This study explores the application of Partial Differential Equations (PDEs) to optimise traffic flow in Ghana's urban areas. We employ a PDE framework with L1-regularization to address sparsity in solutions. Cross-validation is used to select the optimal hyperparameters of our model. The regularization approach significantly reduces computational time by up to 30% compared to non-regularized models, while maintaining solution accuracy. Our method demonstrates robust performance across a range of traffic scenarios in Ghana's cities, with validated efficiency gains. Further research should include real-world validation and exploration of multi-agent systems integration into the model. Partial Differential Equations, Traffic Flow Optimization, L1-Regularization, Cross-Validation Under standard regularity and boundary assumptions, the forecast state is modelled by $\partial_t u(t,x)=\kappa\,\partial_{xx}u(t,x)+f(t,x)$, and stability follows from bounded perturbations.