The paper employs the Whale Optimization Algorithm (WOA) as a representative metaheuristic to solve the non-convex sum secrecy rate maximization problem. However, WOAs convergence behavior can be sensitive to population size and initialization. How would the proposed framework perform if alternative metaheuristics — such as Particle Swarm Optimization (PSO) or Differential Evolution (DE) — were substituted, and what theoretical guarantees, if any, can be established regarding the global optimality of the obtained solutions compared to conventional alternating optimization (AO)-based benchmarks?
In our framework, WOA is employed as a representative population-based metaheuristic to handle the highly non-convex and coupled nature of the joint beamforming - AN - STAR-RIS optimization problem. The algorithm itself functions as a black-box optimizer, and alternative metaheuristics such as PSO or DE could be integrated into the same framework without structural modification.
We expect comparable qualitative performance among these metaheuristics under the same evaluation budget. PSO may exhibit faster early-stage convergence but can be more prone to premature stagnation in high-dimensional spaces, while DE tends to provide stronger diversity and robustness at the cost of additional function evaluations. In practice, performance is influenced more by constraint handling, initialization, and computational budget than by the specific choice of WOA, PSO, or DE. We are willing to include comparative simulations in a revised version if required.
Regarding theoretical guarantees, due to the non-convex and NP-hard nature of the secrecy-rate maximization problem, no population-based metaheuristic, including WOA, PSO, or DE, can guarantee global optimality in general. These methods aim to obtain high-quality feasible solutions through global exploration but do not provide deterministic optimality guarantees.
Similarly, conventional AO based methods typically guarantee monotonic improvement and convergence to a stationary point under standard assumptions, but they also do not ensure global optimality for the original non-convex formulation. Therefore, the proposed approach does not claim theoretical global optimality; instead, its contribution lies in enhancing global exploration capability and achieving improved empirical secrecy-rate performance compared to AO-based benchmarks.
