A Probabilistic Ant-based Heuristic for the Longest Simple Cycle Problem in Complex Networks

TL;DR

This paper introduces ANTH-LS, a probabilistic ant-based heuristic designed to find long simple cycles in complex networks, addressing an NP-hard problem with practical applications in various scientific fields.

Contribution

The paper presents a novel ant-based heuristic that effectively improves the longest cycle found in complex networks, outperforming previous methods on several real-world instances.

Findings

Achieved longer cycles in 6 out of 22 test networks

Effective in social, biological, and graph datasets

Demonstrates the heuristic's practical utility

Abstract

We propose a new probabilistic ant-based heuristic (ANTH-LS) for the longest simple cycle problem. This NP-hard problem has numerous real-world applications in complex networks, including efficient construction of graph layouts, analysis of social networks or bioinformatics. Our algorithm is based on reinforcing the probability of traversing the edges, which have not been present in the long cycles found so far. Experimental results are presented for a set of social networks, protein-protein interation networks, network science graphs and DIMACS graphs. For 6 out of our 22 real-world network test instances, ANTH-LS has obtained an improvement on the longest cycle ever found.