## 4 Stretchable MSP Antenna-Based Strain Sensor
### Optimization
The spline coordinates were considered as the DVs, \(x\), and the minimum and maximum boundaries of the coordinates were determined to bring optimum shape change of the initial MSP antenna. Particularly, the coordinates of feedline in the length direction were firmly restricted to keep the initial shape of the MSP antenna. The optimization process includes significant attention associated with the strain applied along the width direction. On the basis of the equation of the frequency shift, even though the strain occurs along the length direction, which can make the patch's length varied owing to the Poisson's ratio, the variation will not bring a major impact on the variation of the R\({}_{\mathit{f}}\). Thus, design space around the patch had much more design freedom to improve antenna's operation than that around the feedline. To conduct multidisciplinary design optimization, genetic algorithm (GA) was exploited in accordance with the developed ANN-based surrogate model. For the algorithm, \(1000\) iterations, crossover probability of \(0.96\), and mutation probability of \(0.01\) were used. After conducting the optimization process, a butterfly-shaped antenna was garnered, as shown in Figure 7. Locations of the acquired spline coordinates by the optimization were slightly modified to have a smooth contour. As anticipated, it focused on reducing the variations of the width of the antenna patch, not on that of the length. It could boost the antenna's operation under the applied longitudinal strain. The optimization process drew a reasonable outcome, coinciding with the equations mentioned above in Section 2. To assure the exactness of the optimized butterfly-shaped design, HFSS was utilized to evaluate the frequency shift. The results of the undeformed antennas are shown in Figure 8. In accordance with the employed bandwidth of \(-10\) dB, an acceptable R\({}_{\mathit{f}}\) range of the antenna was assigned from \(2.3454\) GHz (a) to \(2.6539\) GHz (b) and from \(4.9130\) GHz (c) to \(5.1070\) GHz (d) under \(0\) mm displacement, as depicted in Figure 8.  
Figure 7: Design of the MSP patch antenna. (**a**) Initial antenna design; (**b**) optimal antenna design. First, the capability of the suggested optimum design was compared with the initial antenna design when the deformation exists for both. Once the deformation of 12 mm is applied to the initial antenna, \(\mathrm{R_{f}}\) drastically shifts, ranging from 2.5 GHz to 2.73 GHz and from 5.05 GHz to 5.23 GHz, which states that the antenna functionality will not be ensured because they deviate from each acceptable \(\mathrm{R_{f}}\) range regarding 2.5 and 5.0 GHz. The return loss also decreased by 27.6% and 31.8%, respectively. As expected, the performance of the antenna was deteriorated under the deformation. Especially the antenna design in 5 GHz should be restricted owing to miserable return loss, which is higher than \(-\)10 dB. Contrary to the initial antenna, on the other hand, the optimized antenna excluding the DR process acquired credits for its flexible possibility under the tensile strain by enabling the \(\mathrm{R_{f}}\) to be maintained in the reliable range (\(\theta\)) and the return loss to be kept under \(-\)10 dB, as elucidated in \[S(x,f_{i},\varepsilon)+\gamma\leq 0, \tag{20}\]0  
Also, a comparison of two additional designs regarding the DR process antenna was conducted. In Table 3, the design of the initial MSP antenna design including DR led to a better operation than that of the initial antenna itself. Although, its improvement is not enough to dominate the initial antenna design with an optimization. As predicted, the optimized antenna design with DR had notable improvement when compared with all other cases. Therefore, the uncertainty-reduced optimal MSP antenna design could be a dominant approach because general wireless receivers would be employed without any additional extension work on the bandwidth.