An Evolutionary Hybrid Approach for Solving 0/1 Knapsack Problem Optimally in Polynomial Time using Genetic Algorithms

Abstract

The 0/1 knapsack is a very well known problem and many approaches have been proposed such as dynamic programming and greedy strategy to solve this problem. But 0/1 knapsack problem is a non polynomial time problem. Solving it in a polynomial time is a challenge. It is becoming an important problem because there are many real life applications based on this. Genetic Algorithms have been proved to be a good approach in solving these types of problem and with the help of Genetic Algorithms it will no longer remain a NP problem. There is a problem in the existing approach for solving 0/1 knapsack problem with the help of Genetic Algorithms and with the existing approach the performance is not good. In this thesis a new improved algorithm is proposed which gives better result than the existing algorithm and improves the performance. A number of numerical experiments are performed and the outcome shows how this approach is better than the previous approach of Genetic Algorithm for solving 0/1 Knapsack Problem.0/1 Knapsack problem now no longer remain NP problem and it can be solved optimally in polynomial time.