## 4 Conclusions  
In this study, a multi-objective optimization algorithm, NSGA II, was employed alongside a TMM to find the SPR based sensor configurations that could present an enhanced sensing performance. The theoretical limit of maximal sensitivity with narrow FWHM and a reflectivity level at a resonance smaller than 1% was achieved for structures modified with a thin material placed on top of silver and graphene, MoS2 or WS2. Moreover, it was shown that the optimal refractive index values for the thin top layer were close to the levels of standard semiconductors, connecting our numerical analyses to real architectures. Sensitivities up to 302 deg/RIU were achieved for the structures containing 43 nm silver, 12 nm BaTiO3 and one monolayer of graphene and 43 nm silver, 10 nm BaTiO3 and one monolayer of WS2, respectively. From our extensive analysis on the effects of additional layers on the sensing performance of SPR based sensors we can draw the conclusion that multi-objective optimization employed together with the TMM could pave the way for the next ultrasensitive SPR based sensors providing solutions that can be easy to implement. The following are available online at [[https://www.mdpi.com/article/10.3390/app11104353/s1](https://www.mdpi.com/article/10.3390/app11104353/s1)]([https://www.mdpi.com/article/10.3390/app11104353/s1](https://www.mdpi.com/article/10.3390/app11104353/s1)), Figure S1: Convergence plots for the Ag-Semicondcutor-2D material-Sensing medium (nsemiconductor) configuration with -sensitivity and FWHM as objectives; Left column: the layer thicknesses convergence and right column: the objectives, Figure S2: Reflectivity curves for the Ag-Semicondcutor-2D material-Sensing medium (nsemiconductor) configuration, Table S1: Additional configurations for the structure: Ag-semiconductor-2D material-Sensing medium, Figure S3: Convergence plots for the Ag-BaTiO3-2D material-Sensing medium configuration with -sensitivity and FWHM as objectives; Left column: the layer thickness convergence and right column: the objectives convergence, Figure S4: Reflectivity curves for the Ag-BaTiO3-2D material-Sensing medium, Figure S5: Convergence plots for the Ag-Semicondcutor-2D material-Sensing medium (nsemiconductor) configuration with -sensitivity, FWHM, and minimum level of reflectivity as objectives; Left column: the layer thickness convergence and right column: the objectives convergence, Figure S6: Reflectivity curves for the Ag-Semicondcutor-2D material-Sensing medium (nsemiconductor) configuration with -sensitivity, FWHM, and minimum level of reflectivity as objectives, Table S3: Additional configurations for the structure: Ag-Semicondcutor-2D material-Sensing medium, Figure S7: Convergence plots for the Ag-BaTiO3/Si-2D material-Sensing medium configuration with -sensitivity, FWHM, and minimum level of reflectivity as objectives; Left column: the layer thickness convergence and right column: the objectives convergence, Figure S8: Reflectivity curves for the Convergence plots for the Ag-BaTiO3/Si-2D material-Sensing medium configuration with -sensitivity, FWHM, and minimum level of reflectivity as objectives, Table S4: Additional configurations for the structure: Ag-BaTiO3-2D material-Sensing medium. Conceptualization, P.V., writing--original draft preparation, P.V. ; writing--review and editing, P.V. and M.K., supervision M.K. Both authors have read and agreed to the published version of the manuscript.