## 1 Introduction  
There has been considerable interest in small converters harvesting energy from various sources available in the environment, such as industrial machinery, civil structures, and even humans or animals. These systems are applicable in sensor networks or monitoring systems [1; 2; 3; 4; 5; 6; 7; 8; 9] that require autonomy of power supply. The use of small generators of electric energy in such systems makes it possible to significantly increase an overall reliability, to eliminate wiring and reduce maintenance service activity over the whole system [3; 10; 11; 12; 13; 14].  
Most of the attention in the literature is focused on systems harvesting energy from mechanical vibrations. The minigenerators applied in these systems use various physical phenomena as the means of energy conversion. The most commonly implemented are piezoelectric, magnetostrictive, magnetoelectric, electrostatic and electromagnetic converters [2; 15; 16]. This work concerns the latter system due to its reasonable power per unity of mass ratio and low manufacturing cost compared to the other types [11; 13].  
The coreless (iron-free) magnetic circuit is a common choice for application in electromagnetic vibration energy harvesting converters due to its simple design guidelines [17]. It is well known that these systems suffer from a low value of induced electromotive force (emf), and thus generated power Their very low volt-per-turn ratio often makes the impedance of the armature coils too high for the electronic boost of the induced voltage to any practical value. Here, we propose a routine that improves the performance of such a system by means of providing an optimal distribution of individual turns within the coil. This allows for a reduction of the impedance to an extent where the microgenerator connected to the electronic converter develops considerable output power.  
In the design of electromagnetic vibration energy harvesters, the electromagnetic part is modelled using either numerical or analytical models [8; 17; 18; 19]. In this work, the model segment of the routine involves determination of useful electromagnetic quantities by combining a 3D integral method, analytical formulas with a steady-state circuit simulation considering the electronic converter. For the purposes of the optimization process, it is not necessary to consider the whole system and its complicated kinematics resulting from the connection of the generator parts with elements of mechanical support [20]. As a consequence, the motional effects are modelled as simply as possible, assuming that the displacement of the moving element of the converter is sinusoidal in time, which means that the system operates at a prescribed frequency and magnitude.  
The optimization segment aims at the maximization of the power generated by the whole system. The considered optimization task is a mixed integer nonlinear programming (MINLP) problem [21]. Due to the considerable evaluation time of the objective function, the kriging surrogate model [22] is involved in the process. Three solution strategies are comparatively examined with respect to their cost and accuracy characteristics. The optimized system is successfully built and tested. The new contributions of this work are:  
* Elaboration of an efficient and uncomplicated routine for the maximization of output power for a class of microgenerators for vibration energy harvesting devices;
* Comparative analysis of features for three solution strategies for the associated MINLP problem using a surrogate model with particular attention focused on the strategy using sequential refinement of the computer experiment grid [23].