Application of Black hole Algorithm for Solving Knapsack problems

Abstract

This paper investigates the application of the Black Hole algorithm (BH) for solving 0–1 knapsack problems. Knapsack problem is a classic and famous problem for testing and analyzing the behavior of optimization and meta-heuristic algorithms. There is no single algorithm which is suitable for all types of the knapsack problem. So it is an open research area to sole knapsack problem using novel optimization algorithms efficiently. BH algorithm is one of the most recent nature-inspired algorithms that is inspired by the black hole phenomenon. Similar to other population-based algorithms, the black hole algorithm starts with an initial population of candidate solutions to an optimization problem and an objective function that is calculated for them. At each iteration of the Black hole algorithm, the best candidate is selected to be the black hole, and others called stars. If a star gets too close to the black hole, it will be swallowed by the black hole and is gone forever. Computational experiments with a set of large-scale instances show that the Black hole algorithm can be an efficient alternative for solving 0–1 knapsack problems. The results show that BH algorithm can find high quality solutions in less time compared to similar meta-heuristic approaches. Based on the obtained results it is clear that BH algorithm is a stable algorithm as the standard deviation of finding solutions in different runs is smaller than other test algorithms.