An effective binary dynamic grey wolf optimization algorithm for the 0-1 knapsack problem

Metaheuristic algorithms are recommended and frequently used methods for solving optimization problems. Today, it has been adapted to many challenging problems and its successes have been identified. The grey wolf optimizer (GWO) is one of the most advanced metaheuristics. Because of the advantages it provides, GWO has been applied to solve many different problems. In this study, a new variant of GWO, the Binary Dynamic Grey Wolf Optimizer (BDGWO), is proposed for the solution of binary optimization problems. The main contributions of BDGWO compared to other binary GWO variants are that it uses the XOR bitwise operation to binarize and is based on the dynamic coefficient method developed to determine the effect of the three dominant wolves (alpha, beta, and delta) in the algorithm. BDGWO is a simple, feasible, and successful method that strikes a balance between local search and global search in solving binary optimization problems. To determine the success and accuracy of the proposed BDGWO, it was tested on the 0-1 knapsack problem (0-1 KP), which is classified as an NP-Hard problem. The BDGWO was compared with 17 different binary methods across a total of 55 data sets from three different studies published in the last four years. The Friedman test was applied to interpret the experimental results more easily and to evaluate the algorithm results statistically. As a result of the experiments, it has been proven that the BDGWO is an effective and successful method in accordance with its purpose.