Industry 5.0 is driving a new era in industrial automation, where the collaboration between artificial intelligence (AI) and human supervision enables the development of smarter, more adaptive, and more efficient systems. Robotic trajectory generation is a clear example of this new paradigm. Metaheuristic techniques help automatically generate optimized trajectories, thereby improving operational efficiency. However, optimizing trajectories using AI alone also presents limitations. Starting from random trajectories, the optimization process becomes computationally expensive, especially in complex environments. In this context, initial input from human experts plays a crucial role: expert-defined trajectories provide structured, feasible, and contextual starting points that guide AI more effectively toward high-quality solutions. Therefore, this work proposes a novel human-guided trajectory optimization algorithm. In this way, human knowledge, Particle Swarm Optimization (PSO), and Pattern Search (PS) are efficiently combined. The results demonstrate that this approach significantly improves robotic system performance, achieving cycle time reductions of up to 16.69% compared to expert-defined trajectories. This approach establishes a solid framework for intelligent automation in Industry 5.0, promoting the development of more efficient, sustainable, and adaptive robotic systems.

In this study a new internal clustering validation index is proposed. It is based on a measure of the uniformity of the data in clusters. It uses the local density of each cluster, in particular, the normalized variability of the density within the clusters to find the ideal partition. The new validity measure allows it to capture the spatial pattern of the data and obtain the right number of clusters in an automatic way. This new approach, unlike the traditional one that usually identifies well-separated compact clouds, works with arbitrary-shape clusters that may be contiguous or even overlapped. The proposed clustering measure has been evaluated on nine artificial data sets, with different cluster distributions and an increasing number of classes, on three highly nonlinear data sets, and on 17 real data sets. It has been compared with nine well-known clustering validation indices with very satisfactory results. This proves that including density in the definition of clustering validation indices may be useful to identify the right partition of arbitrary-shape and different-size clusters.

In this work, we are proposing a trading system where fuzzy logic is applied not only for defining the trading rules, but also for managing the capital to invest. In fact, two fuzzy decision support systems are developed. The first one uses fuzzy logic to design the trading rules and to apply the stock market technical indicators. The second one enhances this fuzzy trading system adding a fuzzy strategy to manage the capital to trade. Additionally, a new technical market indicator that produces short and long entry signals is introduced. It is based on the moving average convergence divergence indicator. Its parameters have been optimized by genetic algorithms. The proposals are compared to a classical nonfuzzy version of the proposed trading systems and to the buy-and-hold strategy. Results favor our fuzzy trading system in the two markets considered, NASDAQ100 and EUROSTOXX. Conclusions suggest that the use of fuzzy logic for capital management is promising and deserves further exploration.