求解高維多目標最佳化問題的演化演算法效能評析

Abstract

演化演算法在求解多目標最佳化問題有很好的表現，也被廣泛使用於各領域的實際應用問題。然而當決策變數的個數增加至數百個甚至數千個時，指數成長的搜尋空間會對多目標演化演算法的求解能力形成嚴峻的挑戰；因此，近年來演化計算領域有越來越多的學者投入高維多目標演化演算法的設計。然而，我們發現到此領域的研究文獻在評估演算法效能時未能使用統一的實驗設定，此舉可能造成實驗結果的偏頗與失真。本論文自文獻中挑選八個具有代表性的高維多目標演化演算法，使用兩套公開測試函式集 LSMOP 與 LMF，檢視這些演算法在四種問題維度和四種計算資源所組合的十六種實驗環境下的求解效能。經由公平且完整的實驗測試，我們得以正確評比演算法的效能與特質，也對各種演算法設計的異同處與其對於求解效能的影響提出解釋與探討。Evolutionary algorithms have shown promising performance in addressing multiobjective optimization problems (MOPs) and are widely applied across various domains. However, as the number of decision variables grows into the hundreds or even thousands, the exponentially growing search space poses significant challenges to the searching capabilities of multiobjective evolutionary algorithms (MOEAs). In response, recent years have seen a growing focus within the evolutionary computation community on designing MOEAs tailored for large-scale MOPs. One issue we have identified in this research area is the inconsistent experimental settings when evaluating algorithm performance, which can result in biased and misleading outcomes. In this thesis, we select eight representative MOEAs from the literature and employ two publicly available test function sets, LSMOP and LMF, to assess the performance of these algorithms across sixteen experimental scenarios, each defined by a combination of four problem dimensions and four levels of computational budgets. Through rigorous and comprehensive testing, we provide a fair comparison of the algorithms' performance and offer insights into the differences in algorithm design and their implications for solving efficiency.