Optimization of the Sierpinski carpet fractal antenna with a multi-repetition factor for multi-band wireless applications utilizing a variant strength Pareto evolutionary algorithm

Designing a multiband, compact, and high-performance antenna is considered a multi-objective and high-dimensional optimization problem, as it requires the simultaneous satisfaction of multiple performance criteria (such as gain and return loss). In this study, a six-variable design problem is formulated for a Sierpinski carpet fractal patch antenna (SCFPA) operating in the 3.5 GHz, 4.1 GHz, 5.1 GHz, 5.8 GHz, and 7.7 GHz frequency bands. Within this scope, a strength Pareto evolutionary algorithm 2 (SPEA2) based approach is developed, and the algorithm is extended with two original variants: (i) an improved archive update mechanism (mSPEA2) to increase solution diversity, and (ii) an adapted crossover/selection strategy (cSPEA2) to improve convergence performance. The proposed method aims to both iteratively incorporate antenna geometry into the optimization and simultaneously achieve multiband performance objectives. According to the results obtained, the proposed variant algorithms perform better compared to the standard SPEA2. Specifically, with the mSPEA2 algorithm, the following values ​​were obtained: 1.32 dB gain and −16.38 dB S 11 at 3.5 GHz, 1.97 dB gain and −25.58 dB S 11 at 4.1 GHz, 0.83 dB gain and −13.11 dB S 11 at 5.1 GHz, 0.60 dB gain and −23.67 dB S 11 at 5.8 GHz, and 5.91 dB gain and −13.84 dB S 11 at 7.7 GHz. These results indicate improvements, particularly in terms of return loss and multiband operation. The proposed antenna structure is as follows: The proposed SPEA2 variants are designed to be compatible with WLAN/Wi-Fi (IEEE 802.11a/ac) and 5.8 GHz ISM applications in the 5–6 GHz band, WiMAX applications in the 3.5 GHz and 4.1 GHz bands, and short-range wireless communication systems such as Bluetooth around 5 GHz. Consequently, the proposed SPEA2 variants offer a flexible and effective optimization approach for multi-band fractal antenna design problems and can be easily adapted to different microwave optimization problems.