When facing certain problems in science, engineering or technology, it is not enough to find a solution, but it is essential to seek and find the best possible solution through optimization. In many cases the exact optimization procedures are not applicable due to the great computational complexity of the problems. As an alternative to exact optimization, there are approximate optimization algorithms, whose purpose is to reduce computational complexity by pruning some areas of the problem search space. To achieve this, researchers have been inspired by nature, because animals and plants tend to optimize many of their life processes. The purpose of this research is to design a novel bioinspired algorithm for numeric optimization: the Mexican Axolotl Optimization algorithm. The effectiveness of our proposal was compared against nine optimization algorithms (artificial bee colony, cuckoo search, dragonfly algorithm, differential evolution, firefly algorithm, fitness dependent optimizer, whale optimization algorithm, monarch butterfly optimization, and slime mould algorithm) when applied over four sets of benchmark functions (unimodal, multimodal, composite and competition functions). The statistical analysis shows the ability of Mexican Axolotl Optimization algorithm of obtained very good optimization results in all experiments, except for composite functions, where the Mexican Axolotl Optimization algorithm exhibits an average performance.

The Lernmatrix is a classic associative memory model. The Lernmatrix is capable of executing the pattern classification task, but its performance is not competitive when compared to state-of-the-art classifiers. The main contribution of this paper consists of the proposal of a simple mathematical transform, whose application eliminates the subtractive alterations between patterns. As a consequence, the Lernmatrix performance is significantly improved. To perform the experiments, we selected 20 datasets that are challenging for any classifier, as they exhibit class imbalance. The effectiveness of our proposal was compared against seven supervised classifiers of the most important approaches (Bayes, nearest neighbors, decision trees, logistic function, support vector machines, and neural networks). By choosing balanced accuracy as a performance measure, our proposal obtained the best results in 10 datasets. The elimination of subtractive alterations makes the new model competitive against the best classifiers, and sometimes beats them. After applying the Friedman test and the Holm post hoc test, we can conclude that within a 95% confidence, our proposal competes successfully with the most effective classifiers of the state of the art.

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The analysis of microarrays that contain information on biomolecules related to different types of cancer is one of the current issues in international scientific research due to the impact it has on public health worldwide. The advances in this scientific research route have been impressive; the different international research groups have applied sophisticated algorithms for machine learning, data mining and related branches with the aim of finding solutions to this problem. The present article contains a study of several the classification algorithms used in the literature, and their application for the prediction of cancer using microarrays analysis. More in detail, we tested six classification models, over microarrays data. The application of the supervised classification algorithms was done over the Weka 3 Software environment, using the Leave One Out validation scheme. In addition, a nonparametric statistical test (the Friedman test) identified the significant differences in the performance of the algorithms, according to the experimental results obtained. The analysis of the hypothesis tests of the experimental results indicates that the Support Vector Machine models outperform others for the prediction of cancer.