Exploring Heuristic Algorithms For The Knapsack Problem: A Comparative Analysis Of Program Complexity And Computational Efficiency - Info and Reading Options

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<div>Abstract</div><div>The knapsack problem is an optimization problem in computer science which involves determining the most</div><div>valuable combination of items that can be packed into a knapsack (a container) with a limited capacity (weight or</div><div>volume); the goal is to maximize the total profit of the items included in the knapsack without exceeding its capacity.</div><div>This study extensively analyzes the knapsack problem, exploring the application of three prevalent heuristics:</div><div>greedy, dynamic programming, and FPTAS algorithms implemented in Python. The study aims to assess how these</div><div>algorithms perform differently, focusing on program complexity and computational speed. Our main objective is to</div><div>compare these algorithms and determine the most effective one for solving the knapsack problem as well as to be</div><div>chosen by the researchers and developers when dealing similar problem in real-world applications. Our</div><div>methodology involved solving the knapsack problem using the three algorithms within a unified programming</div><div>environment. We conducted experiments using varying input datasets and recorded the time complexities of the</div><div>algorithms in each trial. Additionally, we performed Halstead complexity measurements to derive the volume of</div><div>each algorithm for this study. Subsequently, we compared program complexity in Halstead metrics and</div><div>computational speed for the three approaches. The research findings reveal that the Greedy algorithm demonstrates</div><div>superior computational efficiency compared to both Dynamic Programming (D.P) and FPTAS algorithms across</div><div>various test cases. To advance understanding of the knapsack problem, future research should focus on</div><div>investigating the performance of other programming languages in addressing combinatorial optimization</div><div>problems, which would provide valuable insights into language choice impact. Additionally, integrating parallel</div><div>computing techniques could accelerate solution processes for large-scale problem instances.</div>

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