論文快報-2021-10-Multi-task optimization and evolutionary multitasking

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A Multi-Variation Multifactorial Evolutionary Algorithm for Large-Scale Multi-Objective Optimization

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摘要

• For solving large-scale multi-objective problems (LSMOPs), the transformation-based methods have shown promising search efficiency, which varies the original problem as a new simplified problem and performs the optimization in simplified spaces instead of the original problem space. Owing to the useful information provided by the simplified searching space, the performance of LSMOPs has been improved to some extent. However, it is worth noting that the original problem has changed after the variation, and there is thus no guarantee of the preservation of the original global or near-global optimum in the newly generated space. In this paper, we propose to solve LSMOPs via a multi-variation multifactorial evolutionary algorithm. In contrast to existing transformation-based methods, the proposed approach intends to conduct an evolutionary search on both the original space of the LSMOP and multiple simplified spaces constructed in a multi-variation manner concurrently. In this way, useful traits found along the search can be seamlessly transferred from the simplified problem spaces to the original problem space toward efficient problem-solving. Besides, since the evolutionary search is also performed in the original problem space, preserving the original global optimal solution can be guaranteed. To evaluate the performance of the proposed framework, comprehensive empirical studies are carried out on a set of LSMOPs with 2-3 objectives and 500-5000 variables. The experiment results highlight the efficiency and effectiveness of the proposed method compared to the state-of-the-art methods for large-scale multi-objective optimization.
• 對於解決大規模多目標問題（LSMOP），基於變換的方法顯示出良好的搜尋效率，將原始問題轉換為新的簡化問題，並在簡化空間而不是原始問題空間中執行優化。由於簡化的搜尋空間提供了有用的資訊，LSMOPs 的效能得到了一定程度的提高。然而，值得注意的是，原始問題在變異後發生了變化，因此無法保證在新生成的空間中保留原始全域性或近全域性最優。在本文中，我們建議通過多變數多因素進化演算法來解決 LSMOP。與現有的基於變換的方法相比，所提出的方法旨在對 LSMOP 的原始空間和以多變數方式同時構建的多個簡化空間進行進化搜尋。通過這種方式，搜尋過程中發現的有用特徵可以從簡化的問題空間無縫轉移到原始問題空間，以實現高效的問題解決。此外，由於進化搜尋也是在原始問題空間中進行的，所以可以保證保留原始的全域性最優解。為了評估所提出框架的效能，對一組具有 2-3 個目標和 500-5000 個變數的 LSMOP 進行了全面的實證研究。與用於大規模多目標優化的最新方法相比，實驗結果突出了所提出方法的效率和有效性。

Towards Generalized Resource Allocation on Evolutionary Multitasking for Multi-Objective Optimization

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摘要

• Evolutionary multitasking optimization (EMTO) is an emerging paradigm for solving several problems simultaneously . Due to the flexible framework, EMTO has been naturally applied to multi-objective optimization to exploit synergy among distinct multi-objective problem domains. However, most studies barely take into account the scenario where some problems cannot converge under restrictive computational budgets with the traditional EMTO framework. T o dynamically allocate computational resources for multi-objective EMTO problems, this article proposes a generalized resource allocation (GRA) framework by concerning both theoretical grounds of conventional resource allocation and the characteristics of multi-objective optimization. normalized attainment function is designed for better quantifying convergence status, a multi-step nonlinear regression is proposed to serve as a stable performance estimator, and the algorithmic procedure of conventional resource allocation is refined for flexibly adjusting resource allocation intensity and including knowledge transfer information. It has been verified that the GRA framework can enhance the overall performance of the multi-objective EMTO algorithm in solving benchmark problems, complex problems, many-task problems, and a real-world application problem. Notably , the proposed GRA framework served as a crucial component for the winner algorithm in the Competition on Evolutionary Multi-T ask Optimization (Multi-objective Optimization Track) in IEEE 2020 W orld Congress on Computational Intelligence.
• 進化多工優化（EMTO）是一種同時解決多個問題的新興正規化。由於其靈活的框架，EMTO已自然地應用於多目標優化，以利用不同多目標問題領域之間的協同作用。然而，大多數研究幾乎沒有考慮到一些問題在傳統EMTO框架的限制性計算預算下無法收斂的情況。為了動態分配多目標EMTO問題的計算資源，本文結合傳統資源分配的理論基礎和多目標優化的特點，提出了廣義資源分配（GRA）框架。為了更好地量化收斂狀態，設計了歸一化達到函式，提出了一種多步非線性迴歸作為穩定的效能估計器，改進了傳統資源分配的演算法流程，靈活調整資源分配強度，包含知識轉移資訊。經驗證，GRA框架可以提高多目標EMTO演算法在解決基準問題、複雜問題、多工問題和實際應用問題時的整體效能。值得注意的是，在IEEE 2020世界計算智慧大會的進化多工優化（多目標優化軌道）競賽中，所提出的GRA框架是勝利者演算法的關鍵組成部分。

Improving Evolutionary Multitasking Optimization by Leveraging Inter-Task Gene Similarity and Mirror Transformation

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摘要

• Solving a complex optimization task from scratch can be significantly expensive and/or time-consuming. Common knowledge obtained from different (but possibly related) optimization tasks may help enhance the solving of such tasks. In this regard, evolutionary multitasking optimization (EMTO) has been proposed to improve the solving of multiple optimization tasks simultaneously via knowledge transfer in the evolutionary algorithm framework. The effectiveness of knowledge transfer is crucial for the success of EMTO. Multifactorial evolutionary algorithm (MFEA) is one of the most representative EMTO algorithms, however, it suffers from negative knowledge transfer among the tasks with low correlation. To address this issue, in this study, inter-task gene-similarity-based knowledge transfer and mirror transformation are integrated into MFEA (termed as MFEA-GSMT). In the proposed inter-task gene-similarity-based knowledge transfer, a probabilistic model is used to feature each gene and the Kullback-Leibler divergence is employed to measure the inter-task dimension similarity. Guided by the inter-task gene similarity, a selective crossover is used to reproduce offspring solutions. The proposed inter-task knowledge transfer is based on online gene similarity evaluation, instead of individual similarity, to overcome the imprecise estimation of population distributions in a high-dimensional space with only a small number of samples. The proposed mirror transformation is an extension of opposition-based learning to avoid premature convergence and explore additional promising search areas. Experimental results on both single-objective and multi-objective multi-tasking problems demonstrate the effectiveness and efficiency of the proposed MFEA-GSMT.
• 從頭開始解決複雜的優化任務可能非常昂貴和/或耗時。從不同（但可能相關）優化任務中獲得的共同知識可能有助於增強此類任務的解決。在這方面，已經提出了進化多工優化（EMTO），以通過進化演算法框架中的知識轉移來改進同時解決多個優化任務。知識轉移的有效性對於 EMTO 的成功至關重要。多因子進化演算法（MFEA）是最具代表性的 EMTO 演算法之一，但它存在相關性低的任務之間的負知識轉移問題。為了解決這個問題，在本研究中，基於任務間基因相似性的知識轉移和映象轉換被整合到 MFEA（稱為 MFEA-GSMT）中。在提出的基於任務間基因相似性的知識轉移中，使用概率模型來表徵每個基因，並採用 Kullback-Leibler 散度來衡量任務間維度相似性。在任務間基因相似性的指導下，使用選擇性交叉來重現後代解決方案。所提出的任務間知識轉移基於線上基因相似性評估，而不是個體相似性，以克服僅具有少量樣本的高維空間中種群分佈的不精確估計。提議的映象轉換是基於對立的學習的擴充套件，以避免過早收斂並探索其他有希望的搜尋領域。單目標和多目標多工問題的實驗結果證明了所提出的 MFEA-GSMT 的有效性和效率。