Combinatorial optimization plays an important role in real-world problem solving. In the big data era, the dimensionality of a combinatorial optimization problem is usually very large, which poses a significant challenge to existing solution methods. In this paper, we examine the generalization capability of a machine learning model for problem reduction on the classic travelling salesman problems (TSP). We demonstrate that our method can greedily remove decision variables from an optimization problem that are predicted not to be part of an optimal solution. More specifically, we investigate our model's capability to generalize on test instances that have not been seen during the training phase. We consider three scenarios where training and test instances are different in terms of: 1) problem characteristics; 2) problem sizes; and 3) problem types. Our experiments show that this machine learning based technique can generalize reasonably well over a wide range of TSP test instances with different characteristics or sizes. While the accuracy of predicting unused variables naturally deteriorates as a test instance is further away from the training set, we observe that even when tested on a different TSP problem variant, the machine learning model still makes useful predictions about which variables can be eliminated without significantly impacting solution quality.
Machine Learning Constructives and Local Searches for the Travelling Salesman Problem
Università della Svizzera Italiana（瑞士意大利语区大学）；Dalle Molle Institute for Artificial Intelligence（达莱莫勒人工智能研究所）；University of Modena and Reggio Emilia（摩德纳-雷焦艾米利亚大学）
Diversity Optimization for Travelling Salesman Problem via Deep Reinforcement Learning
South China University of Technology（华南理工大学）；Singapore Management University（新加坡管理大学）；Massachusetts Institute of Technology（麻省理工学院）；Eindhoven University of Technology（埃因霍温理工大学）
HeatACO: A Heatmap-Guided Max--Min Ant System for Large-Scale Travelling Salesman Problems
Centre for Data Science；Artificial Intelligence \& the School of Engineering；Computer Science, Victoria University of Wellington, Wellington, 6140, New Zealand
Machine Learning-based Two-Stage Graph Sparsification for the Travelling Salesman Problem
Centre for Data Science and Artificial Intelligence（数据科学与人工智能中心）；School of Engineering and Computer Science（工程与计算机科学学院）；Victoria University of Wellington（惠灵顿维多利亚大学）
