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

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

Chatkaew Jariyatantiwait (Oklahoma State University, Stillwater, OK, USA) and Gary G. Yen (Oklahoma State University, Stillwater, OK, USA)
Copyright: © 2016 |Pages: 22
DOI: 10.4018/IJSIR.2016100101
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Abstract

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.
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Introduction

Antenna design which focuses on converting electric power into radio waves while satisfying stringent, conflicting, and often unusual design specifications has been regarded as one of the most challenging engineering problems. The antenna engineers design the antenna’s electrical and geometrical configurations in order to achieve the optimal performance. The design goals can be specified as maximizing antenna gain while minimizing side lobe level and reflection coefficient. They are usually conflicting objectives to be achieved simultaneously. As a result, the antenna design problems is considered a multiobjective optimization problem (MOP) by nature.

Microstrip antennas are widely used in various wireless communication systems such as mobile communications, radar, missiles, aircraft, satellite communication systems, etc. They are preferred over the other types of antennas due to their low-profile, light weight, conformal ability, ease and low cost of manufacturing, and readily to be integrated within the microwave integrated circuits (Pozar & Schaubert, 1995; Garg, 2001; Waterhouse, 2003). There exists various utilities not only for single element microstrip antennas but most recently wide-ranging applications in microstrip antenna arrays. Microstrip antenna arrays provide higher directivity and gain than the single element antennas and are very versatile (Balanis, 2005). In this paper, a 5x5 microstrip antenna array synthesis for a 12.5 GHz broadcasting satellite service is formulated as a three-objective optimization problem as a case study with sufficient complexity, yet computationally manageable. In addition, for traditional antenna design field, there exist no such a general antenna synthesis methodology. Existing antenna design approaches have been developed but tailored for specific antenna type (Stutzman & Thiele, 2013). Therefore, the need to call for a universal design procedure, even heuristic in nature, is critical to advance the utilities of microstrip antenna arrays.

One of the most powerful heuristic optimization algorithms is Differential Evolution (DE). DE was proposed by Storn and Price in 1995 as a novel evolutionary algorithm (EA) (Storn & Price, 1995; Storn, 1996; Storn & Price, 1997). It is a stochastic, population-based search approach for optimization over a continuous space (Abbass, 2002). DE can efficiently handle the mixed-type variables, various constraints, multimodality and also MOPs. Therefore, we propose in this paper an Improved version of the Fuzzy-based Multiobjective Differential Evolution (FMDE) (Jariyatantiwait & Yen, 2014), in short for IFMDE, in order to exploit the feature capability of the proposed IFMDE under real-world complications. In addition, due to the expensive computations in objective evaluations, a radial basis function neural network is trained as a surrogate model for objective function evaluations, given a limited number of data samples possibly made available.

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