Heuristic techniques (such as genetic algorithm, particle swarm optimization, differential evolution, simulating annealing, harmony search, memetic algorithms, bird mating optimization, and artificial immune system) usually use stochastic methods to identify an optimal solution, which require a large number of device simulations and compromise the accuracy of the solution. The computational cost of heuristic techniques limit their application to a small number of variables (usually under ten), and can generally be applied to simplified models.
In contrast, non-heuristic techniques (such as line search and trust-region methods, the Nelder-Mead method, the Powell algorithm, steepest descents, conjugate gradient methods, Newton and quasi-Newton methods, and linear and quadratic programming) are deterministic and often require computing or approximating the gradient of the objective function [1-4]. Usually these techniques have local convergence and their rate of convergence can be improved by using the Hessian matrix or other second-order derivatives, evaluating the gradient more accurately, or taking advantage of the particular functional form of the objective function. Depending on whether the gradient function can be evaluated or not, as well as on the accuracy with which the first and higher order derivatives can be computed, non-heuristic techniques usually require between a few and 100 iterations to optimize the objective function, while the total number of variables to be optimized could be larger than 105.
In this work we compare heuristic and nonheuristic methods and present a gradient-based technique for the optimization of the catalyst distribution in PEMFCs using finite element models. We demonstrate a non-heuristic technique to determine optimum platinum distribution in the catalyst layer (CL) by allowing the catalyst amount to vary independently at each not inside the CL. Therefore, the total number of finite elements in the CL, in this work, is larger than 104; however, the technique could be extended to systems with even more elements. Optimization is performed by first computing a catalyst sensitivity function, which is the gradient of the objective function with respect to the mass of catalyst at each location in the CL; then an adjoint space technique is employed to evaluate the catalyst sensitivity functions at each node in the finite element discretization. Cell performance is evaluated and compared for the optimized and non-optimized PEMFCs.
References
[1] F. C. Cetinbas, S. G. Advani and A. K. Prasad, Journal of Power Sources, 250, 110 (2014).
[2] J. Lamb, G. Mixon and P. Andrei, Jour of the ECS, 164, E3232 (2017).
[3] P. Andrei and L. Oniciuc, Jour of Appl. Physics, 104, Art. No. 104508 (2008).
[4] P. Andrei and L. Oniciuc, Jour of Comp. Elec., 7, 111 (2008).