Abstract Differential evolution (DE) is a population-based and stochastic search algorithm of evolutionary computation that offers three major advantages: it finds the global minimum regardless of the initial parameter values, it involves fast convergence, and it uses few control parameters. This work presents a global optimization algorithm based on DE approaches combined with local search using the implicit filtering algorithm. The implicit filtering algorithm is a projected quasi-Newton method that uses finite difference gradients. The difference increment is reduced as the optimization progresses, thereby avoiding some local minima, discontinuities, or nonsmooth regions that would trap a conventional gradient-based method. Problems involving optimization procedures of complex mathematical functions are widespread in electromagnetics. Many problems in this area can be described by nonlinear relationships, which introduce the possibility of multiple local minima. In this paper, the shape design of Loney’s solenoid benchmark problem is carried out by DE approaches. The results of DE approaches are also investigated and their performance compared with those reported in the literature
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