{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,15]],"date-time":"2026-05-15T20:26:01Z","timestamp":1778876761584,"version":"3.51.4"},"reference-count":34,"publisher":"MDPI AG","issue":"19","license":[{"start":{"date-parts":[[2022,10,1]],"date-time":"2022-10-01T00:00:00Z","timestamp":1664582400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"UK Engineering and Physical Sciences Research Council (EPSRC)","award":["EP\/N033957\/1"],"award-info":[{"award-number":["EP\/N033957\/1"]}]},{"name":"UK Engineering and Physical Sciences Research Council (EPSRC)","award":["EP\/S035362\/1"],"award-info":[{"award-number":["EP\/S035362\/1"]}]},{"name":"PETRAS National Centre of Excellence for IoT Systems Cybersecurity","award":["EP\/N033957\/1"],"award-info":[{"award-number":["EP\/N033957\/1"]}]},{"name":"PETRAS National Centre of Excellence for IoT Systems Cybersecurity","award":["EP\/S035362\/1"],"award-info":[{"award-number":["EP\/S035362\/1"]}]},{"name":"UK EPSRC","award":["EP\/N033957\/1"],"award-info":[{"award-number":["EP\/N033957\/1"]}]},{"name":"UK EPSRC","award":["EP\/S035362\/1"],"award-info":[{"award-number":["EP\/S035362\/1"]}]},{"name":"Taibah University, Saudi Arabia","award":["EP\/N033957\/1"],"award-info":[{"award-number":["EP\/N033957\/1"]}]},{"name":"Taibah University, Saudi Arabia","award":["EP\/S035362\/1"],"award-info":[{"award-number":["EP\/S035362\/1"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>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 redundancy 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.<\/jats:p>","DOI":"10.3390\/s22197462","type":"journal-article","created":{"date-parts":[[2022,10,10]],"date-time":"2022-10-10T03:07:28Z","timestamp":1665371248000},"page":"7462","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Enhancing Graph Routing Algorithm of Industrial Wireless Sensor Networks Using the Covariance-Matrix Adaptation Evolution Strategy"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1720-5606","authenticated-orcid":false,"given":"Nouf","family":"Alharbi","sequence":"first","affiliation":[{"name":"School of Computing Science, University of Glasgow, Glasgow G12 8LT, UK"},{"name":"School of Computing Science, Taibah University, Madinah 42353, Saudi Arabia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0868-0456","authenticated-orcid":false,"given":"Lewis","family":"Mackenzie","sequence":"additional","affiliation":[{"name":"School of Computing Science, University of Glasgow, Glasgow G12 8LT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0939-378X","authenticated-orcid":false,"given":"Dimitrios","family":"Pezaros","sequence":"additional","affiliation":[{"name":"School of Computing Science, University of Glasgow, Glasgow G12 8LT, UK"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,10,1]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"2233","DOI":"10.1109\/TII.2014.2300753","article-title":"Internet of Things in Industries: A Survey","volume":"10","author":"Xu","year":"2014","journal-title":"IEEE Trans. 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