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This article describes a new genetic-programming-based optimization method using a multi-gene approach along with a niching strategy and periodic domain constraints. The method is referred to as Niching MG-PMA, where MG refers to multi-gene and PMA to parameter mapping approach. Although it was designed to be a multimodal optimization method, recent tests have revealed its suitability for unimodal optimization. The definition of Niching MG-PMA is provided in a detailed fashion, along with an in-depth explanation of two novelties in our implementation: the feedback of initial parameters and the domain constraints using periodic boundary conditions. These ideas can be potentially useful for other optimization techniques. The method is tested on the basis of the CEC’2015 benchmark functions. Statistical analysis shows that Niching MG-PMA performs similarly to the winners of the competition even without any parametrization towards the benchmark, indicating that the method is robust and applicable to a wide range of problems.

Scalability problems have hindered the progress of Evolvable Hardware in tackling complex circuits. The two key issues are the amount of testing (for example, a 64-bit \(\times \) 64-bit add-shift multiplier problem has \(2^{64 + 64}\) test cases) and low level that hardware works at: a circuit to implement 64-bit \(\times \) 64-bit add-shift multiplier would require approximately 33,234 gates when synthesized using the powerful Yosys Open SYnthesis Suite tool. We use Grammatical Evolution and SystemVerilog, a Hardware Description Language (HDL), to evolve fully functional parameterized adder, multiplier and selective parity circuits with default input bit-width sizes of 64-bit + 64-bit, 64-bit \(\times \) 64-bit and 128-bit respectively.

This paper investigates the potential of evolutionary algorithms, developed using a combination of genetic programming and automatic differentiation, to obtain symbolic solutions to stochastic differential equations. Using the MATLAB programming environment and based on the theory of stochastic calculus, we develop algorithms and conceive a new methodology of resolution. Relative to other methods, this method has the advantages of producing solutions in symbolic form and in continuous time and, in the case in which an equation of interest is completely unknown, of offering the option of algorithms that perform the specification and estimation of the solution to the equation via a real database. The last advantage is important because it determines an appropriate solution to the problem and simultaneously eliminates the difficult task of arbitrarily defining the functional form of the stochastic differential equation that represents the dynamics of the phenomenon under analysis. The equation for geometric Brownian motion, which is usually applied to model prices and returns from financial assets, was employed to illustrate and test the quality of the algorithms that were developed. The results are promising and indicate that the proposed methodology can be a very effective alternative for resolving stochastic differential equations.

This study presents the crude oil scheduling problem with four objectives divided in two different levels of importance. It comes from a real refinery where the scheduling starts on the offloading of ships, encompasses terminal and refinery tanks, a crude pipeline, and finishes on the output streams of the crude distillation units. We propose a new approach for the Quantum-Inspired Grammar-based Linear Genetic Programming (QIGLGP) evolutionary algorithm to handle the multiple objectives of the problem using the non-dominance concept. The modifications are concentrated on the population updating and sorting steps of QIGLGP. We tackle difference of importance among the objectives using the principle of violation of constraints. The problem constraints define if an instruction will or not be executed but do not affect the violation equation of the objectives. The individuals which have objective values under a pre-defined upper limit are better ranked. Results from five scenarios showed that the proposed model was able to significantly increase the percentage of runs with acceptable solutions, achieving success ratio of 100% in 3 cases and over 70% in 2 other ones. They also show that the Pareto front of these accepted runs contains a set of non-dominated solutions that could be analyzed by the decision maker for his a posteriori decision.

Genetic programming techniques allow flexibility in the optimization process, making it possible to use them in different areas of knowledge and providing new ways for specialists to advance in their areas more quickly and more accurately. This work presents a preliminary analysis of a new method using multi-gene genetic programming to multimodal numerical optimization. The new algorithm uses some niching techniques based on the clear procedure to maintain the population diversity, in order to perform a multivariate mapping among initial guesses to optimal parameters for a system. We used a multi-modal benchmark set with different characteristics and difficulty levels to evaluate this new algorithm. Statistical analysis suggested that this new multi-modal method using multi-gene genetic programming can be used for problems that requires more than a single solution.

Econometric Genetic Programming (EGP) evolves multiple linear regressions through Genetic Programming (GP), which is responsible for model selection, aiming to generate high accuracy regressions with potential interpretability of parameters. It uses statistical significance as a feature selection tool, directly and efficiently identifying introns and controlling bloat. In this paper, EGP is tested against traditional feature-selection econometric algorithms in regression tasks - namely Partial Least Squares Regression, Ridge Regression and Stepwise Forward Regression - outperforming them in all three datasets. The way EGP explores search space of possible regressors and models is crucial for its results. EGP is carefully constructed considering econometric theory on cross-sectional datasets, giving rigorous treatment on topics like homoscedasticity and heteroscedasticity, statistical inference for estimated parameters and sampling criteria. It also benefits by the mathematical proof on accuracy and statistical significance: accuracy will only increase if the regressor presents a test's statistics module in a two-sided hypothesis testing higher than a predefined value.

Logistic Regression and Genetic Programming (GP) have already been compared to each other in classification tasks. In this paper, Econometric Genetic Programming (EGP), first introduced as a regression methodology, is extended to binary classification tasks and evolves logistic regressions through GP, aiming to generate high accuracy classifications with potential interpretability of parameters, while uses statistical significance as a feature-selection tool and GP for model selection. EGP-Classification (or EGP-C), the name of this proposed EGP’s extension, was tested against a large group of algorithms in three cross-sectional datasets, showing competitive results in most of them. EGP-C successfully competed against highly non-linear algorithms, like Support Vector Machines and Multilayer Perceptron with Back Propagation, and still allows interpretability of parameters and models generated.

Recently, it has been shown that complementarity models are an attracting tool for representing power converters in both open- and closed-loop configuration. A unique dynamical complementarity model captures all the modes of a power converter, without assuming the a priori knowledge of the sequence of modes or of the switching time instants. In this paper, we derive the complementarity model of a single-phase active filter with cascaded multilevel inverter. A combination of the unipolar and the phase-disposition PWM techniques is used with the goal of regulating the dc-link voltage. As benchmark for comparison, the time evolution of inductors currents and capacitors voltages computed with the complementarity procedure is compared with the ones obtained with PSIM software.

This paper investigates the potential of evolutionary algorithms, developed by the combination of genetic programming (GP) and automatic differentiation methods (AD), in determining analytic solutions to ordinary and partial differential equations (ODE and PDE). In turn, AD is a set of techniques based on the mechanical application of the chain rule to numerically evaluate the derivative of a function specified by a computer program. The AD method has a fundamental role in this work since it calculates the exact values of the derivatives of a function for a given set of input values while numerical differentiation methods introduce unacceptable round-off errors in the discretization process. With this purpose, and using the Matlab programming environment, we developed several algorithms (namely GPAD) and addressed problems of different kinds of differential equations. The results are promising, with exact solutions obtained for most of the addressed problems, which include equations where not even commercial systems could find a symbolic solution. These results empirically indicate that GPAD can be an efficient and robust methodology to find analytic solutions for ODE and PDE.