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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 S warm O ptimized N on-dominated sorting G enetic 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-energy 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.

SONG: A Multi-Objective Evolutionary Algorithm for Delay and Energy Aware Facility Location in Vehicular Fog Networks