Constrained Multi-Objective Genetic Algorithm Variants for Design and Optimization of Tri-Band Microstrip Patch Antenna loaded CSRR for IoT Applications: A Comparative Case Study

Abstract: This paper presents an automated antenna design and optimization framework employing multi-objective genetic algorithms (MOGAs) to investigate various evolutionary optimization approaches, with a primary emphasis on multi-band frequency optimization. Five MOGA variants were implemented and compared: the Pareto genetic algorithm (PGA), non-dominated sorting genetic algorithm with niching (NSGA-I), non-dominated sorting genetic algorithm with elitism (NSGA-II), non-dominated sorting genetic algorithm using reference points (NSGA-III), and strength Pareto evolutionary algorithm (SPEA). These algorithms are employed to design and optimize microstrip patch antennas loaded with complementary split-ring resonators (CSRRs). A weighted-sum scalarization approach was adopted within a single-objective genetic algorithm framework enhanced with domain-specific constraint handling mechanisms. The optimization addresses the conflicting objectives of minimizing the return loss ($S_{11} < -10$~dB) and achieving multi-band resonance at 2.4~GHz, 3.6~GHz, and 5.2~GHz. The proposed method delivers a superior overall performance by aggregating these objectives into a unified fitness function encompassing $S_{11}$(2.4~GHz), $S_{11}$(3.6~GHz), and $S_{11}$(5.2~GHz). This approach effectively balances all three frequency bands simultaneously, rather than exploring trade-off solutions typical of traditional multi-objective approaches. The antenna was printed on a Rogers RT5880 substrate with a dielectric constant of 2.2 , loss tangent of 0.0009 , and thickness of 1.57~mm . Scalarization approach achieved return loss values of $-21.56$~dB, $-16.60$~dB, and $-27.69$~dB, with corresponding gains of 1.96~dBi, 2.6~dB, and 3.99~dBi at 2.4~GHz, 3.6~GHz, and 5.2~GHz, respectively.