Improved Memetic Algorithm for Solving the Minimum Weight Vertex Independent Dominating Set

Yupeng Zhou,Yong Lai,Jianan Wang,Yang Liu,Shuai Lv,Jinshu Li

doi:10.3390/math8071155

Abstract

The minimum weight vertex independent dominating set (MWVIDS) problem is an important version of the minimum independent dominating set. The MWVIDS problem has a number of applications in many fields. However, the MWVIDS problem is known to be NP-hard and thus computationally challenging. In this work, we present the improved memetic algorithm called MSSAS for solving the MWVIDS problem. The proposed MSSAS algorithm combines probability-based dynamic optimization (PDO) (to generate good and diverse offspring solutions by assembling elements of existing good solutions) as well as a local search phase named C_LS (to seek high-quality local optima by combining the idea of constrained-based two-level configuration checking strategy and tabu mechanism). The extensive results on popular DIMACS and BHOLIB benchmarks demonstrate that MSSAS competes favorably with the state-of-the-art algorithms. In addition, we analyze the benefits of the newly raised components including two above proposed ideas with our memetic framework. It is worth mentioning that the combination of both components has excellent effects for the MWVIDS problem.

Highlights

Given an undirected graph G, an independent dominating set (IDS) is a subset of vertices D such that every vertex that is not in D is adjacent to a vertex that is in D and there are no pairs of adjacent vertices in D
We propose an improved memetic algorithm called sequential self-adaptive search (MSSAS) for solving the minimum weight vertex independent dominating set (MWVIDS) problem, which explores the synergy between the process of local search process (C_LS) and a combination operator (PDO)
With the group of combination operator and improvement operator taking into account the solution structure, our algorithm definitely achieves a high performance in quality and diversity compared with other algorithms

Summary

Introduction

Given an undirected graph G, an independent dominating set (IDS) is a subset of vertices D such that every vertex that is not in D is adjacent to a vertex that is in D and there are no pairs of adjacent vertices in D. There are many variants of MIDS, consisting of minimum weight independent dominating set (MWIDS), minimum weight vertex independent dominating set (MWVIDS) and minimum weight edge independent dominating set (MWEIDS). Among these different versions of MIDS, MWIDS considers both vertex and edge weights, while MWEIDS only considers the weight of edge. The aim of MWVIDS is to identify the minimum weight of IDS in the given graph.

Results

Discussion

Conclusion