# A Simple Fitness Function for Minimum Attribute Reduction

## TL;DR

This paper introduces a simple and effective fitness function for finding minimal attribute reductions in data classification.

## Contribution

A new fitness function based on positive domain that ensures equivalence between optimal solutions and minimal attribute reductions.

## Key findings

- The proposed fitness function satisfies the equivalence between optimal solutions and minimal attribute reductions.
- Experimental results show the new function outperforms existing ones across tested algorithms.
- The function is simpler and more effective for solving nonlinearly constrained combinatorial optimization problems.

## Abstract

The goal of minimal attribute reduction is to find the minimal subset R of the condition attribute set C such that R has the same classification quality as C. This problem is well known to be NP-hard. When only one minimal attribute reduction is required, it was transformed into a nonlinearly constrained combinatorial optimization problem over a Boolean space and some heuristic search approaches were used. In this case, the fitness function is one of the keys of this problem. It required that the fitness function must satisfy the equivalence between the optimal solution and the minimal attribute reduction. Unfortunately, the existing fitness functions either do not meet the equivalence, or are too complicated. In this paper, a simple and better fitness function based on positive domain was given. Theoretical proof shows that the optimal solution is equivalent to minimal attribute reduction. Experimental results show that the proposed fitness function is better than the existing fitness function for each algorithm in test.