Improved Nutcracker Optimization Algorithm and Its Application to Antenna and Array Designs

Abstract

Metaheuristic algorithms play a crucial role in tackling the increasing complexity and challenges in antenna design. The nutcracker optimization algorithm (NOA), a novel metaheuristic inspired by nutcrackers' food-gathering, storing, searching, and retrieving behaviors, has shown excellent performance on 23 standard test functions and CEC—2014/2017/2020 test suites compared to well-established algorithms, yet it remains unapplied in antenna design. This study proposes a multi-strategy improved NOA (MINOA) to resolve NOA's unbalanced exploration and exploitation issues, applying it to ultra-wideband antenna design optimization and linear antenna array sidelobe suppression. MINOA employs Bernoulli chaotic mapping for uniform population initialization, a dynamic boundary strategy for balanced exploration and exploitation, and adaptive t-distribution disturbance to accelerate convergence and enhance local exploitation. Extensive tests on 23 benchmark functions prove MINOA's superiority in optimization accuracy, convergence speed, and stability over advanced algorithms such as NOA, WOA, GWO, SSA, DEA, SCSO, and HBMO. The Wilcoxon signed-rank test validates its significant improvement in accuracy. In broadband antenna optimization via an artificial neural network (ANN)-based surrogate model, MINOA reduces the mean square error (MSE) by 40.9% at the same iteration number and by 28.6% with 10 fewer iterations and 29 fewer fitness function calls compared to NOA during the preliminary training phase, achieving the widest bandwidth (3.62–11 GHz) among the eight algorithms. The Wilcoxon signed-rank test confirms MINOA's superiority. In the 16-element linear antenna array optimization, although MINOA performs slightly worse than DEA and WOA, it still achieves a low-sidelobe level of −41.38 dB, verifying its feasibility.