Citation: Alharbi, N.; Mackenzie, L.;
Pezaros, D. Enhancing Graph
Routing Algorithm of Industrial
Wireless Sensor Networks Using the
Covariance-Matrix Adaptation
Evolution Strategy. Sensors 2022, 22,
7462. https://doi.org/10.3390/
s22197462
Academic Editors: Daniele Giusto
and Matteo Anedda
Received: 26 August 2022
Accepted: 29 September 2022
Published: 1 October 2022
Publisher’s Note: MDPI stays neutral
with regard to jurisdictional claims in
published maps and institutional affil-
iations.
Copyright: © 2022 by the authors.
Licensee MDPI, Basel, Switzerland.
This article is an open access article
distributed under the terms and
conditions of the Creative Commons
Attribution (CC BY) license (https://
creativecommons.org/licenses/by/
4.0/).
Article
Enhancing Graph Routing Algorithm of Industrial Wireless
Sensor Networks Using the Covariance-Matrix Adaptation
Evolution Strategy
Nouf Alharbi
1,2,
* , Lewis Mackenzie
1
and Dimitrios Pezaros
1
1
School of Computing Science, University of Glasgow, Glasgow G12 8LT, UK
2
School of Computing Science, Taibah University, Madinah 42353, Saudi Arabia
* Correspondence: n.alharbi.3@research.gla.ac.uk
Abstract:
The emergence of the Industrial Internet of Things (IIoT) has accelerated the adoption of
Industrial Wireless Sensor Networks (IWSNs) for numerous applications. Effective communication
in such applications requires reduced end-to-end transmission time, balanced energy consumption
and increased communication reliability. Graph routing, the main routing method in IWSNs, has a
significant impact on achieving effective communication in terms of satisfying these requirements.
Graph routing algorithms involve applying the first-path available approach and using path redun-
dancy to transmit data packets from a source sensor node to the gateway. However, this approach can
affect end-to-end transmission time by creating conflicts among transmissions involving a common
sensor node and promoting imbalanced energy consumption due to centralised management. The
characteristics and requirements of these networks encounter further complications due to the need
to find the best path on the basis of the requirements of IWSNs to overcome these challenges rather
than using the available first-path. Such a requirement affects the network performance and prolongs
the network lifetime. To address this problem, we adopt a Covariance-Matrix Adaptation Evolution
Strategy (CMA-ES) to create and select the graph paths. Firstly, this article proposes three best
single-objective graph routing paths according to the IWSN requirements that this research focused
on. The sensor nodes select best paths based on three objective functions of CMA-ES: the best Path
based on Distance (PODis), the best Path based on residual Energy (POEng) and the best Path based
on End-to-End transmission time (POE2E). Secondly, to enhance energy consumption balance and
achieve a balance among IWSN requirements, we adapt the CMA-ES to select the best path with
multiple-objectives, otherwise known as the Best Path of Graph Routing with a CMA-ES (BPGR-ES).
A simulation using MATALB with different configurations and parameters is applied to evaluate
the enhanced graph routing algorithms. Furthermore, the performance of PODis, POEng, POE2E
and BPGR-ES is compared with existing state-of-the-art graph routing algorithms. The simulation
results reveal that the BPGR-ES algorithm achieved 87.53% more balanced energy consumption
among sensor nodes in the network compared to other algorithms, and the delivery of data packets
of BPGR-ES reached 99.86%, indicating more reliable communication.
Keywords:
industrial internet of things; industry 4.0; industrial wireless sensor networks; Wire-
lessHART; graph routing; optimisation techniques; covariance-matrix adaptation evolution strategy;
best path
1. Introduction
As one of the key components of the Fourth Industrial Revolution (Industry 4.0) and
the Industrial Internet of Things (IIoT) [
1
], IEEE 802.15.4-based Industrial Wireless Sensor
Networks (IWSN) are a promising paradigm for smart industrial automation, due to their
advantages of flexibility, low deployment costs and self-organising capabilities. They can
potentially significantly improve industrial efficiency and productivity at sites such as oil
Sensors 2022, 22, 7462. https://doi.org/10.3390/s22197462 https://www.mdpi.com/journal/sensors
