A novel evolutionary formulation of the maximum independent set problem

TL;DR

This paper presents a new evolutionary heuristic for the maximum independent set problem, leveraging acyclic orientations of graphs, and demonstrates its competitiveness on benchmark graphs.

Contribution

It introduces a novel evolutionary approach based on acyclic orientations, offering a new perspective and heuristic for solving the maximum independent set problem.

Findings

Competitive performance on DIMACS benchmark graphs

Effective use of graph structure in evolutionary operators

Outperforms several existing heuristics

Abstract

We introduce a novel evolutionary formulation of the problem of finding a maximum independent set of a graph. The new formulation is based on the relationship that exists between a graph's independence number and its acyclic orientations. It views such orientations as individuals and evolves them with the aid of evolutionary operators that are very heavily based on the structure of the graph and its acyclic orientations. The resulting heuristic has been tested on some of the Second DIMACS Implementation Challenge benchmark graphs, and has been found to be competitive when compared to several of the other heuristics that have also been tested on those graphs.