## 1 Introduction  
In recent years, electromagnetic imaging has been extensively applied in the medical imaging fields, such as CT and MR. In medical imaging, for instance, the technology is superior to that of X-ray, with a better performance in scattered field information collection. This has motivated scholars to research deeper into related studies, with significant progress having been achieved. In general, the methods for solving electromagnetic scattering problems can be categorized into two main domains: the first is the approximate solution method and the second is the rigorous numerical method. The main approximate imaging theory for conductors is described by [PERSON]'s equation [1; 2; 3; 4], which was proposed by [PERSON] in 1967 based on the assumption of physical optics. This equation shows that there is a Fourier transformation between the backscattered field and the shape of the object, so that the image can be reconstructed using the scattered field. Since this method is only applicable to far-field imaging, some scholars have extended it to near-field imaging [5]. However, these methods are based on the assumptions of physical optics, and only one scattering condition is considered. The image object must be \"convex\" with a smooth surface and the size must be much larger than the wavelength. All these problems have limited its widespread application. This research can be applied to biomedical imaging (e.g., shapes and sizes of breast cancer and tumors), remote sensing and non-destructive testing. It is worth mentioning that biomedical imaging on breast cancer has been widely discussed in recent years. As far as the rigorous methods in the inverse scattering theory are concerned, most of them are based on an integral equation with the moment method [6; 7; 8; 9; 10; 11; 12; 13; 14]. Depending on the properties of the object, inverse scattering theory can be divided into two cases:conductors and dielectric objects. In the case of conductors, the inverse scattering problem is usually transformed into an optimization problem. The first form of the objective function is defined by the root-mean-square error between the measured and calculated scattered fields [7; 8; 9; 10]. By searching for the minimum value of the objective function, an optimal solution satisfying the boundary conditions can be found. The second form of the objective function is composed of two summations: one is the objective function of the first type and the other is the root-mean-square error of the set of integral equations satisfying the boundary condition [11; 12; 13; 14]. In addition, a regularization term can be added after the above objective functions to remove the ill-posedness. Then, the two forms of objective functions are completed by numerical iterations, such as the Newton-Kantorovitch method [7; 8; 9], the Levenberg-Marquardt algorithm [11; 12; 13], the successive overrelaxation method [14] and discrete dipole approximation [15]. However, almost all of these rigorous methods search for the solution by the gradient of the objective function. Therefore, when the preliminary estimation is further away from the real value, the solution is often a local extreme rather than a global extreme. A vast amount of literature on the heuristic algorithm has been published recently [16; 17; 18; 19; 20; 21; 22; 23; 24; 25; 26; 27; 28; 29]. The first was published in 1975, when [PERSON] proposed the concept and theoretical basis of genetic evolution based on [PERSON]'s concept of \"natural selection\", using the genetic mechanism of \"survival of the fittest\" to simulate the biological evolutionary process of genetic selection and natural elimination to find the best solution by a random search [16]. In 2018, [PERSON] et al. applied the self-adaptive dynamic differential evolution (SADDE) method to reconstruct two-dimensional dielectric objects and highlighted its robustness and searching speed [17].