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

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.