0/1 Knapsack Benchmark Dataset

This dataset contains 16,000 reproducible instances of the 0/1 Knapsack Problem, together with certified exact solutions, linear programming relaxations, deterministic greedy solutions, and associated metadata. For the 0/1 Knapsack Problem, a collection of items is given, each with an integer weight and profit, together with a knapsack capacity. The objective is to select a subset of the items that maximises total profit without exceeding the capacity. The dataset is intended as a benchmark resource for computational experiments in combinatorial optimisation, integer programming, dynamic programming, approximation and heuristic algorithms, and machine learning for optimisation. It may also be useful for algorithm benchmarking and teaching in operations research and computer science. The benchmark contains the problem dimensions n = 10, 20, 30, 50, 75, 100, 150, 250, 400, 650, 1,000, 1,600, 2,500, 4,000, 6,500, and 10,000, where n denotes the number of items. Ten instance families are included: uncorrelated, weakly correlated, strongly correlated, subset sum, inverse strongly correlated, almost equal weights, multiple optima, greedy trap, small capacity, and large capacity. Each family–dimension combination contains 100 instances, giving 16,000 instances in total. For each instance, the dataset provides the item weights and profits, knapsack capacity, exact optimal objective value and a corresponding optimal solution, fractional-knapsack linear programming relaxation, three deterministic greedy solutions, generation seed, summary statistics, and additional solution and difficulty metadata. Every instance has a certified exact optimum. Exact solutions were obtained using a combination of dynamic programming and mixed-integer programming, while the linear programming relaxation and greedy baselines were generated deterministically. The release consists of CSV benchmark files, separate ZIP archives for each problem dimension, self-contained Python scripts used to generate, package, and validate the dataset, a validation report, and accompanying documentation provided in a Markdown file.