{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,17]],"date-time":"2026-07-17T23:31:33Z","timestamp":1784331093480,"version":"3.55.0"},"reference-count":69,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,1,6]],"date-time":"2023-01-06T00:00:00Z","timestamp":1672963200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Prince Sultan University, Riyadh, Saudi Arabia"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>With the emergence of delay- and energy-critical vehicular applications, forwarding sense-actuate data from vehicles to the cloud became practically infeasible. Therefore, a new computational model called Vehicular Fog Computing (VFC) was proposed. It offloads the computation workload from passenger devices (PDs) to transportation infrastructures such as roadside units (RSUs) and base stations (BSs), called static fog nodes. It can also exploit the underutilized computation resources of nearby vehicles that can act as vehicular fog nodes (VFNs) and provide delay- and energy-aware computing services. However, the capacity planning and dimensioning of VFC, which come under a class of facility location problems (FLPs), is a challenging issue. The complexity arises from the spatio-temporal dynamics of vehicular traffic, varying resource demand from PD applications, and the mobility of VFNs. This paper proposes a multi-objective optimization model to investigate the facility location in VFC networks. The solutions to this model generate optimal VFC topologies pertaining to an optimized trade-off (Pareto front) between the service delay and energy consumption. Thus, to solve this model, we propose a hybrid Evolutionary Multi-Objective (EMO) algorithm called Swarm Optimized Non-dominated sorting Genetic algorithm (SONG). It combines the convergence and search efficiency of two popular EMO algorithms: the Non-dominated Sorting Genetic Algorithm (NSGA-II) and Speed-constrained Particle Swarm Optimization (SMPSO). First, we solve an example problem using the SONG algorithm to illustrate the delay\u2013energy solution frontiers and plotted the corresponding layout topology. Subsequently, we evaluate the evolutionary performance of the SONG algorithm on real-world vehicular traces against three quality indicators: Hyper-Volume (HV), Inverted Generational Distance (IGD) and CPU delay gap. The empirical results show that SONG exhibits improved solution quality over the NSGA-II and SMPSO algorithms and hence can be utilized as a potential tool by the service providers for the planning and design of VFC networks.<\/jats:p>","DOI":"10.3390\/s23020667","type":"journal-article","created":{"date-parts":[[2023,1,9]],"date-time":"2023-01-09T06:38:27Z","timestamp":1673246307000},"page":"667","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["SONG: A Multi-Objective Evolutionary Algorithm for Delay and Energy Aware Facility Location in Vehicular Fog Networks"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6371-2545","authenticated-orcid":false,"given":"Md. Muzakkir","family":"Hussain","sequence":"first","affiliation":[{"name":"Department of Computer Science and Engineering, SRM University, Amaravati 522502, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7869-6373","authenticated-orcid":false,"given":"Ahmad Taher","family":"Azar","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"},{"name":"Faculty of Computers and Artificial Intelligence, Benha University, Benha 13511, Egypt"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5952-611X","authenticated-orcid":false,"given":"Rafeeq","family":"Ahmed","sequence":"additional","affiliation":[{"name":"Department of CSE, Koneru Lakshmaiah Education Foundation, Vaddeswaram 522302, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4718-0155","authenticated-orcid":false,"given":"Syed","family":"Umar Amin","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7389-519X","authenticated-orcid":false,"given":"Basit","family":"Qureshi","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3945-6171","authenticated-orcid":false,"given":"V.","family":"Dinesh Reddy","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, SRM University, Amaravati 522502, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8596-907X","authenticated-orcid":false,"given":"Irfan","family":"Alam","sequence":"additional","affiliation":[{"name":"Department of Computer Science and Engineering, Delhi Technological University, Delhi 110042, India"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5079-2902","authenticated-orcid":false,"given":"Zafar Iqbal","family":"Khan","sequence":"additional","affiliation":[{"name":"College of Computer and Information Sciences, Prince Sultan University, Riyadh 11586, Saudi Arabia"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2023,1,6]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"70","DOI":"10.1109\/MNET.001.1900527","article-title":"When vehicular fog computing meets autonomous driving: Computational resource management and task offloading","volume":"34","author":"Zhou","year":"2020","journal-title":"IEEE Netw."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"e6085","DOI":"10.1002\/cpe.6085","article-title":"An operative constellation rate for smart safety units using Internet of Things","volume":"33","author":"Manoharan","year":"2021","journal-title":"Concurr. 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