工程科学与技术 (Jul 2025)
Research on Stacking Distribution of Steel Plates Input Based on Improved Multi-objective Particle Swarm Optimization
Abstract
ObjectiveDifferent from the basic layout of traditional automated three-dimensional warehouses, steel plate goods are often stacked in the automated storage and retrieval system (AS/RS) rather than stored on high-rise shelves. This difference renders the classic AS/RS storage allocation model and job scheduling strategy inapplicable in steel plate warehouses. This study analyzes the overall warehouse layout and operational flow, proposes a multi-objective optimization model, and designs an efficient multi-objective algorithm to address the problem.Methods Based on the actual demand of the principle of priority in warehouse delivery, the principle of stacking safety, the principle of minimum stacking amount, and the principle of inventory balance, three indices were proposed: warehouse delivery efficiency, plate and stack difference, and inventory balance. First, warehouse delivery efficiency was one of the important indicators utilized to measure the palletizing plan. Since the warehouse served production purposes and was based on the principle of efficiency priority, the steel plate delivery time was minimized as much as possible. The influencing factors were primarily determined by the equipment operation mode and the palletizing position. Second, in order to ensure the stability of steel plate stacking and reduce the frequency of stacking, the steel plate and stacking position were assigned characteristic indices based on length, width, and item number to classify the steel plate and stacking type and to establish the difference degree index of plate stacking. The inventory balance index was established based on the standard deviation of the number of steel plates allocated to each reservoir to fully mobilize and balance material storage resources during operation. These three indices were utilized to evaluate the degree of stack allocation and served as the objective function to establish a multi-objective decision optimization model for the stack allocation problem of steel plates. This problem was classified as a Type A packing problem with constraints. In addition, when multiple conflicting optimization objectives were present, it was difficult to construct a single mathematical model and apply traditional analytic algorithms to solve it. A multi-objective particle swarm optimization algorithm (PCDMOPSO) based on species clustering degree was designed to solve this model using the concept of Pareto dominance and the classical particle swarm optimization algorithm. The algorithm adopted convergence and diversity of the solution as basic requirements and used the species clustering degree mechanism to monitor and adjust the algorithm's cognitive parameters and the evolution state of particles in real time. Convergence and diversity of solutions were adaptively adjusted, and a local search strategy was introduced to improve the diversity of the Pareto solution set distribution in the external archive after population updates. Then, the crowding distance strategy was utilized to maintain the external archive. The improved algorithm addressed problems such as high dependence on parameter setting, unstable solving efficiency, and a tendency to fall into local optimality.Results and DiscussionsThe automatic steel plate warehouse of a steel structure intelligent processing and manufacturing base was taken as the research object to verify the practical performance of PCDMOPSO in solving the steel plate loading and palletizing problem. Parameters and data under actual working conditions were used for simulation. The simulation results showed that compared to the classical multi-objective algorithms NSGA‒Ⅱ, MOEA/D‒DE, and MOPSO, PCDMOPSO demonstrated clear advantages in optimization ability for each target under different storage scales. Although NSGA‒Ⅱ achieved a better minimum value than PCDMOPSO in the index of the difference degree of plate and stack in 20 tests, PCDMOPSO showed stronger overall optimization ability. However, the difference was slight. Since the output of the multi-objective algorithm was a Pareto solution set, four indices, uniformity, convergence, diversity, and dominance, were selected to evaluate the distribution in the solution space and to compare the solution results of each algorithm. Among the convergence indices, NSGA‒Ⅱ yielded slightly better results than PCDMOPSO with small batch data scales. However, as batch size increased, the mean and variance of the S value obtained by PCDMOPSO significantly outperformed the other algorithms. PCDMOPSO showed clear advantages in the remaining three indicators, demonstrating high solving efficiency under varying input data as well as strong adaptability and robustness. The distribution of Pareto solution sets from different algorithms further illustrated these conclusions. Then, to verify the feasibility of the improved strategy in the proposed multi-objective particle swarm optimization algorithm, a comparative test of the algorithm improvement strategy was conducted. The Levy flight speed update mode, which served as the core of the improvement, and the local search strategy of the external archive were removed separately. The simulation was conducted using a small-batch data scale that best fit the actual production requirements of the steel sheet stock warehouse. The algorithm without the Levy flight speed update strategy exhibited significantly reduced convergence, while the algorithm without the local search strategy showed a marked reduction in diversity. The evaluation indices solved by the improved algorithm were optimized to varying degrees. Finally, the stacking situations before and after optimization were compared. Compared to the traditional stacking method used before optimization, the optimized stacking distribution scheme improved by 19.35%, 4.97%, and 62.23% under the three objectives, respectively, indicating a more significant optimization effect.ConclusionsBased on the actual demand of enterprises for optimizing automatic steel plate warehouse loading decisions, the PCDMOPSO algorithm has demonstrated good performance in the simulation test of solving the stack allocation model. The results indicate that the levy flight update strategy and the local search strategy are significant for maintaining population diversity and assisting in escaping local optima, respectively. The proposed improvement measures have an apparent positive effect on the quality of the solution. In addition, satisfactory solutions can be obtained for warehousing tasks of different scales, and the quality of the output Pareto solution set is obviously superior to that of the traditional algorithm. This effectively meets the practical requirements of various evaluation indicators in the steel plate warehousing problem and provides a valuable reference for research in the same field. It also provides strong decision support for pallet distribution and warehouse management of steel plate goods in the AS/RS.
