Numerical simulation of a Proton-Exchange Membrane Fuel Cell (PEMFC) requires an adequate model and precise parameters for reproducing their operational performance quantified by the polarization curve. Bio-inspired algorithms are well-suited for estimating unknown parameters; nevertheless, the simulator is stressed by inputting thousands of randomly-generated parameters. As a consequence, they require a robust numerical model. Once the model with the proper parameters reproduces the experimental data, it is applicable for optimizing the PEMFC. This article proposes a reformulation of a macro-homogeneous mathematical model by analyzing its relation with singularly perturbed differential equations to provide higher numerical stability to the solutions. This formulation introduces a boundary value problem instead of the usual initial value problem. Hence, we propose an assembly of the proper numerical methods for solving this version of the problem. Then, we introduce optimization problems for parameter estimation and design optimization; three bio-inspired algorithms solve the first. The most consistent of them is applied to optimize the PEMFC design by maximizing its performance or minimizing the platinum mass loading, highly related to the cost. To the best of our knowledge, there is no other research for optimizing the cell design, neither its performance nor its cost, using numerical simulation and optimization. The results are validated as follows: a) Comparing experimental polarization curves with the simulation with the parameters estimated by bio-inspired algorithms. b) Comparing a base design's performance with the optimized for maximum performance, and c) comparing a base design with the optimized for minimum platinum mass loading.