Artificial Intelligence continues to demand robust and adaptable training methods for neural networks, particularly in scenarios involving limited computational resources or noisy, complex data. This study presents a comparative analysis of four training algorithms, Backpropagation, Genetic Algorithm, Black-hole Algorithm, and Particle Swarm Optimization, evaluated across both classification and regression tasks. Each method was implemented from scratch in MATLAB ver. R2024a, avoiding reliance on pre-optimized libraries to isolate algorithmic behavior. Two types of datasets were used, namely a synthetic benchmark dataset and a real-world dataset preprocessed into classification and regression formats. All algorithms were tested in both basic and advanced forms using consistent network architectures and training constraints. Results indicate that while Backpropagation maintained strong performance in smooth regression settings, the Black-hole and PSO algorithms demonstrated more stable and faster initial progress in noisy or discrete classification tasks. These findings highlight the practical viability of the Black-hole Algorithm as a competitive, gradient-free alternative for neural network training, particularly in early-stage learning or hybrid optimization frameworks.

Nowadays, the development of higher efficient processes and procedures is the key for success in industrial environment. The companies have machines, production lines, software and hardware tools with high level principles of efficient working. Example: the Industry 4.0 concept use the machines and methods of the near past, upgrade them, and gave them new purpose, as a more efficient tool. Some of the bases of those tools are not as efficient as which many would think, like in group generating or in other word clustering. Clustering is a very hard process, and it is in almost every decision making in every company’s lives. It is important to sometimes examine its significance and flaws. This paper presents the clustering briefly and shows its errors through an example.

Supply chain planning is becoming increasingly important today, as it is essential for efficient operations to design supply chains that are flexible, sustainable, highly available and able to respond quickly and efficiently to dynamically changing customer needs, while operating cost-effectively. When designing supply chains, it is important to consider not only the investment cost but also the operational cost. This requires the most accurate forecasting of future supply chain needs. In this paper, the authors present a new method for the optimal design of a multicentre distribution network, which uses evolutionary optimisation and Monte Carlo simulation to determine the optimal distribution network structure in an arbitrary geographical area. The design takes into account investment and operational costs, with particular emphasis on the question of how to estimate the average transportation distances in a distribution network with an unknown structure.

Time series forecasting performance is strongly influenced by the structural properties of the underlying data, yet learning-based models are often applied without sufficient validation of this dependency. This study evaluates a uniformly configured Long Short-Term Memory (LSTM) model on five real-world weekly time series with different levels of periodicity, noise, and volatility. Forecasting is performed in a single-step setting using a fixed sliding window of 12 weeks under a consistent training, validation, and testing framework. Model performance is assessed using mean squared error (MSE) and the coefficient of determination R². The results show that for well-structured series, both the LSTM model and Holt’s exponential smoothing achieve very low MSE values with R² scores close to one, indicating excellent predictive accuracy. For other items, performance varies across methods, with either the LSTM or Holt model providing the best results depending on the data structure. These findings confirm that high forecasting accuracy can be achieved with both advanced and classical methods, and that data characteristics play a more decisive role than model complexity.