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Metaheuristic optimization algorithms are typically used to solve some complex optimization problems including nonconvex and nonlinear ones, which generally cannot be well solved by conventional mathematical methods. Although the solution generated by heuristic algorithms may not be equal to the exact optimal one, it is generally acceptable for real world engineering optimization problems. Therefore, heuristic optimization algorithms have gained considerable interests during the past few decades (Abualigah et al., 2021; Hashim & Hussien, 2022). Several excellent representatives include genetic algorithm (GA) (Holland, 1992), particle swarm optimization (PSO) (Kennedy & Eberhart, 1995), differential evolution (DE) (G. Wang et al., 2022), grey wolf optimizer (GWO) (Nadimi-Shahraki et al., 2022), harmony search (HS) (Abarajithan & Vijayarani, 2022), ant colony optimization (ACO) (Dorigo & Gambardella, 1997), and bat algorithm (BA) (X. Yang, 2010; Akila & Christe, 2022).
Nearly all heuristic optimization algorithms proposed at the beginning are devoted to solving continuous variable optimization problems. However, many optimization problems in reality have discrete binary search space such as feature selection (El-Kenawy et al., 2022), 0–1 knapsack problem (Du et al., 2023), and unit commitment problem (Reddy et al., 2018). Therefore, some binary optimization algorithms are proposed according to their corresponding continuous versions to deal with binary optimization problems. For example, a sine cosine hybrid optimization algorithm with modified whale optimization algorithm (SCMWOA) was proposed by El-Kenawy et al. (2022). Its aim was to take advantage of WOA and SCA to solve problems with continuous and binary decision variables. An artificial algae algorithm's binary version (Turkoglu et al., 2022) was put forward to solve optimal attribute set for classification algorithms. A new binary multi-objective grey wolf optimizer was applied to dimensionality reduction problem in classification by Al-Tashi et al. (2020). By comparing and analyzing eight transfer functions including V-shaped and S-shaped, a binary quilibrium optimization algorithm was proposed by Abdel-Basset et al. (2021). A novel binary DE algorithm based on Taper-shaped transfer function (He et al., 2022) was proposed for solving knapsack problem and uncapacitated facility location problem. Besides, several other binary algorithms were proposed (Hichem et al., 2022; Pashaei & Pashaei, 2022; Usman et al., 2022) to solve feature selection problems. Although binary algorithms are proposed on the basis of continuous ones, there exist essential differences between them. Particularly, a transfer function is always required to map continuous space to a binary one in binary algorithm.