The Application of a Modified Differential Evolution Strategy to Some Array Pattern Synthesis Problems

• Published in: IEEE transactions on antennas and propagation Vol. 56; no. 7; pp. 1919 - 1927
• Main Authors: Chen, Yikai, Yang, Shiwen, Nie, Zaiping
• Format: Journal Article
• Language: English
• Published: New York, NY IEEE 01.07.2008; Institute of Electrical and Electronics Engineers; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Antenna arrays; Antennas; Applied sciences; Arrays; Constraint optimization; Convergence; Convergence of numerical methods; Cost function; differential evolution (DE); Evolution; Exact sciences and technology; Exploration; Genetic algorithms; Gradient methods; Mathematical models; Optimization; Optimization methods; pattern synthesis; Power engineering and energy; Radiocommunications; Robustness; Simulated annealing; Stochastic processes; Strategy; Synthesis; Telecommunications; Telecommunications and information theory; Performance evaluation; Global optimum; Optimization; Mathematical function; Algorithm performance; differential evolution (DE); Heuristic method; Convergence rate; Numerical simulation; Antenna array; Numerical convergence; Pattern synthesis; Antenna radiation patterns; Antenna synthesis; Antenna arrays
• DOI: 10.1109/TAP.2008.924713
• ISSN: 0018-926X

A high convergence rate and a robust exploration ability constitute a contradiction in modern heuristic optimization techniques. This paper describes a modified differential evolution strategy (MDES) that builds up a balanced relationship between the two contradictive elements by introducing several modifications into the conventional differential evolution strategy (DES). The novel MDES opens up an effective and robust approach for global optimization problems. Several representative mathematical functions are minimized using various optimization methods and the convergence rates are compared to evaluate the performance of MDES. Moreover, array synthesis examples which can be formulated as non-convex problems are presented, including the optimal synthesis of sum and difference patterns and the synthesis of unequally spaced arrays. Numerical results demonstrate that the proposed approach improves the performance of the algorithm significantly, in terms of both the convergence rate and the exploration ability.