Solving Large 0–1 Multidimensional Knapsack Problems by a New Simplified Binary Artificial Fish Swarm Algorithm

Abstract

The artificial fish swarm algorithm has recently been emerged in continuous global optimization. It uses points of a population in space to identify the position of fish in the school. Many real-world optimization problems are described by 0–1 multidimensional knapsack problems that are NP-hard. In the last decades, several exact as well as heuristic methods have been proposed for solving these problems. In this paper, a new simplified binary version of the artificial fish swarm algorithm is presented, where a point/fish is represented by a binary string of 0/1 bits. Trial points are created by using crossover and mutation in the different fish behavior that are randomly selected by using two user defined probability values. In order to make the points feasible, the presented algorithm uses a random heuristic drop-item procedure followed by an add-item procedure aiming to increase the profit throughout the adding of more items in the knapsack. A cyclic reinitialization of 50 % of the population, and a simple local search that allows the progress of a small percentage of points towards optimality and after that refines the best point in the population greatly improve the quality of the solutions. The presented method is tested on a set of benchmark instances and a comparison with other methods available in literature is shown. The comparison shows that the proposed method can be an alternative method for solving these problems.