在最近幾年多速率transmultiplexer系統已經常用來表示為一些流行的通信應用，如CDMA、FDMA等。在現今，許多研究已經廣泛地研究了濾波器設計在多速率transmultiplexer系統上。他們大部分都集中研究在單一設計目標問題。但是，多個濾波器設計目標的問題，常常會自然會出現在真實的生活場景中，而且往往這幾個多目標問題會相互的衝突。因此，對於多目標問題的濾波器設計，最佳解可能不存在於生活上，因此有效的方法應該提供幾個Pareto 最佳解。在不確定輸入信號和附加雜訊的transmultiplexer系統上，我們考慮兩個濾波器設計目標，一方面，在transmultiplexer系統中，我們期望重建信號的均方誤差越低越好。另一方面，所有可能不確定的雜訊對信號重建誤差的影響我們也期望應盡量減少，從強健H∞的濾波器設計的觀點來看。相對於一些的濾波器的設計，提出多目標過濾器的設計可以同時降低上述兩個信號重建問題。首先，，提出suboptimal MOP技術，多目標重構濾波器設計問題可以轉化為 blinear矩陣不等式（BMI）-constrained MOP。然後一個線性矩陣不等式（LMI）為基礎的多目標進化算法（MOEA）方法，提出獲得一組 BMI-constrained MOP之信號重構濾波器設計的多速率transmultiplexer系統的Pareto 最佳解，設計人員可以從中選擇一個過濾器設計根據自己的喜好。此外，多目標濾波器設計問題的基礎上，加權的方法也解決了transmultiplexer系統且進行比較。

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