Transfer learning in optimization: Interpretable self-organizing maps driven similarity indices to identify candidate source functions

In the design evolution of a product, designers often require solving similar functions repeatedly across different designs. These functions are usually related to each other and typically share topology, common features and physics. Thus, solving one function referred to as a source that characterizes a problem can yield knowledge that can be reused to solve other related function referred to as target. Re-purposing such shared knowledge, especially in cases of complex optimization, aids in faster convergence, more accurate solutions, and reduced computational costs, among others. The concept of transfer learning (TL) is built on this notion of passing the gained knowledge between related problems to lessen the algorithmic and/or modeling complexities. Transfer of knowledge between source and target that are not related leads to negative transfer circumstances, where the algorithm’s performance degrades on transferring. Hence, identifying a similar source to share the knowledge is of fundamental importance in transfer learning approaches. Literature has often skipped this step of identifying related or similar functions by artificially constructing functions or assuming apriori that the considered functions are similar to each other. Current work proposes to use interpretable self-organizing map and an image comparison technique to quantify the topological similarity between the source and the target. Metrics such as mean squares, structural similarity index, and Cosine similarity are used to quantify the level of similarity mathematically. The proposed approach is implemented on a suite of benchmark analytical functions with varying order, complexity, and dimensions, engineering examples, and real-world application functions. It is demonstrated that the proposed approach is able to identify appropriate source function for a given target, even when they are of varying dimensions. Results of engineering examples show that functions representing problems with similar physics are identified correctly. Hence, the proposed approach can be used to identify appropriate source functions for a given target, permitting transfer learning and thus accelerating convergence, and reducing computational cost. •A new scheme is proposed to identify similar functions, to apply TL in optimization.•iSOM-based techniques are used for similarity analysis between functions.•Suitable metrics are provided for the mathematical quantification of similarity.•Source and target functio