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Metaheuristic algorithms are nature-inspired heuristic techniques designed to find suitable solutions by exploring the solution space in a broader and more flexible manner than classical optimization methods. These algorithms are specifically engineered to reach global optimal solutions for complex problems characterized by high dimensionality, multimodality, or discrete or continuous structures. They typically rely on stochastic processes and offer general search strategies that are not problem

The knapsack problem is a classic combinatorial optimization problem that models decision-making processes aimed at maximizing benefit under limited resources. It derives its name from the metaphor of packing the most valuable items into a bag with a fixed carrying capacity. The problem first gained attention in 1957 through the work of M. D. Weingartner and was later formalized mathematically in the 1960s through research by George Dantzig on linear programming.Problem DefinitionThe knapsack pr