Improved A* algorithm design for container relocation problem in four-way shuttle vehicle-based digital warehousing systems

• Designs a bi-objective optimization model to solve the relocation problem involved in the double-ended outbound process of pallets in the palletized FWSBS/RS scenario. • Integrates Genetic Programming (GP) design rules to improve the A* algorithm for addressing the double-ended relocation problem in outbound operations of the palletized FWSBS/RS with multiple storage areas and pallets groups. • Proposes a dataset generation and algorithm configuration method for the relocation optimization problem in this specific scenario. • Rigorously validates the solution effectiveness of the innovative optimization algorithm through practical experiments. The Container Relocation Problem (CRP) in palletized FWSBS/RS(Four-Way-Shuttle-Based Storage and Retrieval System) presents a new challenge in automated warehousing research, emphasizing the need for effective strategy rules to optimize the movement of pallets within storage areas. This paper innovatively integrates the genetic programming (GP) design rule to improve the A* algorithm for the CRPMG (Container Relocation Problem with Multiple Groups), which involves a palletized FWSBS/RS with multiple storage areas and groups of palletized cargos on both ends. First, a bi-objective optimization model is designed to solve the CRP involved in the double-ended pallets outbound process. This model conforms to a realistic palletized FWSBS/RS scenario and minimizes the operating time of the four-way shuttle while reducing the number of CRP times. The optimal solution is obtained using a Gurobi solver firstly. Then, a set of construction criteria with a scenario-specific solution for the palletized FWSBS/RS is proposed to adapt the genetic programming and generate the relocation rules. This is the first time that genetic programming has been applied to the optimization model of the palletized FWSBS/RS. Numerical experiments demonstrate that the designed bi-objective optimization model and the improved A* algorithm significantly enhance problem-solving performance, offering excellent convergence speed and robustness, thereby proving their effectiveness and feasibility.