Linear representation of categorical values

TL;DR

This paper introduces a linear binary representation for categorical values that preserves neighborhood structure, enabling efficient mutation in evolutionary algorithms and demonstrating promising results in puzzle-solving tasks.

Contribution

It presents a novel linear encoding method for categorical data that improves mutation efficiency and performance in evolutionary algorithms compared to traditional encodings.

Findings

Effective in reaching all categorical values with a single mutation

Shows promising results in Sudoku puzzle experiments

Performs well in high and low dimension instances

Abstract

We propose a binary representation of categorical values using a linear map. This linear representation preserves the neighborhood structure of categorical values. In the context of evolutionary algorithms, it means that every categorical value can be reached in a single mutation. The linear representation is embedded into standard metaheuristics, applied to the problem of Sudoku puzzles, and compared to the more traditional direct binary encoding. It shows promising results in fixed-budget experiments and empirical cumulative distribution functions with high dimension instances, and also in fixed-target experiments with small dimension instances.