The 0–1 Knapsack problem is a non-deterministic polynomial-time-hard combinatorial optimization problem that cannot be solved in reasonable time using traditional methods. Therefore, researchers have turned to metaheuristic algorithms for their ability to solve several combinatorial problems in a reasonable amount of time. This paper adapts the Kepler optimization algorithm using eight V-shaped and S-shaped transfer functions to create a binary variant called BKOA for solving the 0–1 Knapsack problem. Several experiments were conducted to compare the efficacy of the binary Kepler optimization algorithm to several competing optimizers when solving 20 well-known knapsack instances with dimensions ranging from 4 to 75. The experimental results demonstrate the superiority of this algorithm over other metaheuristic algorithms, except for the genetic algorithm, which is marginally superior. To further improve the binary Kepler optimization algorithm, it is combined with an enhanced improvement strategy to create a new hybrid variant. This hybrid variant, termed HBKOA, has superior exploration and exploitation capabilities that make it better than genetic algorithm and other optimizers for all performance metrics considered. The enhanced improvement strategy is also integrated with several competing optimizers, and the experimental results show that HBKOA, hybrid binary manta ray foraging optimization, and hybrid binary equilibrium optimizer are competitive for small and medium-dimensional instances and superior for the higher dimensions.