Quadratic Bounded Knapsack Problem Solving with Particle Swarm Optimization and Golden Eagle Optimization

Abstract

Optimization problems are the most interesting problems to discuss in mathematics. Optimization is used to modeling problems in various field to achieve the effectiveness and efficiency of the desired target. One of the optimization problems that are often encountered in everyday life is the selection and packaging of items with limited media or knapsack to get maximum profit. This problem is well-known as knapsack problem. There are various types of knapsack problems, one of them is quadratic bounded knapsack problem. In this paper, the authors proposed a old and new algorithm, which is Particle Swarm Optimization (PSO) and Golden Eagle Optimization (GEO). Furthermore, the implementation of the proposed algorithm, PSO is compared to the GEO. Based on the results of this study, PSO algorithm performs better and produces the best solution than the GEO algorithm on all data used. The advantage obtained by the PSO algorithm is better and in accordance with the knapsack capacity. In addition, although the convergent iteration of the PSO takes longer time than GEO with the same number of iterations, GEO is able to find better solutions faster and able to escape from the local optimum. However, the computation time required by the PSO algorithm is faster than the GEO algorithm.