A Study on Solving Knapsack Problem by Deep Reinforcement Learning

Abstract

In recent years, with the development of machine learning, there has been an increase in research on the application of deep reinforcement learning to optimization problems. In this study, we applied reinforcement learning (Actor-Critic) and Pointer network to solving the Knapsack problem used in cryptography, and applied reinforcement learning (Actor-Critic) and Pointer network to solving the TSP. We propose a method for solving the trapdoor (Knapsack problem) of the Knapsack cipher based on the work of Google Brain, which applied reinforcement learning (Actor-Critic) and the Pointer network to solve the TSP. Specifically, we solve random, hyper-accretive, and modulo hyper-accretive trapdoors, obtain exact solutions, and compare the results with the LLL algorithm. The results showed that both problems can be solved up to 30 dimensions, and the LLL algorithm was more accurate than the LLL algorithm for some problems, but the LLL algorithm was basically better for higher dimensions and lower densities.