## 4 Earthquake Algorithm  
The optimization of the inductance selection in this paper is made through the first geo-inspired metaheuristic algorithm, called Earthquake Algorithm (EA), which is based on the behavior of the \(P\) and \(S\) waves existing in earthquakes (as explained in [16]). The EA allows easy suitability to different kinds of optimization problems, since the combination of searching velocities given by the combination of the P and S velocities, provides to address both wide and fine searching paths; since, as discussed in [17], the EA require less parameters calibration to suite different optimization applications, compared to other metaheuristic algorithms. Hence, the EA allows suiting easily combining an aggressive searching behavior through the P-wave velocity with a smaller area optimization through the S-wave velocity. The first complete version of the algorithm was delivered in [15], for the Optimization of the PID (Proportional Integrative Derivative) gains of a speed controller in a DC motor. The PID gains optimization showed the basic conceptualization of the ITAE performance index as cost function, which inspired the criteria utilization for this proposed methodology in DC-DC converters design, as explored in [2]. Summarizing the basic concepts for the deduction of the EA, the \(P\)-waves are faster and the \(S\)-waves are finer, which are the key elements that the algorithm takes advantage from. Consequently, as explained in [16], Equations (6) and (7) describe the estimation of \(P\)- and \(S\)-wave velocities. \[v_{p}=\sqrt{\frac{\lambda+2\mu}{\rho}} \tag{6}\]  
Figure 4: Example of inductor current profile optimization. \[v_{s}=\sqrt{\frac{\mu}{\rho}} \tag{7}\]  
where \(v_{p}\) and \(v_{s}\), are the \(P\)- and \(S\)-wave velocities, respectively, \(\lambda\) and \(\mu\) are the Lame parameters, and \(\rho\) is the density of the earth propagation material. Nevertheless, as explained in [15; 16], the lame parameters can be equal under some circumstances, maintaining then for this application that \(\lambda=\mu=1.5\) GPa. On the other hand, the density of the solids (\(\rho\)) is used as a random value, which gives the heuristic behavior to the algorithm, so as not to leave the geo-inspiration of the algorithm, the selected range for the density parameter is taken between 2200 and 3300 Kg/m\({}^{3}\), inspired by the real geological properties of the materials described in Table 1.  
With all the main parameters of the algorithm already defined, the use of \(v_{s}\) or \(v_{p}\) is not yet clarified. Thus, it is crucial for the algorithm to define an operating range for the \(v_{s}\) to be used, in order to define when to use a velocity or the other one; which, as explained in [15; 16], is defined as the \(S\)_-range_ or \(Sr\). The \(Sr\), as shown in Figure 5, is always defined around the best solution; therefore the nearest particles (red epicenter in Figure 5) to the global solution (blue epicenter) will use the \(v_{s}\) equation, meanwhile the epicenters out of the defined \(Sr\) will take the \(v_{p}\) equation. Thus, it could be implied that the epicenters \"orbit\" around the global best solution, however, the \(Sr\) should be assigned (as explained in [16]) with the previous knowledge of the problem requirements. However, from [15; 16] implementations, the Sr is recommended to be 2% from the best solution. It is important to highlight that since both speeds are calculated by a square root, the final result is a positive number. The architecture of the algorithm contemplates the random selection of a positive or a negative velocity value, regardless of whether it is \(v_{s}\) or \(v_{p}\), in order to select whether \(\pm v_{s}\) or \(\pm v_{p}\). Consequently, the position of the epicenters is updated through Equation (8). \[X_{i}^{t}=X_{i}^{t-1}+V_{i}, \tag{8}\]