Modeling without categorical variables: a mixed-integer nonlinear program for the optimization of thermal insulation systems |
| |
Authors: | Kumar Abhishek Sven Leyffer Jeffrey T Linderoth |
| |
Affiliation: | 1.Enterprise Optimization,United Airlines,Elk Grove Village,USA;2.Mathematics and Computer Science Division,Argonne National Laboratory,Argonne,USA;3.Department of Industrial and Systems Engineering,University of Wisconsin-Madison,Madison,USA |
| |
Abstract: | Optimal design applications are often modeled by using categorical variables to express discrete design decisions, such as
material types. A disadvantage of using categorical variables is the lack of continuous relaxations, which precludes the use
of modern integer programming techniques. We show how to express categorical variables with standard integer modeling techniques,
and we illustrate this approach on a load-bearing thermal insulation system. The system consists of a number of insulators
of different materials and intercepts that minimize the heat flow from a hot surface to a cold surface. Our new model allows
us to employ black-box modeling languages and solvers and illustrates the interplay between integer and nonlinear modeling
techniques. We present numerical experience that illustrates the advantage of the standard integer model. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|