Evolutionary transfer optimization (ETO) has been gaining popularity in research over the years due to its outstanding knowledge transfer ability to address various challenges in optimization. However, a pressing issue in this field is that the invention of new ETO algorithms has far outpaced the development of fundamental theories needed to clearly understand the key factors contributing to the success of these algorithms for effective generalization. In response to this challenge, this study aims to establish theoretical foundations for analogy-based ETO, specifically to support various algorithms that frequently reference a key concept known as similarity. First, we introduce analogical reasoning and link its subprocesses to three key issues in ETO. Then, we develop theories for analogy-based knowledge transfer, rooted in the principles that underlie the subprocesses. Afterwards, we present two theorems related to the performance gain of analogy-based knowledge transfer, namely unconditionally nonnegative performance gain and conditionally positive performance gain, to theoretically demonstrate the effectiveness of various analogy-based ETO methods. Last but not least, we offer a novel insight into analogy-based ETO that interprets its conditional superiority over traditional evolutionary optimization through the lens of the no free lunch theorem for optimization.

翻译：进化迁移优化（ETO）因其出色的知识迁移能力，能够应对优化中的各种挑战，近年来在研究中日益受到关注。然而，该领域的一个紧迫问题是，新ETO算法的发明速度远远超过了基础理论的发展，而这些理论对于清晰理解促成这些算法成功实现有效泛化的关键因素至关重要。为应对这一挑战，本研究旨在为基于类比的ETO建立理论基础，特别为那些频繁引用一个称为相似性的关键概念的各种算法提供支持。首先，我们引入类比推理，并将其子过程与ETO中的三个关键问题联系起来。接着，我们基于这些子过程所依据的原理，发展了基于类比的知识迁移理论。随后，我们提出了两个与基于类比的知识迁移性能增益相关的定理，即无条件非负性能增益和条件正性能增益，从而从理论上证明了各种基于类比的ETO方法的有效性。最后同样重要的是，我们为基于类比的ETO提供了一个新颖的见解，通过优化中的无免费午餐定理视角，阐释了其相对于传统进化优化的条件优越性。