# Solving Large-Scale 0-1 Knapsack Problems and its Application to Point Cloud Resampling

## TL;DR

This paper introduces a deep learning-based approach inspired by Lagrange multipliers and game theory to efficiently solve large-scale 0-1 knapsack problems, outperforming existing methods in speed and stability, with applications to point cloud resampling.

## Contribution

The paper proposes a novel deep learning method for large-scale 0-1 knapsack problems, incorporating adaptive gradient ascent for stability, and demonstrates its effectiveness and versatility in applications.

## Key findings

- Solves large-scale benchmark KP instances in under a minute.
- Outperforms existing methods with stable runtime.
- Applicable to point cloud resampling and other tasks.

## Abstract

0-1 knapsack is of fundamental importance in computer science, business, operations research, etc. In this paper, we present a deep learning technique-based method to solve large-scale 0-1 knapsack problems where the number of products (items) is large and/or the values of products are not necessarily predetermined but decided by an external value assignment function during the optimization process. Our solution is greatly inspired by the method of Lagrange multiplier and some recent adoptions of game theory to deep learning. After formally defining our proposed method based on them, we develop an adaptive gradient ascent method to stabilize its optimization process. In our experiments, the presented method solves all the large-scale benchmark KP instances in a minute whereas existing methods show fluctuating runtime. We also show that our method can be used for other applications, including but not limited to the point cloud resampling.