Many real-world applications require solving optimization functions that share certain common features and physics. Thus solving one problem can yield knowledge that can be reused to solve other problems related to it. Repurposing such shared knowledge, especially in cases of complex functions, aids in aspects such as faster convergence, more accurate solutions, reduced computational costs, among others. The concept of Transfer Learning (TL) is built on this notion of passing the gained knowledge between related but different problems to lessen the algorithmic and/or modeling complexities. Transfer of knowledge between problems that are not related leads to negative transfer circumstances and deterioration in algorithm performance. Hence, identifying related tasks is of fundamental importance in transfer learning approaches. Literature has often skipped this step of identifying related or similar problems by independently and artificially constructing problems or assuming apriori that the considered problems are similar to each other. Current work proposes to identify similar functions from the perspective of their topologies. We use interpretable Self Organizing Maps (iSOM), which is an unsupervised machine learning technique used to produce a low-dimensional (typically two-dimensional) representation of a higher dimensional data set while preserving the topological structure of the data, to compare the functions. Metrics such as mean squares, structural similarity index, cosine similarity are used to quantify the level of similarity mathematically. The proposed approach is demonstrated on a class of diverse optimization problems containing benchmark mathematical optimization functions with varying order, complexity and dimensions, and engineering examples. Future work will discuss means to transfer knowledge from source to target function, identified through the proposed approach, to permit accelerated convergence in terms of reduced function evaluations.

Keywords: Transfer Leaning, optimization, similarity, visualization.