Research on Knapsack Problem and its Algorithm

Peichi Li ()
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Peichi Li: Stamford American International School Singapore

A chapter in Proceedings of the 2026 11th International Conference on Social Sciences and Economic Development (ICSSED 2026), 2026, pp 387-396 from Springer

Abstract: Abstract Resource allocation and constraint optimization problems are prevalent in real life and engineering, such as loading in logistics transportation, asset portfolio management in financial investment, and task scheduling in computer systems. The knapsack problem is an abstract model of these problems and is widely used to describe optimal choices under limited resource conditions. As one of the classic problems in combinatorial optimization, the knapsack problem not only has significant theoretical research value but also has wide applications in practice. This paper systematically introduces several typical knapsack problems, including the 0–1 knapsack problem, the complete knapsack problem, the two-dimensional knapsack problem. The paper primarily focuses on dynamic programming methods and analyzes the state transition equations and algorithmic approaches for each type of problem in detail. This research helps readers understand the different types of knapsack problems and their algorithmic frameworks, and provides a reference for further exploration of more efficient optimization methods.

Keywords: Knapsack problem; Dynamic programming; Optimization (search for similar items in EconPapers)
Date: 2026
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Persistent link: https://EconPapers.repec.org/RePEc:spr:advbcp:978-94-6239-701-9_40

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DOI: 10.2991/978-94-6239-701-9_40

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