Abstract:The 0-1 knapsack problem (KP) is a classical NP-hard problem in the field of combinatorial optimization. To overcome the tendency of the deep Q-network (DQN) algorithm to become trapped in local optima and their limited global exploration capability when applied to high-dimensional KP instances, this study proposes an improved Double-DQN algorithm within a multi-agent framework. The algorithm first incorporates an item selection mechanism and a mutation strategy, and then integrates a multi-agent collaborative framework with a monotonic value function decomposition (QMIX) module, thus significantly enhancing solution diversity and global exploration capability. The proposed method is evaluated on five test sets, including 500 0-1 KP instances of varying scales, a multi-knapsack test set containing 50 instances, and a fractional knapsack test set with 50 instances. Experimental results show that 86% of the 0-1 KP instances (429) reach optimal solutions, while the corresponding rates are 84% (42) and 85% (43) for the multi- and fractional knapsack instances, respectively. Comparative experimental results with the Gurobi solver demonstrate that the proposed algorithm exhibits strong stability and effectiveness, fully confirming the feasibility of the improved approach.