Analyzing The Most Effective Algorithm For Knapsack Problems

Knapsack problem is a classical optimization problem in computer science and programming. Knapsack problem main objective is to solve how much the maximum profit can be carried with the knapsack maximum capacity. The item has its own weight and profit. In this paper, we research which algorithm is most effective in solving the 0/1 knapsack and the fractional knapsack problem. The algorithm used for this research is brute force, greedy, dynamic programming, and branch and bound algorithm. Those algorithms will be tested on both knapsack problems, using several datasets on each problem. The program used to execute the algorithm is Python programming language. The results from this research are the dynamic programming has 100% success rate on both problem, the brute force has 100% success rate on the 0/1 knapsack however it only has 20% success rate on the fractional knapsack problem, the greedy algorithm surprisingly has 100% success rate on the fractional knapsack problem and 60% success rate on the 0/1 knapsack problem, and the branch and bound algorithm has 100% success rate on the fractional knapsack while has 0% success rate on the 0/1 knapsack problem. This research also considered the time complexity of each algorithm to make the conclusion. Graphs are provided for better visualization on the results.