Surrogate-Assisted Search with Competitive Knowledge Transfer for Expensive Optimization

TL;DR

This work addresses the cold-start problem in expensive optimization by introducing SAS-CKT, a plug-and-play competitive knowledge transfer module for surrogate-assisted search. It integrates source-task solutions with target-task promising solutions through a competition framework that selects the most promising candidate for real evaluation, supported by a surrogate-based similarity measure and a translation-based task adaptation. Theoretical analysis establishes a lower bound on convergence gain and identifies conditions for positive transfer, while extensive experiments across STOP benchmarks and a petroleum production case demonstrate portability, reliability, and adaptivity of SAS-CKT across diverse backbone SAEAs. The approach yields tangible speedups and improved solution quality, offering a practical pathway to leverage historical optimization experiences in real-world, computationally expensive problems, with publicly available code for reproducibility.

Abstract

Expensive optimization problems (EOPs) have attracted increasing research attention over the decades due to their ubiquity in a variety of practical applications. Despite many sophisticated surrogate-assisted evolutionary algorithms (SAEAs) that have been developed for solving such problems, most of them lack the ability to transfer knowledge from previously-solved tasks and always start their search from scratch, making them troubled by the notorious cold-start issue. A few preliminary studies that integrate transfer learning into SAEAs still face some issues, such as defective similarity quantification that is prone to underestimate promising knowledge, surrogate-dependency that makes the transfer methods not coherent with the state-of-the-art in SAEAs, etc. In light of the above, a plug and play competitive knowledge transfer method is proposed to boost various SAEAs in this paper. Specifically, both the optimized solutions from the source tasks and the promising solutions acquired by the target surrogate are treated as task-solving knowledge, enabling them to compete with each other to elect the winner for expensive evaluation, thus boosting the search speed on the target task. Moreover, the lower bound of the convergence gain brought by the knowledge competition is mathematically analyzed, which is expected to strengthen the theoretical foundation of sequential transfer optimization. Experimental studies conducted on a series of benchmark problems and a practical application from the petroleum industry verify the efficacy of the proposed method. The source code of the competitive knowledge transfer is available at https://github.com/XmingHsueh/SAS-CKT.

Figures (14)

• Figure 1: High-level structure of SAS.
• Figure 2: Flow chart of the proposed SAS-CKT.
• Figure 3: Relations between the three lemmas and Theorem 1.
• Figure 4: Illustration of the impacts of $\lambda^t$ and $\Delta^*_\tau$ on the lower bound of the conditional similarity for positive convergence gain (i.e., $\tilde{s}_*$): (a) the lower bound of the similarity with respect to $\lambda^t$ when $\Delta^*_\tau=50$; (b) a 3D surface for demonstrating the joint impact of $\lambda^t$ and $\Delta^*_\tau$ on $\tilde{s}_*$; (c) the lower bound of the similarity with respect to $\Delta^*_\tau$ when $\lambda^t=0.16$.
• Figure 5: Averaged convergence curves of SAS-CKT against SAS with the six backbone optimizers on four problems: (a) STOP 2; (b) STOP 5; (c) STOP 8; (d) STOP 9.

Theorems & Definitions (11)

• Definition 1
• Theorem 1
• Definition S-2
• Lemma 1
• Lemma S-1
• Definition S-3
• Lemma S-2
• Lemma 2
• Definition S-4
• Lemma 3