使用 Lagrangian Dual Framework 近似求解背包问题
Approximating Solutions to the Knapsack Problem using the Lagrangian Dual Framework
AI总结：
本文基于 Lagrangian Dual Framework 构建神经网络近似求解背包问题，研究输出解释与模型选择，在仅轻微损失最优性的情况下显著增强约束满足。
摘要：
背包问题（Knapsack Problem）是组合优化中的经典问题。求解这些问题在计算上可能代价高昂。近年来，人们越来越关注使用深度学习方法来近似求解此类问题。一个核心问题是如何在预测解中强制或鼓励约束满足。基于 Lagrangian Relaxation（拉格朗日松弛）方法构建的 Lagrangian Dual Framework，是预测约束优化问题解的一种有前景的方法。本文中，我们开发神经网络模型，使用 Lagrangian Dual Framework 近似背包问题的解，同时改善约束满足。我们探讨了在此背景下的输出解释和模型选择问题。实验结果表明，与未显式建模约束的基线神经网络相比，该方法实现了很强的约束满足，而最优性仅有轻微下降。
英文摘要：
The Knapsack Problem is a classic problem in combinatorial optimisation. Solving these problems may be computationally expensive. Recent years have seen a growing interest in the use of deep learning methods to approximate the solutions to such problems. A core problem is how to enforce or encourage constraint satisfaction in predicted solutions. A promising approach for predicting solutions to constrained optimisation problems is the Lagrangian Dual Framework which builds on the method of Lagrangian Relaxation. In this paper we develop neural network models to approximate Knapsack Problem solutions using the Lagrangian Dual Framework while improving constraint satisfaction. We explore the problems of output interpretation and model selection within this context. Experimental results show strong constraint satisfaction with a minor reduction of optimality as compared to a baseline neural network which does not explicitly model the constraints.
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