Hybrid cuckoo search algorithm for the minimum dominating set problem

TL;DR

This paper introduces a hybrid cuckoo search algorithm enhanced with genetic crossover and intensification techniques to effectively solve the NP-Complete minimum dominating set problem in graphs, outperforming existing methods.

Contribution

A novel hybrid metaheuristic combining cuckoo search with genetic crossover and intensification for the minimum dominating set problem.

Findings

Outperforms state-of-the-art algorithms in experiments

Effective exploration and exploitation balance achieved

Demonstrates robustness across various graph instances

Abstract

The notions of dominating sets of graphs began almost 400 years ago with the game of chess, which sparked the analysis of dominating sets of graphs, at first relatively loosely until the beginnings of the 1960s, when the issue was given mathematical description. It's among the most important problems in graph theory, as well as an NP-Complete problem that can't be solved in polynomial time. As a result, we describe a new hybrid cuckoo search technique to tackle the MDS problem in this work. Cuckoo search is a well-known metaheuristic famed for its capacity for exploring a large area of the search space, making it useful for diversification. However, to enhance performance, we incorporated intensification techniques in addition to the genetic crossover operator in the suggested approach. The comparison of our method with the corresponding state-of-the-art techniques from the literature is presented in an exhaustive experimental test. The suggested algorithm outperforms the present state of the art, according to the obtained results.