<p>Transfer function plays a crucial role in discretizing metaheuristic algorithms to solve combinatorial optimization problems. However, existing transfer functions not only have few classes, but their design methods also rely too much on the curve shape. Kepler optimization algorithm (KOA) is a novel metaheuristic algorithm that performs well in solving optimization problems on continuous domains, but cannot be directly applied to solve combinatorial optimization problems on discrete domains. In order to design more transfer functions and solve combinatorial optimization problems by KOA, this paper first proposes a practical method to construct transfer functions. From this, two new classes of transfer functions are given: A-shaped transfer functions and B-shaped transfer functions. Then, based on the transfer function, the first discrete Kepler optimization algorithm (DKOA) suitable for binary optimization problems is proposed. To verify the practicality of the new transfer functions and the efficiency of DKOA, DKOA is used to solve 0–1 knapsack problem and knapsack problem with a single continuous variable, respectively. Comparison with existing transfer functions and the state-of-the-art metaheuristic algorithms for solving these two problems shows that DKOA using A-shaped and B-shaped transfer functions is more competitive in terms of the ability to obtain optimal solutions, average performance and stability. This shows that the proposed new transfer functions are very practical, and the DKOA based on them is an effective metaheuristic algorithm for solving binary optimization problems.</p>