Zobrist Hash-based Duplicate Detection in Symbolic Regression

TL;DR

This paper introduces a Zobrist hash-based caching mechanism to improve the efficiency of genetic programming in symbolic regression, achieving up to 34% speedups without compromising search quality.

Contribution

The paper presents a novel Zobrist hash-based caching method integrated into GP for symbolic regression, reducing redundant evaluations and enhancing computational efficiency.

Findings

Up to 34% speedup in symbolic regression tasks.

No negative impact on search quality observed.

Effective caching reduces redundant evaluations in GP.

Abstract

Symbolic regression encompasses a family of search algorithms that aim to discover the best fitting function for a set of data without requiring an a priori specification of the model structure. The most successful and commonly used technique for symbolic regression is Genetic Programming (GP), an evolutionary search method that evolves a population of mathematical expressions through the mechanism of natural selection. In this work we analyze the efficiency of the evolutionary search in GP and show that many points in the search space are re-visited and re-evaluated multiple times by the algorithm, leading to wasted computational effort. We address this issue by introducing a caching mechanism based on the Zobrist hash, a type of hashing frequently used in abstract board games for the efficient construction and subsequent update of transposition tables. We implement our caching approach using the open-source framework Operon and demonstrate its performance on a selection of real-world regression problems, where we observe up to 34\% speedups without any detrimental effects on search quality. The hashing approach represents a straightforward way to improve runtime performance while also offering some interesting possibilities for adjusting search strategy based on cached information.