5 by 5 Microstrip Antenna Array Design by Multiobjective Differential Evolution based on Fuzzy Performance Feedback

Differential evolution is often regarded as one of the most efficient evolutionary algorithms to tackle multiobjective optimization problems. The key to success of any multiobjective evolutionary algorithms (MOEAs) is maintaining a delicate balance between exploration and exploitation throughout the evolution process. In this paper, the authors develop an Improved version of the Fuzzy-based Multiobjective Differential Evolution (IFMDE) that exploits performance metrics, specifically hypervolume, spacing, and maximum spread, to measure the state of the evolution progress. They apply the fuzzy inference rules, derived from domain knowledge, to these metrics in order to dynamically adjust the associated control parameters of a chosen mutation and crossover strategy used in this algorithm. One mutation parameter controls the degree of greedy or exploitation, while another regulates the degree of diversity or exploration of the reproduction phase. On the other hand, crossover rate controls the fraction of trial vector elements inherited from the mutant vectors. In doing so collectively, the authors can appropriately adjust the degree of exploration and exploitation through performance feedback. A 5 by 5 microstrip antenna array design problem is formulated as a three-objective optimization problem. The proposed IFMDE is applied to tackle this problem under real-world complications. Since the objective evaluations of a 5 by 5 microstrip antenna array are computationally very expensive, a radial basis function neural network is trained as a surrogate model for the fitness function approximations. The experimental results demonstrate the ability of IFMDE that it can find not only one, but a set of Pareto optimal solutions, specifically in terms of side lobe level and reflection coefficient. These multiple Pareto-optimal configurations can then be chosen from by a decision maker given dynamic operating environments, constraints and uncertainties.