DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems

Ruizhong Qiu, Zhiqing Sun, Yiming Yang

Keywords: Combinatorial Optimization, Graph Neural Network, Meta Learning, Traveling Salesman Problem (TSP), Minimum Indepedent Set (MIS)

Abstract: Recently, deep reinforcement learning (DRL) models have shown promising results in solving NP-hard Combinatorial Optimization (CO) problems. However, most DRL solvers can only scale to a few hundreds of nodes for combinatorial optimization problems on graphs, such as the Traveling Salesman Problem (TSP). This paper addresses the scalability challenge in large-scale combinatorial optimization by proposing a novel approach, namely, DIMES. Unlike previous DRL methods which suffer from costly autoregressive decoding or iterative refinements of discrete solutions, DIMES introduces a compact continuous space for parameterizing the underlying distribution of candidate solutions. Such a continuous space allows stable REINFORCE-based training and fine-tuning via massively parallel sampling. We further propose a meta-learning framework to enable the effective initialization of model parameters in the fine-tuning stage. Extensive experiments show that DIMES outperforms recent DRL-based methods on large benchmark datasets for Traveling Salesman Problems and Maximal Independent Set problems.

TL;DR: We proposed a differentiable meta solver that is able to solve large-scale combinatorial optimization problems (e.g., TSP and MIS) effectively and efficiently.