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Elastic scattering between $\ensuremath{\alpha}$ particles and $^{12}\mathrm{C}$ nuclei plays a crucial role in understanding resonance phenomena in light nuclear systems. In this work, we construct inverse potentials for resonant states in $\ensuremath{\alpha}\text{\ensuremath{-}}^{12}\mathrm{C}$ elastic scattering using the variable phase approach, in tandem with a genetic-algorithm-based optimization technique. The reference function for the potential in the phase equation is chosen as a combination of three smoothly joined Morse-type functions. The parameters of the reference function are genetically evolved to minimize the the mean-squared error (MSE) between the numerically obtained scattering phase shifts and the expected values. To avoid overfitting and ensure model generalization, we employ a fivefold cross-validation strategy, where the genetic algorithm (GA) minimizes the average validation error across folds. The resulting inverse potentials accurately reproduce the resonance energies (${E}_{r}$) and the resonance widths (${\mathrm{\ensuremath{\Gamma}}}_{r}$) for the ${\ensuremath{\ell}}^{\ensuremath{\pi}}$ states, ${1}^{\ensuremath{-}}$, ${2}^{+}$, ${3}^{\ensuremath{-}}$, and ${4}^{+}$, showing excellent agreement with experimental data. This computational approach to constructing inverse potentials serves as a complement to conventional direct methods for investigating nuclear-scattering phenomena.