## 1 Introduction
The Topological-Shape Sensitivity Method in various fields of technology, including shape and topology optimization [23], inverse problems [24] and damage development modeling [25], has been used. [PERSON] et al. [26; 27] used the topological derivative method to solve a pollution sources reconstruction problem governed by a steady-state convection-diffusion equation. [PERSON] et al. [28] applied the contingent probability method to track sources of pollutants in open air with a constant emission. [PERSON] et al. [29] proposed a new approach to the problem of damage identification in plate structures based on the method of topological derivatives. Three inclusions were identified with 32% confidence. [PERSON] et al. [30] developed an approach based on an improved particle swarm optimization (PSO) algorithm for damage detection in structures. [PERSON] et al. [31] applied extended isogeometric analysis (X-IGA) combined with PSO for crack identification in two-dimensional linear elastic problems based on the inverse problem. [PERSON] et al. [32] developed numerical identification and characterization of damage propagation using a new optimization technique called Lichtenberg optimization (LA). [PERSON] et al. [33] presented a new geometry-based crack detection approach for plate structures based on the integration of the dynamic extended finite element method (XFEM) and an optimization algorithm called the enhanced vibrating particle system (EVPS). [PERSON] et al. [34] focused on the detection of objects immersed in an anisotropic medium by boundary measurements. A one-iteration algorithm based on the Kona-Vogelius formulation and the topological gradient method was proposed. The inverse problem was formulated as a topological optimization approach. [PERSON] et al. [35] proposed rewriting the inverse source problem as an optimization problem, where the functional Con-Vogelius type was minimized with respect to the set of admissible point sources. [PERSON] et al. [36] considered the identification of acoustic parameters in the frequency domain using a topological problem optimization approach. [PERSON] et al. [37] applied active time-harmonic infrared thermography to detect defects inside of thin plates. [PERSON] et al. [38] reviewed bioinspired methods for solving various inverse problems for mechanical systems. [PERSON] et al. [39] proposed an approach based on the so-called energy-like error functional, in combination with the topological sensitivity method. The topological derivative of the energy-like error functional was calculated using the topological shape sensitivity method. Numerical tests to indicate the effectiveness of the developed approach were performed. [PERSON] et al. [40; 41; 42; 43] proposed the application of topological optimization methods based on temperature and heat flux measurements. The effects on the optimal topology of the composite in the presence of two competing materials were investigated, in addition to the optimality criteria, using linear weight functions. Pareto spaces were constructed, providing an in-depth understanding of how these goals compete to achieve optimal topology. The problem of topological optimization of multilayer structural elements of MEMS/NEMS resonators with an adhesive layer under the action of mechanical loads was also considered. The problems of the finite element method were solved using the method of sliding asymptotes. According to the author's knowledge, and as summarized in the above review, the application of topological optimization methods for the identification of holes/inclusions is still finite. The available publications are devoted to the identification of single holes/inclusions of the simplest geometry (ellipse and circle), and the quality of the identification work described is not acceptable. Therefore, the main aim of this work was to develop a new approach to identifying an arbitrary number of inclusions, their geometries and locations in 2D and 3D structures, with high recognition quality.