Discrete PSO for Order Batching: A Comparative Study of Binary and Set-Based Solution Representations

Order batching is a key decision problem in warehouse operations, directly affecting order picking efficiency and operational costs. As a combinatorial NP-hard problem, it motivates the use of metaheuristics for large-scale instances. This study evaluates discrete Particle Swarm Optimization (PSO) variants for order batching, focusing on solution representation. Two paradigms are investigated through three variants: the binary representation, instantiated as MBPSO and MBPSOzt, and the structural set-based representation, instantiated as SBPSO. A computational study on benchmark instances compares solution quality and convergence using the number of items picked from selected aisles as the main metric. Results indicate that representation significantly impacts performance. SBPSO consistently outperforms the binary variants on larger instances, demonstrating more stable convergence, while binary variants remain competitive in smaller instances. These findings highlight the importance of representation design in discrete PSO and reinforce the effectiveness of set-based strategies for combinatorial optimization in logistics.