NP Hard

NP-hard problems represent a class of computationally challenging optimization tasks where finding an optimal solution requires time that grows exponentially with the problem size. Current research focuses on developing efficient approximation algorithms, often leveraging machine learning techniques such as neural networks (including graph convolutional networks and attention mechanisms), reinforcement learning, and metaheuristics like genetic algorithms and Monte Carlo Tree Search. These advancements aim to find near-optimal solutions within reasonable timeframes for real-world applications across diverse fields, including logistics, cybersecurity, and bioinformatics, where exact solutions are often intractable.