Multiobjective differential evolution based on fuzzy performance feedback: Soft constraint handling and its application in antenna designs

Abstract

The recently emerging Differential Evolution is considered one of the most powerful tools for solving optimization problems. It is a stochastic population-based search approach for optimization over the continuous space. The main advantages of differential evolution are simplicity, robustness and high speed of convergence. Differential evolution is attractive to researchers all over the world as evidenced by recent publications. There are many variants of differential evolution proposed by researchers and differential evolution algorithms are continuously improved in its performance. Performance of differential evolution algorithms depend on the control parameters setting which are problem dependent and time-consuming task. This study proposed a Fuzzy-based Multiobjective Differential Evolution (FMDE) that exploits three performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution process. We apply the fuzzy inference rules to these metrics in order to adaptively adjust the associated control parameters of the chosen mutation strategy used in this algorithm. The proposed FMDE is evaluated on the well known ZDT, DTLZ, and WFG benchmark test suites. The experimental results show that FMDE is competitive with respect to the chosen state-of-the-art multiobjective evolutionary algorithms. The advanced version of FMDE with adaptive crossover rate (AFMDE) is proposed. The proof of concept AFMDE is then applied specifically to the designs of microstrip antenna array. Furthermore, the soft constraint handling technique incorporates with AFMDE is proposed. Soft constraint AFMDE is evaluated on the benchmark constrained problems. AFMDE with soft constraint handling technique is applied to the constrained non-uniform circular antenna array design problem as a case study.