Knapsack Problem

The knapsack problem, a classic combinatorial optimization challenge, seeks to maximize the value of items selected within a weight constraint. Current research focuses on extending the problem to dynamic, stochastic, and constrained environments, employing diverse approaches such as evolutionary algorithms, Lagrangian dual frameworks, and learning-augmented algorithms to improve solution quality and efficiency. These advancements have significant implications for various fields, including multi-robot coordination, resource allocation, and even securing neural networks, by providing efficient and robust solutions to complex real-world problems involving resource optimization under uncertainty.