A Simulated Annealing-Based Multiobjective Optimization Algorithm for Minimum Weight Minimum Connected Dominating Set Problem

TL;DR

The paper tackles the minimum weight minimum connected dominating set problem (MWMCDS) on edge-weighted graphs, a challenging NP-hard problem with important applications in networks. It proposes a multiobjective greedy simulated annealing (GSA) algorithm that combines a scalarized objective—balancing CDS size and total weight—with a greedy constructive seed and flexible neighbor generation. Empirical results on standard benchmarks show GSA generally outperforms a recent multiobjective genetic algorithm and a single-objective approach, achieving lower energy consumption and smaller CDS sizes in most scenarios. The work advances practical methods for energy-efficient CDS design in networks and suggests future exploration of Pareto-based strategies to capture the full trade-off frontier.

Abstract

Minimum connected dominating set problem is an NP-hard combinatorial optimization problem in graph theory. Finding connected dominating set is of high interest in various domains such as wireless sensor networks, optical networks, and systems biology. Its weighted variant named minimum weight connected dominating set is also useful in such applications. In this paper, we propose a simulated annealing algorithm based on a greedy heuristic for tackling a variant of the minimum connected dominating set problem and that by exploiting two objectives together namely the cardinality and the total weight of the connected dominating set. Experimental results compared to those obtained by a recent proposed research show the superiority of our approach.

Figures (3)

• Figure 1: Example of DS (Dominating Set), CDS (Connected DS), MCDS (Minimum CDS) and MWCDS (Minimum weighted CDS) in a simple undirected graph.
• Figure 2: Energy consumption in GSA, MOGA and mcds
• Figure 3: Size of CDS in GSA, MOGA and mcds