A BRANCH-AND-BOUND ALGORITHM FOR A PSEUDO-BOOLEAN OPTIMIZATION PROBLEM WITH BLACK-BOX FUNCTIONS

We consider a conditional pseudo-Boolean optimization problem with both the objective function and all constraint functions given algorithmically (black-box functions) and defined on {0, 1}n only. We suppose that these functions have certain properties, for example, unimodality and monotonicity. To solve problems of this type, we propose an optimization algorithm based on finding boundary points of the feasible region and the branch-and-bound method. The developed algorithm is aimed at the reception of an exact solution of an optimization problem. In addition, this algorithm can be used as an improvement of approximate algorithms such as the greedy heuristic and the random search algorithms for finding boundary points. Even after a small number of iterations (branchings), a significant improvement of the found feasible solution is achieved

Prediction of Critical Filling of a Storage Area Network by Machine Learning Methods

The introduction of digital technologies into the activities of companies is based on software and hardware systems, which must function reliably and without interruption. The forecasting of the completion of storage area networks (SAN) is an essential tool for ensuring the smooth operation of such systems. The aim of this study is to develop a system of the modelling and simulation of the further loading of SAN on previously observed load measurements. The system is based on machine learning applied to the load prediction problem. Its novelty relates to the method used for forming input attributes to solve the machine learning problem. The proposed method is based on the aggregation of data on observed loading measurements and the formalization of the problem in the form of a regression analysis problem. The artificial dataset, synthesized stochastically according to the given parameter intervals and simulating SAN behavior, allowed for more extensive experimentation. The most effective algorithm is CatBoost (gradient boosting on decision trees), which surpasses other regression analysis algorithms in terms of R2 scores and MAE. The selection of the most significant features allows for the simplification of the prediction model with virtually no loss of accuracy, thereby reducing the number of confessions used. The experiments show that the proposed prediction model is adequate to the situation under consideration and allows for the prediction of the SAN load for the planning period under review with an R2 value greater than 0.9. The model has been validated on a series of real data on SAN

A Study on a Probabilistic Method for Designing Artificial Neural Networks for the Formation of Intelligent Technology Assemblies with High Variability

Currently, ensemble approaches based, among other things, on the use of non-network models are powerful tools for solving data analysis problems in various practical applications. An important problem in the formation of ensembles of models is ensuring the synergy of solutions by using the properties of a variety of basic individual solutions; therefore, the problem of developing an approach that ensures the maintenance of diversity in a preliminary pool of models for an ensemble is relevant for development and research. This article is devoted to the study of the possibility of using a method for the probabilistic formation of neural network structures developed by the authors. In order to form ensembles of neural networks, the influence of parameters of neural network structure generation on the quality of solving regression problems is considered. To improve the quality of the overall ensemble solution, using a flexible adjustment of the probabilistic procedure for choosing the type of activation function when filling in the layers of a neural network is proposed. In order to determine the effectiveness of this approach, a number of numerical studies on the effectiveness of using neural network ensembles on a set of generated test tasks and real datasets were conducted. The procedure of forming a common solution in ensembles of neural networks based on the application of an evolutionary method of genetic programming is also considered. This article presents the results of a numerical study that demonstrate a higher efficiency of the approach with a modified structure formation procedure compared to a basic approach of selecting the best individual neural networks from a preformed pool. These numerical studies were carried out on a set of test problems and several problems with real datasets that, in particular, describe the process of ore-thermal melting

Paired Patterns in Logical Analysis of Data for Decision Support in Recognition

Logical analysis of data (LAD), an approach to data analysis based on Boolean functions, combinatorics, and optimization, can be considered one of the methods of interpretable machine learning. A feature of LAD is that, among many patterns, different types of patterns can be identified, for example, prime, strong, spanned, and maximum. This paper proposes a decision-support approach to recognition by sharing different types of patterns to improve the quality of recognition in terms of accuracy, interpretability, and validity. An algorithm was developed to search for pairs of strong patterns (prime and spanned) with the same coverage as the training sample, having the smallest (for the prime pattern) and the largest (for the spanned pattern) number of conditions. The proposed approach leads to a decrease in the number of unrecognized observations (compared with the use of spanned patterns only) by 1.5–2 times (experimental results), to some reduction in recognition errors (compared with the use of prime patterns only) of approximately 1% (depending on the dataset) and makes it possible to assess in more detail the level of confidence of the recognition result due to a refined decision-making scheme that uses the information about the number and type of patterns covering the observation

Paired Patterns in Logical Analysis of Data for Decision Support in Recognition

Logical analysis of data (LAD), an approach to data analysis based on Boolean functions, combinatorics, and optimization, can be considered one of the methods of interpretable machine learning. A feature of LAD is that, among many patterns, different types of patterns can be identified, for example, prime, strong, spanned, and maximum. This paper proposes a decision-support approach to recognition by sharing different types of patterns to improve the quality of recognition in terms of accuracy, interpretability, and validity. An algorithm was developed to search for pairs of strong patterns (prime and spanned) with the same coverage as the training sample, having the smallest (for the prime pattern) and the largest (for the spanned pattern) number of conditions. The proposed approach leads to a decrease in the number of unrecognized observations (compared with the use of spanned patterns only) by 1.5–2 times (experimental results), to some reduction in recognition errors (compared with the use of prime patterns only) of approximately 1% (depending on the dataset) and makes it possible to assess in more detail the level of confidence of the recognition result due to a refined decision-making scheme that uses the information about the number and type of patterns covering the observation

Formation of Fuzzy Patterns in Logical Analysis of Data Using a Multi-Criteria Genetic Algorithm

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability

Prediction of Critical Filling of a Storage Area Network by Machine Learning Methods

The introduction of digital technologies into the activities of companies is based on software and hardware systems, which must function reliably and without interruption. The forecasting of the completion of storage area networks (SAN) is an essential tool for ensuring the smooth operation of such systems. The aim of this study is to develop a system of the modelling and simulation of the further loading of SAN on previously observed load measurements. The system is based on machine learning applied to the load prediction problem. Its novelty relates to the method used for forming input attributes to solve the machine learning problem. The proposed method is based on the aggregation of data on observed loading measurements and the formalization of the problem in the form of a regression analysis problem. The artificial dataset, synthesized stochastically according to the given parameter intervals and simulating SAN behavior, allowed for more extensive experimentation. The most effective algorithm is CatBoost (gradient boosting on decision trees), which surpasses other regression analysis algorithms in terms of R2 scores and MAE. The selection of the most significant features allows for the simplification of the prediction model with virtually no loss of accuracy, thereby reducing the number of confessions used. The experiments show that the proposed prediction model is adequate to the situation under consideration and allows for the prediction of the SAN load for the planning period under review with an R2 value greater than 0.9. The model has been validated on a series of real data on SAN

Formation of Fuzzy Patterns in Logical Analysis of Data Using a Multi-Criteria Genetic Algorithm

The formation of patterns is one of the main stages in logical data analysis. Fuzzy approaches to pattern generation in logical analysis of data allow the pattern to cover not only objects of the target class, but also a certain proportion of objects of the opposite class. In this case, pattern search is an optimization problem with the maximum coverage of the target class as an objective function, and some allowed coverage of the opposite class as a constraint. We propose a more flexible and symmetric optimization model which does not impose a strict restriction on the pattern coverage of the opposite class observations. Instead, our model converts such a restriction (purity restriction) into an additional criterion. Both, coverage of the target class and the opposite class are two objective functions of the optimization problem. The search for a balance of these criteria is the essence of the proposed optimization method. We propose a modified evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm-II (NSGA-II) to solve this problem. The new algorithm uses pattern formation as an approximation of the Pareto set and considers the solution’s representation in logical analysis of data and the informativeness of patterns. We have tested our approach on two applied medical problems of classification under conditions of sample asymmetry: one class significantly dominated the other. The classification results were comparable and, in some cases, better than the results of commonly used machine learning algorithms in terms of accuracy, without losing the interpretability