Knapsack Constraint

The knapsack constraint problem involves selecting a subset of items with maximum value, subject to a weight limit (the "knapsack's capacity"). Current research focuses on improving approximation algorithms for various knapsack problem variants, including those with non-monotone submodular objectives, stochastic profits or weights, and additional constraints like matroids or graph-theoretic properties. These advancements leverage techniques such as threshold greedy algorithms, multi-objective evolutionary algorithms, and semi-bandit learning to achieve better approximation ratios and reduced query complexity. The improved efficiency and solution quality of these algorithms have significant implications for diverse applications in machine learning, operations research, and resource allocation.