BE-GWO: Binary extremum-based grey wolf optimizer for discrete optimization problems

Since most metaheuristic algorithms for continuous search space have been developed, a number of transfer functions have been proposed including S-shaped, V-shaped, linear, U-shaped, and X-shaped to convert the continuous solution to the binary one. However, most existing transfer functions do not provide exploration and exploitation required to solve complex discrete problems. Thus, in this study, an improved binary GWO named extremum-based GWO (BE-GWO) algorithm is introduced. The proposed algorithm proposes a new cosine transfer function (CTF) to convert the continuous GWO to the binary form and then introduces an extremum (Ex) search strategy to improve the efficiency of converted binary solutions. The performance of the BE-GWO was evaluated through solving two binary optimization problems, the feature selection and the 0-1 multidimensional knapsack problem (MKP). The results of feature selection problems were compared with several well-known binary metaheuristic algorithms such as BPSO, BGSA, BitABC, bALO, bGWO, BDA, BSSA, and BinABC. Moreover, the results were compared with four versions of the binary GWO, the binary PSO, and the binary ABC. In addition, the BE-GWO algorithm was evaluated to solve the 0-1 MKP with difficult and very difficult benchmark instances and the results were compared with several binary GWO variants. The results of two binary problems were statistically analyzed by the Friedman test. The experimental results showed that the proposed BE-GWO algorithm enhances the performance of binary GWO in terms of solution accuracy, convergence speed, exploration, and balancing between exploration and exploitation.