Reinforcement learning-assisted multi-layered binary exponential distribution optimizer for 0–1 knapsack problem

The 0–1 knapsack problem (0-1KP) is a well-known discrete combinatorial optimization problem with various applications across multiple fields. Compared with traditional methods, metaheuristic algorithms show higher efficiency and flexibility in solving the 0-1KP and thus have received widespread attention. Exponential distribution optimizer (EDO) is a mathematically inspired optimization algorithm that successfully solves continuous complex optimization problems. However, extending its capabilities to discrete problems and enhancing its local search ability remain significant challenges. Hence, we propose a novel binary EDO with a reinforcement learning-driven multi-layered mechanism (RMBEDO) to address the 0-1KP. Specifically, the S-shaped, U-shaped, Z-shaped, V-shaped, X-shaped, and Taper-shaped transfer functions are employed to map continuous values into binary ones. To tackle capacity constraints, a repair mechanism is adopted to fix infeasible solutions and improve feasible solutions. Furthermore, collaborating with two novel single-example learning models and a med-point example learning model using reinforcement learning, a novel reinforcement learning-driven multi-layered mechanism is proposed to enhance the algorithm’s local search capability. RMBEDO is validated on 0–1KP datasets. The effect of six types of transfer functions on the performance of the proposed binary algorithm is examined in depth. Then, the effectiveness of two mechanisms for EDO is verified, and the results exhibit that these mechanisms can effectively boost the algorithm’s performance. Finally, RMBEDO is compared with some well-known algorithms, and the comparative findings illustrate that it is more effective in solving 0-1KPs than existing algorithms.