This paper proposes a Deep Reinforcement Learning (DRL) approach for solving
knapsack problem. The proposed method consists of a state aggregation step
based on tabular reinforcement learning to extract features and construct
states. The state aggregation policy is applied to each problem instance of the
knapsack problem, which is used with Advantage Actor Critic (A2C) algorithm to
train a policy through which the items are sequentially selected at each time
step. The method is a constructive solution approach and the process of
selecting items is repeated until the final solution is obtained. The
experiments show that our approach provides close to optimal solutions for all
tested instances, outperforms the greedy algorithm, and is able to handle
larger instances and more flexible than an existing DRL approach. In addition,
the results demonstrate that the proposed model with the state aggregation
strategy not only gives better solutions but also learns in less timesteps,
than the one without state aggregation.

本文提出了一种基于深度强化学习的解决背包问题的方法，该方法采用状态聚合策略和 Advantage Actor Critic 算法处理背包问题的每个问题实例，在每个时间步骤逐个选择物品，重复选择直到得到最终解决方案，实验表明该方法能够提供接近于最优解的解决方案，且优于贪心算法，而且处理规模更大和更灵活的问题。此外，本文提出的模型不仅提供更好的解决方案，而且在更少的时间步骤内学习，有着良好的表现。