Knapsack- and Dynamic Programming-Based Symmetric Optimization for Material Multi-Objective Storage

Large-scale composite equipment manufacturing imposes stringent requirements on the lean management of multi-specification fiber prepreg sheet storage, while existing optimization methods suffer from poor process adaptability, insufficient multi-objective collaborative optimization capability, and low space utilization of static layouts. This study constructs a symmetric optimization framework for multi-objective composite sheet storage to address these critical bottlenecks. Specifically, the multi-dimensional process value of fiber sheets is quantified, and the layered storage optimization problem is transformed into a 0–1 knapsack problem with symmetric constraints. An improved Dynamic Programming–Backtracking (DP-BT) material selection algorithm and an adaptive dynamic programming iterative space optimization algorithm are proposed to achieve a symmetric balance of inter-layer space utilization and global optimization. Experimental validation with actual production data of 17 fiber sheet types verifies that the proposed method enables space optimization for specified layer counts to maximize average space utilization, with the rate rising from 79.4% (initial 4-layer layout) to 95.7% (3-layer) and 99.9% (2-layer), and a peak single-layer utilization of 100%. This framework achieves favorable optimization performance in the target production scenario and provides a referenceable symmetric optimization approach for the lean storage management of similar fiber sheet storage scenarios in composite manufacturing.