIMIZATION AND ENGINEERING》 (最优化与工程学)

年 卷 期：2001年第2卷第1期

页      面：5-29页

核心收录：

学科分类：12[管理学] 1201[管理学-管理科学与工程(可授管理学、工学学位)] 08[工学] 0701[理学-数学] 

基　　金：NSERC (Natural Sciences and Engineering Research Council) [PDF-207432-1998] DOE [DE-FG03-95ER25257] AFOSR [F49620-01-1-0013] Boeing Company, Sandia [LG-4253] Exxon-Mobil CRPC [CCR-9120008] 

主　　题：optimization thermal insulation heat intercepts categorical variables mixed variable programming (MVP) pattern search algorithm 

摘      要：In the literature, thermal insulation systems with a fixed number of heat intercepts have been optimized with respect to intercept locations and temperatures. The number of intercepts and the types of insulators that surround them were chosen by parametric studies. This was because the optimization methods used could not treat such categorical variables. Discrete optimization variables are categorical if the objective function or the constraints can not be evaluated unless the variables take one of a prescribed enumerable set of values. The key issue is that categorical variables can not be treated as ordinary discrete variables are treated by relaxing them to continuous variables with a side constraint that they be discrete at the solution. A new mixed variable programming (MVP) algorithm makes it possible to optimize directly with respect to mixtures of discrete, continuous, and categorical decision variables. The result of applying MVP is shown here to give a 65% reduction in the objective function over the previously published result for a thermal insulation model from the engineering literature. This reduction is largely because MVP optimizes simultaneously with respect to the number of heat intercepts and the choices from a list of insulator types as well as intercept locations and temperatures. The main purpose of this paper is to show that the mixed variable optimization algorithm can be applied effectively to a broad class of optimization problems in engineering that could not be easily solved with earlier methods.