Multi-objective optimization for 3D heterogeneous WSN deployment using an enhanced Genghis Khan shark algorithm

Abstract

Abstract Heterogeneous three-dimensional (3D) wireless sensor network (WSN) deployment requires balancing sensing coverage, communication connectivity, and deployment cost under coupled K -coverage and C -connectivity constraints. This setting yields a constrained mixed discrete optimization landscape where many conventional multi-objective methods lose diversity or handle feasibility inconsistently. We formulate heterogeneous 3D WSN deployment as a constrained multi-objective problem and propose the Enhanced Multi-Objective Genghis Khan Shark Optimizer (EnMOGKSO). The core novelty is the integration of leader-pursuit dynamics with (i) dual archive-guided selection (elite and neighborhood memories), (ii) bounded external archive diversity control, and (iii) feasibility-first environmental selection for fragmented feasible regions. On the Congress on Evolutionary Computation (CEC) 2020 suite, EnMOGKSO obtains the best Friedman mean ranks in hypervolume (HV) (2.04) and inverted generational distance (IGD) (2.38), with statistically significant differences against most competitors ( $$p<0.05$$ , Wilcoxon/Friedman). In heterogeneous 3D WSN deployment, EnMOGKSO yields higher coverage/connectivity values (typically coverage means around 11–12 and connectivity around 7) than weaker baselines (often coverage 5–7 and connectivity 4–5), with higher but stable deployment cost. Overall, the results indicate a stronger convergence-diversity balance and more reliable feasibility-aware search under tight constraints, with practical applicability to 3D monitoring tasks such as industrial facilities, smart buildings, and environmental sensing.