2021/07/05 by Jaeseung Lee, Woojin Choi, Lee, Jaeseung +3
Computer Science · Decision Sciences · #Artificial Intelligence (cs.AI) #Computational Geometry (cs.CG) #Constraint Satisfaction and Optimization #FOS: Computer and information sciences #Metaheuristic Optimization Algorithms Research #Scheduling and Timetabling Solutions
paper · pdf · doi:10.48550/arxiv.2107.01759
openalex publication_date 2021/07/05 · openalex created_date 2023/04/19 · openalex updated_date 2026/07/28
Combinatorial optimization problems (COPs) are an important research topic in various fields. In recent times, there have been many attempts to solve COPs using deep learning-based approaches. We propose a novel neural network model that solves COPs involving geometry based on self-attention and a new attention mechanism. The proposed model is designed such that the model efficiently learns point-to-point relationships in COPs involving geometry using self-attention in the encoder. We propose efficient input and output sequence ordering methods that reduce ambiguities such that the model learns the sequences more regularly and effectively. Geometric COPs involve geometric requirements that need to be satisfied. In the decoder, a new masking scheme using domain knowledge is proposed to provide a high penalty when the geometric requirement of the problem is not satisfied. The proposed neural net is a flexible framework that can be applied to various COPs involving geometry. We conduct experiments to demonstrate the effectiveness of the proposed model for three COPs involving geometry: Delaunay triangulation, convex hull, and the planar Traveling Salesman problem. Our experimental results show that the proposed model exhibits competitive performance in finding approximate solutions for solving these problems.