Scalable genetic programming by gene-pool optimal mixing and input-space entropy-based building-block learning

Abstract

e Gene-pool Optimal Mixing Evolutionary Algorithm (GOMEA) is a recently introduced model-based EA that has been shown to be capable of outperforming state-of-the-art alternative EAs in terms of scalability when solving discrete optimization problems. One of the key aspects of GOMEA's success is a variation operator that is designed to extensively exploit linkage models by e ectively combining partial solutions. Here, we bring the strengths of GOMEA to Genetic Programming (GP), introducing GP-GOMEA. Under the hypothesis of having li le problem-speci c knowledge, and in an e ort to design easy-to-use EAs, GP-GOMEA requires no parameter speci cation. On a set of well-known benchmark problems we nd that GP-GOMEA outperforms standard GP while being on par with more recently introduced, state-of-the-art EAs. We furthermore introduce Input-space Entropy-based Building-block Learning (IEBL), a novel approach to identifying and encapsulating relevant building blocks (subroutines) into new terminals and functions. On problems with an inherent degree of modularity, IEBL can contribute to compact solution representations, providing a large potential for knock-on e ects in performance. On the di cult, but highly modular Even Parity problem, GP-GOMEA+IEBL obtains excellent scalability, solving the 14-bit instance in less than 1 hour.

Symbolic regression and feature construction with GP-GOMEA applied to radiotherapy dose reconstruction of childhood cancer survivors

“…The Gene-pool Optimal Mixing Evolutionary Algorithm for GP (GP-GOMEA), recently introduced in [19], was shown capable of finding much smaller solutions than Standard GP (SGP) and other EAs for well-known synthetic benchmarks and Binary circuit regression, while achieving similar, or superior, scalability.…”

“…The Linkage Tree (LT) FOS is often used in GOMEA because it has been shown to achieve solid performance on different problems [16,19]. The LT captures hierarchical degrees of interdependency among nodes.…”

“…This is often a negligible overhead in GP, where computing the output of solutions is typically the performance bottleneck. Further details on the LT can be found in [16,19]. In this work, GP-GOMEA was always run with the LT FOS.…”

“…SGP bounded uses the same maximum tree height of GP-GOMEA, i.e., 5. Lastly, both GP-GOMEA and SGP use the caching of node outputs (i.e., partial evaluations) to speed up solution evaluation time [13,19].…”

“…The Gene-pool Optimal Mixing Evolutionary Algorithm for GP (GP-GOMEA) is a recent, model-based algorithm which has been shown to achieve excellent scalability on synthetic Boolean benchmark problems [19], while evolving much smaller solutions than various competing algorithms. GP-GOMEA prevents bloat by construction, and performs variation based on a linkage model, i.e., a model that captures genotypic interdependencies.…”