Hierarchical Decomposition Framework for Steiner Tree Packing Problem

Hanbum Ko, Minu Kim, Han-Seul Jeong, Sunghoon Hong, Deunsol Yoon, Youngjoon Park, Woohyung Lim, Honglak Lee, Moontae Lee, Kanghoon Lee, Sungbin Lim, Sungryull Sohn

Abstract: In this paper, we address the complex combinatorial optimization (CO) challenge of efficiently connecting objects at minimal cost, specifically within the context of the Steiner Tree Packing Problem (STPP). Traditional methods often involve subdividing the problem into multiple Steiner Tree Problems (STP) and solving them in parallel. However, this approach can fail to provide feasible solutions. To overcome this limitation, we introduce a novel hierarchical combinatorial optimizer (HCO) that applies an iterative process of dividing and solving sub-problems. HCO reduces the search space and boosts the chances of getting feasible solutions. This paper proposes for the first time a learning-based approaches to address STPP, introducing an iterative decomposition method, HCO. Our experiments demonstrate that HCO outperforms existing learning-based methods in terms of feasibility and the quality of solutions, and showing better training efficiency and generalization performance than prev