A Hybrid Harmony Search–Nondominated Sorting Approach for Cost-Efficient and Deadline-Aware Fog-Enabled IoT Placement

The heterogeneity and dynamic behavior of fog computing environments introduce major challenges to achieving optimal application placement. Limited fog resources and varying workloads often necessitate offloading applications beyond their local clusters, making it difficult to maintain the required level of service quality under varying conditions. In this context, placement methods must ensure a balanced trade-off between multiple objectives, such as time and cost, while maintaining reliable adherence to constraints like application deadlines and limited fog-node memory. Existing solutions, including heuristic, metaheuristic, learning-based, and hybrid optimization approaches, have been proposed to address these challenges. However, many of these methods rely on weighted objective formulations with limited visibility into trade-offs among conflicting objectives, emphasize local refinement over sustained exploration, or handle resource and deadline constraints implicitly, reducing their effectiveness in resource-constrained and dynamic fog environments. To overcome these limitations, this paper proposes a hybrid Harmony Search–Nondominated Sorting Genetic Algorithm (HS–NSGA), which integrates the improvisation operators of HS with the Pareto-based elitist selection of NSGA-II. The proposed algorithm advances the state of the art by enabling unbiased trade-off exploration and preserving high-quality solutions while explicitly enforcing memory constraints and deadline requirements. HS serves as the primary search mechanism, generating diverse candidate placements through memory consideration, randomization, and pitch adjustment, while nondominated sorting and crowding distance guide the selection of high-quality trade-off solutions across iterations. To further improve robustness against constraint violations in dynamic conditions, a fraction of the population is diversified using NSGA-II mutation and crossover operators. Experimental evaluations across heterogeneous fog–cloud scenarios demonstrate that HS–NSGA consistently achieves superior cost–time reduction compared with representative hybrid genetic and swarm-based methods while satisfying application deadline requirements and fog-node memory constraints. For makespan, HS–NSGA achieved reductions of 14.5% over LD-NPGA (Local Draft Niche-Pareto Genetic Algorithm), 16.8% over FSPGA (Fog Service Placement Genetic Algorithm), 19.5% over FSPPSO (Fog Service Placement Particle Swarm Optimization), and 16.1% over GA-FSA (Genetic Algorithm Flamingo Search Algorithm), with consistent improvements across varying task volumes. For cost, reductions reached 32.7%, 35.5%, 42.9%, and 30.7% over LD-NPGA, FSPGA, FSPPSO, and GA-FSA, respectively.