The \emph{Optimist}: Towards Fully Automated Graph Theory Research

• URL: http://arxiv.org/abs/2411.09158v1
• Date: Thu, 14 Nov 2024 03:24:45 GMT
• Title: The \emph{Optimist}: Towards Fully Automated Graph Theory Research
• Authors: Randy Davila,
• Abstract summary: Leveraging mixed-integer programming (MIP) and methods, the emphOptimist generates conjectures that both rediscover established theorems and propose novel inequalities. Initial experiments reveal the emphOptimist's potential to uncover foundational results in graph theory, as well as to produce conjectures of interest for future exploration.
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• Abstract: This paper introduces the \emph{Optimist}, an autonomous system developed to advance automated conjecture generation in graph theory. Leveraging mixed-integer programming (MIP) and heuristic methods, the \emph{Optimist} generates conjectures that both rediscover established theorems and propose novel inequalities. Through a combination of memory-based computation and agent-like adaptability, the \emph{Optimist} iteratively refines its conjectures by integrating new data, enabling a feedback process with minimal human (\emph{or machine}) intervention. Initial experiments reveal the \emph{Optimist}'s potential to uncover foundational results in graph theory, as well as to produce conjectures of interest for future exploration. This work also outlines the \emph{Optimist}'s evolving integration with a counterpart agent, the \emph{Pessimist} (a human \emph{or machine} agent), to establish a dueling system that will drive fully automated graph theory research.

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