Anton Bouter

Jasper Post, Johannes Koch, Anton Bouter et al.

GP-GOMEA is a state-of-the-art evolutionary algorithm for symbolic regression, known for discovering small and interpretable models. However, its computational cost remains substantial, limiting its applicability to larger datasets and more complex target expressions. In contrast, the rise of modern subsymbolic approaches, particularly deep learning, has been driven largely by the massive parallelism offered by GPUs. In this work, we take the first major step toward a fully GPU-accelerated GP-GOMEA by introducing a GPU-based fitness evaluation scheme. We design a GPU-friendly representation of GP-GOMEA's template-based individuals and a corresponding evaluation strategy that exploits the inherent parallelism of population-based search. This substantially increases evaluation throughput, enabling orders of magnitude more evaluations within the same time budget. Across four standard symbolic regression benchmarks, this increased evaluation capacity yields performance improvements, particularly for larger datasets and larger population sizes. Moreover, the ability to efficiently evaluate much larger datasets and more complex templates enables analyses that were previously infeasible, allowing us to systematically analyze what makes expressions increasingly difficult for GP-GOMEA, providing new insights into how expression structure affects search difficulty. Finally, for the first time, this expanded capability allows a problem-agnostic evolutionary algorithm to reliably regress one of the largest Feynman equations within four hours.

Georgios Andreadis, Joas I. Mulder, Anton Bouter et al.

The transformation model is an essential component of any deformable image registration approach. It provides a representation of physical deformations between images, thereby defining the range and realism of registrations that can be found. Two types of transformation models have emerged as popular choices: B-spline models and mesh models. Although both models have been investigated in detail, a direct comparison has not yet been made, since the models are optimized using very different optimization methods in practice. B-spline models are predominantly optimized using gradient-descent methods, while mesh models are typically optimized using finite-element method solvers or evolutionary algorithms. Multi-objective optimization methods, which aim to find a diverse set of high-quality trade-off registrations, are increasingly acknowledged to be important in deformable image registration. Since these methods search for a diverse set of registrations, they can provide a more complete picture of the capabilities of different transformation models, making them suitable for a comparison of models. In this work, we conduct the first direct comparison between B-spline and mesh transformation models, by optimizing both models with the same state-of-the-art multi-objective optimization method, the Multi-Objective Real-Valued Gene-pool Optimal Mixing Evolutionary Algorithm (MO-RV-GOMEA). The combination with B-spline transformation models, moreover, is novel. We experimentally compare both models on two different registration problems that are both based on pelvic CT scans of cervical cancer patients, featuring large deformations. Our results, on three cervical cancer patients, indicate that the choice of transformation model can have a profound impact on the diversity and quality of achieved registration outcomes.

Arkadiy Dushatskiy, Marco Virgolin, Anton Bouter et al.

When it comes to solving optimization problems with evolutionary algorithms (EAs) in a reliable and scalable manner, detecting and exploiting linkage information, i.e., dependencies between variables, can be key. In this article, we present the latest version of, and propose substantial enhancements to, the Gene-pool Optimal Mixing Evoutionary Algorithm (GOMEA): an EA explicitly designed to estimate and exploit linkage information. We begin by performing a large-scale search over several GOMEA design choices, to understand what matters most and obtain a generally best-performing version of the algorithm. Next, we introduce a novel version of GOMEA, called CGOMEA, where linkage-based variation is further improved by filtering solution mating based on conditional dependencies. We compare our latest version of GOMEA, the newly introduced CGOMEA, and another contending linkage-aware EA DSMGA-II in an extensive experimental evaluation, involving a benchmark set of 9 black-box problems that can only be solved efficiently if their inherent dependency structure is unveiled and exploited. Finally, in an attempt to make EAs more usable and resilient to parameter choices, we investigate the performance of different automatic population management schemes for GOMEA and CGOMEA, de facto making the EAs parameterless. Our results show that GOMEA and CGOMEA significantly outperform the original GOMEA and DSMGA-II on most problems, setting a new state of the art for the field.