Identification of Control Parameters Using Taguchi Method for Hybrid Real-Binary Differential Evolution Algorithm and Its Applications in Electromagnetic Optimization

The hybrid real-binary differential evolution (HDE) algorithm has been proficient in addressing electromagnetic optimization problems (EOPs) involving both real and binary variables. However, its optimization performance on different control parameter (CP) settings is not further studied, and the method to determine the values of CPs is more likely to use the trial-and-error method, which lacks universality on both unimodal and multimodal benchmarks. To completely account for the effect of CPs in HDE, the Taguchi method is utilized to identify the values of each CP. The orthogonal experiment result is the average rank of the mean values of 23 benchmark functions obtained by HDE and other classic optimization algorithms. Based on the analysis of variance results, three CPs that have a major effect on the performance of HDE are selected, and each of them is changed from level 1 to level 5 to further obtain the best combination of CPs, which is indicated as <math xmlns="http://www.w3.org/1998/Math/MathML" id="M1"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>1</mn></mrow></msub></math> . To further enhance the local search ability of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M2"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>1</mn></mrow></msub></math> for the global best, a modified algorithm ( <math xmlns="http://www.w3.org/1998/Math/MathML" id="M3"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>2</mn></mrow></msub></math> ) is proposed based on a novel mutation strategy selection method, and the simulation results demonstrate that the minimum values obtained by <math xmlns="http://www.w3.org/1998/Math/MathML" id="M4"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>2</mn></mrow></msub></math> are smaller than those obtained by <math xmlns="http://www.w3.org/1998/Math/MathML" id="M5"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>1</mn></mrow></msub></math> . Two EOPs, including planar microwave absorber and Yagi-Uda antenna designs, are solved to validate the performance of <math xmlns="http://www.w3.org/1998/Math/MathML" id="M6"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M7"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>2</mn></mrow></msub></math> . The results reveal that the <math xmlns="http://www.w3.org/1998/Math/MathML" id="M8"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>1</mn></mrow></msub></math> and <math xmlns="http://www.w3.org/1998/Math/MathML" id="M9"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>2</mn></mrow></msub></math> outperform HDE, demonstrating the efficacy of the proposed method for identifying the CPs of HDE. In the end, a low profile and wideband RCS reduction pixelated checkboard metasurface is optimized utilizing the <math xmlns="http://www.w3.org/1998/Math/MathML" id="M10"><msub><mrow><mtext>HDE</mtext></mrow><mrow><mi>N</mi><mn>2</mn></mrow></msub></math> , proving that the proposed algorithm can be a good candidate for hybrid real-binary electromagnetic problems.