A Polynomial-Decay and Pinhole-Imaging Whale Optimization Algorithm for UAV Relay Communication Deployment

Unmanned aerial vehicle (UAV) relays deliver flexible, on-demand wireless coverage, but jointly tuning the position, altitude, transmit power and bandwidth of the relay is a non-convex, heavily constrained optimization task that easily traps swarm-based optimizers in poor local optima. We propose PWOA, a Polynomial-decay and Pinhole-imaging Whale Optimization Algorithm with three complementary improvements: (i) a Good Nodes Set (GNS) initialization that spreads the initial population uniformly across the search space; (ii) a polynomial nonlinear schedule for the convergence factor that prolongs early exploration and sharpens late exploitation; and (iii) a stagnation-triggered pinhole-imaging opposition-based learning (POBL) operator paired with an elite Gaussian local search, which together escape local optima while refining the leader. On a five-dimensional UAV relay deployment problem with five inequality constraints ($N=30$, $T=500$, 30 independent runs), PWOA simultaneously attains the lowest Best, Worst, Mean and standard deviation among PWOA, WOA, SCA and IPSO, cutting the mean by $1.4$–$18.5\mathrm{\%}$ and the standard deviation by $15$–$87\mathrm{\%}$ over the three baselines, and exhibits the fastest average convergence.