Gradient Based Optimization

Secanell et al. [125] presented a gradient-based optimization of fuel cell performance. They found that a significant increase in performance could be achieved by increasing Pt loading and reaching a Nafion mass fraction around 20-30 wt% in the CL. 

The problem of local minima in function minimization or optimization problems has given rise to the development of a variety of algorithms which are able to seek global minima. Traditional gradient based optimizers proceed by the selection of fruitful search directions and subsequent numerical one-dimensional optimization along these paths. Such methods are therefore inherently prone to the discovery of local minima in the vicinity of their starting point, as illustrated in Fig. 5.4(b). This property is in fact desirable in... 

Hiilsmann, M., Koddermann, T., Vrabec, J., Reith, D. GROW A gradient-based optimization workflow for the automated development of molecular models. Comput Phys. Commun. 181,... 

Gradient methods discussed above use a quadratic function (energy, gradient and approximate Hessian) to model the energy surface near the transition state. Distance-weighted interpolants provide a more flexible functional form that can interpolate arbitrarily spaced points with a smooth differentiable function. For a gradient-based optimization, the Shepard interpolation functions seem appropriate... 

With the feasible path approach the optimization algorithm automatically performs case studies by variing input data. There are several drawbacks the process equations (32c) have to be solved every time the performance index is evaluated. Efficient gradient-based optimization techniques can only be used with great difficulties because derivatives can only be evaluated by perturbing the entire flowsheet with respect to the decision variables. This is very time consuming. Second, process units are often described by discrete and discontinuous relations or by functions that may be nondifferentiable at certain points. To overcome these problems quadratic module models can be... 

Particle diffusion was studied with a separate code written in MS Excel utilizing the step-by-step routine and gradient-based optimization (Eq. 15.13). The particles were assumed to be spherical. The calculations were made with the highest reaction rate present in the reactor. In practice this meant a place close to feed point location in the beginning of the experiment Results of calculations are shown in Figure 15.3, where the dimensionless concentrations (C,/Qs) of stearic add and heptadecane are illustrated. 

Here, the tangent-sigmoid was used as the activation function because of its non-Unearity, suitability for gradient-based optimization algorithms, and speed due to antisymmetric properties. 

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