Ant Colony Optimization and Hypergraph Covering Problems

TL;DR

This paper analyzes the runtime of an Ant Colony Optimization algorithm on hypergraph covering problems, showing that heuristic information significantly improves expected optimization time, with some instances solved efficiently.

Contribution

It provides the first runtime analysis of MMAS* ACO on hypergraph covering problems, highlighting the impact of heuristic information on optimization efficiency.

Findings

Heuristic information greatly influences optimization time.

MMAS* achieves constant expected runtime on certain hypergraph instances.

Pheromone values have less impact compared to heuristics.

Abstract

Ant Colony Optimization (ACO) is a very popular metaheuristic for solving computationally hard combinatorial optimization problems. Runtime analysis of ACO with respect to various pseudo-boolean functions and different graph based combinatorial optimization problems has been taken up in recent years. In this paper, we investigate the runtime behavior of an MMAS*(Max-Min Ant System) ACO algorithm on some well known hypergraph covering problems that are NP-Hard. In particular, we have addressed the Minimum Edge Cover problem, the Minimum Vertex Cover problem and the Maximum Weak- Independent Set problem. The influence of pheromone values and heuristic information on the running time is analysed. The results indicate that the heuristic information has greater impact towards improving the expected optimization time as compared to pheromone values. For certain instances of hypergraphs, we show that the MMAS* algorithm gives a constant order expected optimization time when the dominance of heuristic information is suitably increased.