A First Look at Kolmogorov-Arnold Networks in Surrogate-assisted Evolutionary Algorithms

TL;DR

This work investigates applying Kolmogorov-Arnold Networks (KANs) as surrogate models in surrogate-assisted evolutionary algorithms to tackle expensive optimization problems. It introduces two SAE frameworks, SPS and SAS, and demonstrates how KANs can be trained for regression or classification to guide candidate selection, reducing costly function evaluations. Across benchmark functions and visualization experiments, KANs outperform traditional surrogates and MLPs, and their integration into SPS/SAS yields notable gains in optimization efficiency. The findings suggest KANs are a promising, interpretable, and scalable alternative for expensive optimization problems, with publicly available code for replication.

Abstract

Surrogate-assisted Evolutionary Algorithm (SAEA) is an essential method for solving expensive expensive problems. Utilizing surrogate models to substitute the optimization function can significantly reduce reliance on the function evaluations during the search process, thereby lowering the optimization costs. The construction of surrogate models is a critical component in SAEAs, with numerous machine learning algorithms playing a pivotal role in the model-building phase. This paper introduces Kolmogorov-Arnold Networks (KANs) as surrogate models within SAEAs, examining their application and effectiveness. We employ KANs for regression and classification tasks, focusing on the selection of promising solutions during the search process, which consequently reduces the number of expensive function evaluations. Experimental results indicate that KANs demonstrate commendable performance within SAEAs, effectively decreasing the number of function calls and enhancing the optimization efficiency. The relevant code is publicly accessible and can be found in the GitHub repository.

Figures (5)

• Figure 1: Framework of KANs-assisted EA.
• Figure 2: Use KANs as a regression model
• Figure 3: Use KANs as a classification model
• Figure 4: Performance of KANs and MLPs on 2D regression tasks. In the first row, the red dots represent the training data, and the surface illustrates the true function. In the second and third rows, the surfaces represent the predicted results from KANs and MLPs, respectively. The R2 score is used to measure the accuracy of the fit, with values closer to 1 indicating better fitting performance.
• Figure 5: Performance of KANs and MLPs on 2D classification tasks. In the figure, the dots represent the training data, with red and blue colors used to distinguish the categories. In the first row, the differently colored shaded areas indicate the true distribution of classes. In the second and third rows, the shaded areas represent the predictive results of KANs and MLPs, respectively.