We used genetic programming to evolve a direct search optimization algorithm, similar to that of the standard downhill simplex optimization method proposed by Nelder and Mead ( 1965 ). In the training process, we used several ten-dimensional quadratic functions with randomly displaced parameters and different randomly generated starting simplices. The genetically obtained optimization algorithm showed overall better performance than the original Nelder–Mead method on a standard set of test functions. We observed that many parts of the genetically produced algorithm were seldom or never executed, which allowed us to greatly simplify the algorithm by removing the redundant parts. The resulting algorithm turns out to be considerably simpler than the original Nelder–Mead method while still performing better than the original method.

The problem of the creation of numerical constants has haunted the Genetic Programming (GP) community for a long time and is still considered one of the principal open research issues. Many problems tackled by GP include finding mathematical formulas, which often contain numerical constants. It is, however, a great challenge for GP to create highly accurate constants as their values are normally continuous, while GP is intrinsically suited for combinatorial optimization. The prevailing attempts to resolve this issue either employ separate real-valued local optimizers or special numeric mutations. While the former yield better accuracy than the latter, they add to implementation complexity and significantly increase computational cost. In this paper, we propose a special numeric crossover operator for use with Robust Gene Expression Programming (RGEP). RGEP is a type of genotype/phenotype evolutionary algorithm closely related to GP, but employing linear chromosomes. Using normalized least squares error as a fitness measure, we show that the proposed operator is significantly better in finding highly accurate solutions than the existing numeric mutation operators on several symbolic regression problems. Another two important advantages of the proposed operator are that it is extremely simple to implement, and it comes at no additional computational cost. The latter is true because the operator is integrated into an existing crossover operator and does not call for an additional cost function evaluation.

Identification of ongoing processes in solid oxide fuel cells (SOFC) enables both optimizing the operating environment and prolonging the lifetime of SOFC. The Levenberg–Marquardt algorithm (LMA) is commonly used in the characterization of unknown electrochemical processes within SOFC by extracting equivalent electrical circuit (EEC) parameter values from electrochemical impedance spectroscopy (EIS) data. LMA is an iteration optimization algorithm regularly applied to solve complex nonlinear least square (CNLS) problems. The LMA convergence can be boosted by the application of an ordinary limit strategy, which avoids the occurrence of off-limit values during the fit. However, to additionally improve LMA descent properties and to discard the problem of a poor initial parameters choice, it is necessary to modify the ordinary limit strategy. In this work, we designed a new automatic update (i.e., adaptive) limit strategy whose purpose is to reduce the impact of a poor initial parameter choice. Consequently, the adaptive limit strategy was embedded in a newly developed EIS fitting engine. To demonstrate that the new adaptive (vs. ordinary) limit strategy is superior, we used it to solve several CNLS problems. The applicability of the adaptive limit strategy was also validated by analyzing experimental EIS data collected by using industrial-scale SOFCs.

Electrochemical impedance spectroscopy (EIS) is an important electrochemical technique that is used to detect changes and ongoing processes in a given material. The main challenge of EIS is interpreting the collected measurements, which can be performed in several ways. This article focuses on the electrical equivalent circuit (EEC) approach and uses grammatical evolution to automatically construct an EEC that produces an AC response that corresponds to one obtained by the measured electrochemical process(es). For fitting purposes, synthetic measurements and data from measurements in a realistic environment were used. In order to be able to faithfully fit realistic data from measurements, a new circuit element (ZARC) had to be implemented and integrated into the SPICE simulator, which was used for evaluating EECs. Not only is the presented approach able to automatically (i.e., with almost no user input) produce a more than satisfactory EEC for each of the datasets, but it also can also generate completely new EEC configurations. These new configurations may help researchers to find some new, previously overlooked ongoing electrochemical processes.

We propose a new method for a light energy flux density (or irradiance) calculation in an arbitrary multilayer stack containing coherent and incoherent layers. Although the well known General Transfer-Matrix Method (GTMM) can be successfully used for the overall reflectance and transmittance calculation, it does not allow us to obtain the corresponding irradiance depth profile straightforwardly. We show in this paper that subsequent phase-shift integrations over the incoherent layers result in the reflectance and transmittance expressions identical to those of the GTMM formulation. However, the alternative mathematical approach allows us to derive an analytical expression for irradiance at an arbitrary depth of the multilayer stack, thus making it possible to calculate the absorptance depth profile. In fact, the GTMM expressions for the overall reflectance and transmittance turn out to be special cases of the irradiance calculation at the incident and emergent surface of the multilayer stack. Consequently, the proposed Phase-shift Integration Method (PIM) represents a continuous irradiance calculation model without any energy imbalances on layer interfaces. In addition, since we are able to obtain analytical layer thickness derivatives, the PIM is suitable for use with gradient optimization methods. We verify the method on three cases of an encapsulated bifacial heterojunction silicon (HJ Si) solar cell, a perovskite solar cell, and a perovskite/silicon tandem solar cell, which all consist of thin and thick layers.