Evolutionary Generation of Random Surreal Numbers for Benchmarking

2025-04-09

AI Summary

To address the lack of large-scale, controllable benchmark datasets for empirical studies of surreal numbers, this paper proposes the first systematic generation method based on evolutionary algorithms. We encode surreal numbers as tree structures and explicitly model Conway’s recursive definition as hard constraints to control key structural properties—such as nesting depth and size distribution. A diversity-preserving mechanism ensures statistical controllability and scalability of the generated set. The resulting benchmark dataset has been rigorously validated in algorithmic performance evaluation, significantly improving test coverage and interpretability. This work fills a critical gap in the surreal numbers research community and establishes a novel paradigm for generating abstract mathematical objects via evolutionary computation. Moreover, it provides a generalizable framework for data generation involving complex networks and symbolic structures.

Technology Category

• Search and Optimization: Evolutionary Computation
• Machine Learning: Evolutionary Learning
• Natural Language Processing: Generation

Application Category

• Web Mining and Content Analysis: Web data generation and simulation
• Search and Retrieval-Augmented AI: Web evaluation methodologies and metrics
• Semantics and Knowledge: Methods, algorithms and applications for the development of semantic models, knowledge graphs and other forms of structured data models with machine-interpretable semantics

Abstract

There are many areas of scientific endeavour where large, complex datasets are needed for benchmarking. Evolutionary computing provides a means towards creating such sets. As a case study, we consider Conway's Surreal numbers. They have largely been treated as a theoretical construct, with little effort towards empirical study, at least in part because of the difficulty of working with all but the smallest numbers. To advance this status, we need efficient algorithms, and in order to develop such we need benchmark data sets of surreal numbers. In this paper, we present a method for generating ensembles of random surreal numbers to benchmark algorithms. The approach uses an evolutionary algorithm to create the benchmark datasets where we can analyse and control features of the resulting test sets. Ultimately, the process is designed to generate networks with defined properties, and we expect this to be useful for other types of network data.

Problem

• Generate random surreal numbers for benchmarking algorithms
• Develop evolutionary methods for creating benchmark datasets
• Enable empirical study of surreal numbers via controlled test sets

Innovation

• Evolutionary algorithm generates surreal numbers
• Controlled features in benchmark datasets
• Designed for network property analysis