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Heuristic and exact techniques for solving a temperature estimation model.

机译：求解温度估计模型的启发式和精确技术。

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摘要

This dissertation provides several techniques for solving a class of nonconvex optimization problems that arise in the thermal analysis of electronic chip packages. The topic is of interest because in systems containing delicate electronic components both performance and reliability are impacted by thermal behavior. A modeling paradigm, called Compact Thermal Modeling (CTM), has been demonstrated to show promise for accurately estimating steady state thermal behavior without resorting to computationally intensive finite element models or expensive direct experimentation. The CTM is a network model that gives rise to a nonconvex optimization problem. A solution to this nonconvex optimization problem provides a reasonably accurate characterization of the steady state temperature profile the chip will attain under arbitrary boundary conditions, which allows the system designer to model the application of a wide range of thermal design strategies with useful accuracy at reasonable computational cost. This thesis explores several approaches to solving the optimization problem. We present a heuristic technique that is an adaptation of the classical coordinate search method that has been adapted to run efficiently by exploiting the algebraic structure of the problem. Further, the heuristic is able to avoid stalling in poor local optima by using a partitioning scheme that follows from an examination of special structure in the problem's feasible region. We next present several exact approaches using a globally optimal method based on the Reformulation Linearization Technique (RLT). This approach generates and then solves convex relaxations of the original problem, tightening the approximations within a branch and bound framework. We then explore several approaches to improving the performance of the RLT technique by introducing variable substitutions and valid inequalities, which tighten the convex relaxations. Computational results, conclusions; and recommendations for further research are also provided.
机译：本文提供了几种解决电子芯片封装热分析中出现的非凸优化问题的技术。这个话题很有趣，因为在包含精密电子组件的系统中，性能和可靠性都会受到热行为的影响。已经证明了称为紧凑热建模（CTM）的建模范例，显示出可以准确估计稳态热行为的希望，而无需借助计算密集型有限元模型或昂贵的直接实验。 CTM是一种网络模型，会引起非凸优化问题。解决此非凸优化问题的方法可对芯片在任意边界条件下将获得的稳态温度分布进行合理准确的表征，从而使系统设计人员能够以合理的计算量以有用的精度对各种热设计策略的应用进行建模。成本。本文探索了解决优化问题的几种方法。我们提出了一种启发式技术，该技术是对经典坐标搜索方法的一种改进，该经典坐标搜索方法已通过利用问题的代数结构而得以有效运行。此外，启发式方法能够通过使用分区方案来避免在较差的局部最优中停滞，该分区方案是根据问题可行区域中特殊结构的检查得出的。接下来，我们将基于重构线性化技术（RLT），使用全局最优方法介绍几种精确方法。这种方法生成并解决了原始问题的凸松弛，从而在分支定界框架内加强了近似值。然后，我们通过引入变量替换和有效不等式来探索提高RLT技术性能的几种方法，从而加强了凸松弛。计算结果，结论；并提供了进一步研究的建议。

著录项

  • 作者

    Henderson, Dale Lawrence.;

  • 作者单位

    The University of Arizona.;

  • 授予单位 The University of Arizona.;
  • 学科 Engineering System Science.
  • 学位 Ph.D.
  • 年度 2005
  • 页码 104 p.
  • 总页数 104
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 系统科学;
  • 关键词

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