# Exploiting Problem Structure in Combinatorial Landscapes: A Case Study on Pure Mathematics Application

## TL;DR

This paper introduces an AI-based method that leverages problem structure in combinatorial landscapes to efficiently solve a pure mathematics problem involving narrow admissible tuples, demonstrating significant search space reduction and solution effectiveness.

## Contribution

It presents a novel approach that exploits local search structures to improve combinatorial optimization in pure mathematics applications.

## Key findings

- Efficiently finds best known solutions
- Reduces search space significantly
- Effectively escapes local minima

## Abstract

In this paper, we present a method using AI techniques to solve a case of pure mathematics applications for finding narrow admissible tuples. The original problem is formulated into a combinatorial optimization problem. In particular, we show how to exploit the local search structure to formulate the problem landscape for dramatic reductions in search space and for non-trivial elimination in search barriers, and then to realize intelligent search strategies for effectively escaping from local minima. Experimental results demonstrate that the proposed method is able to efficiently find best known solutions. This research sheds light on exploiting the local problem structure for an efficient search in combinatorial landscapes as an application of AI to a new problem domain.