As a new attempt to effectively tackle the high-dimensional 0–1 knapsack (01KP) instances with uncorrelated, weakly-correlated, and strongly-correlated characteristics, in this paper, five lately-proposed meta-heuristic algorithms: horse herd optimization algorithm (HOA), gradient-based optimizer (GBO), red fox search optimizer (RFSO), golden eagle optimizer (GEO), and Bonobo optimizer (BO) have been transformed into binary ones by investigating the various V-shaped and S-shaped transfer functions to be applied to those high-dimensional 01KP problems, which are discrete ones; these binary variants are named BHOA, BGEO, BBO, BRFSO, and BBO. Furthermore, some genetic operators such as the one-point crossover operator and mutation operators have been borrowed to discover more permutations as a trying to avoid stuck into local minima for reaching better outcomes. These two operators are effectively integrated with those binary variants to propose other ones with better performance for achieving further improvements for tackling the high-dimensional 01KP instances called BIHOA, BIGEO, BIGBO, BIBO, and BIRFSO. Those genetic operators and recently-developed meta-heuristic algorithms-based high dimensional binary techniques have been extensively validated using 21 uncorrelated, weakly-correlated, and strongly-correlated 01KP instances with high-dimensions ranging between 100 and 10000, and the obtained outcomes were compared even witnessing which algorithm is the best. The experimental findings show the superiority of BIRFSO for the instances with dimensions greater than 500, and its competitivity for the others.