設計一個能夠有效且快速求解高目標最佳化問題的演算法,已成為當領域的 重要課題之一。我們以 Deb 與 Jain [8] 所提出的 NSGA-III 為基礎演算法,從 親代選擇機制、環境選擇機制以及平行化,試圖改良此優秀演算法中尚為欠缺的 部分,經由實驗佐證,不管在演算法的求解能力以及執行速度上,都收到相當不 錯的成效。
在親代選擇機制,我們希望藉由 NSGA-III 的參考點概念來加強選擇親代時 的辨別能力,以期能夠辨認出族群中哪些區域需要優先進行改進,並透過鄰居選 取機制,增強演算法整體的求解效能。鄰居親代選擇機制將目標空間中相近的個 體交配,能夠有效地加強演算法的求解能力,我們在實驗中測試了各種鄰居大小 的設定,當此值設為族群大小的 10% 效果最好。
關於強化劣勢參考點的親代選擇機制,由於其選取的取向集中性強,因此不 適合族群尚未收歛完整時使用,我們的實驗結果顯示,此機制大約在演化代數經 過 70%~90% 時使用較為適當,並能有效加強演算法的求解能力,此機制與鄰 居親代選擇機制配合下,與原版的 NSGA-III 演算法相比,於總計 15 個測試問 題中,能有著 12 勝 3 和的顯著改進,成效相當優異。
在將 NSGA-III 平行化的機制中,我們嘗試將權重向量用各種不同的方式切 割給予子族群去各自演化,其中效能最好的分割方法為保留角的依序整批分配法,
搭配遷徙以及我們所提出的親代選擇機制,演算法的效能不管在執行速度或是求
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解能力上,都勝過原版的 NSGA-III,在總計 15 個測試問題中,有著 11 勝 3 和
1 負的顯著改善。
雖然我們所提出的親代選擇機制以及平行化,求解能力比 NSGA-III 演算法 優異,但這些機制都需要設定一些參數,在我們的實驗中,有提供建議的參數調 整方向。我們未來會致力於提出一套自動調整參數的版本,以加強這些機制的實 用性,並嘗試求解各種具限制以及現實世界中的高目標最佳化問題,驗證我們的 機制在各種情況下都能有著優異的表現。
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