利用非線性規劃對高扇入多工器作最佳化設計

Abstract

本論文提出了一個新的混成樹狀多工器(Heterogeneous-Tree Multiplexer) 的設計方法。我們利用曲線圖近似技術(curve fitting technique)來建立多工器的延遲模型，然後把混成樹狀多工器的設計問題模擬成混合整數非線性規劃(mixed-integer nonlinear programming)的問題，利用混合整數非線性規劃的特性，儘管在不同的製程條件下，我們也可以得到合理的設計參數。為了改善混成樹狀多工器的速度，我們引進了一個新的設計參數來表示多工器每一級的開關尺寸。我們也提出了三種最佳化的方法來幫助設計者根據設計規格來決定出最佳的多工器架構與每一級開關的尺寸，這三種方法分別是延遲最小化、在面積限制下的延遲最小化、與在延遲限制下的面積最小化。

In this thesis, a novel strategy to design heterogeneous-tree multiplexer is proposed. We build the multiplexer delay model by curve fitting and then formulate the heterogeneous-tree multiplexer design problem as a special type optimization problem called Mixed-Integer Nonlinear Programming (MINLP). Because of the feature of Mixed-Integer Nonlinear Programming, we can get the reasonable design parameters directly, no matter what kind of technology is used. In order to improve the speed performance of the heterogeneous-tree multiplexer, a new design parameter, the switch size in each stage, is introduced. The proposed strategy can determine the multiplexer architecture and the switch size in each stage simultaneously. We provide three optimization methods, which are delay minimization, delay minimization under area constraint, and area minimization under delay constraint, to help designers to determine the multiplexer architecture and the switch size in each stage according to the design specification.