DIMES: A Differentiable Meta Solver for Combinatorial Optimization Problems
About
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.
Related benchmarks
| Task | Dataset | Result | Rank | |
|---|---|---|---|---|
| Traveling Salesman Problem | TSP-500 (test) | Gap1.76 | 85 | |
| Maximum Independent Set | ER [700-800] | Solution Size42.06 | 48 | |
| Traveling Salesperson Problem | TSP-100 | Solution Length7.7617 | 42 | |
| Traveling Salesman Problem | TSP-1000 (test) | Optimality Gap2.46 | 36 | |
| Traveling Salesman Problem | TSP-500 | Solution Length16.87 | 32 | |
| Traveling Salesperson Problem | TSP-1k | Solution Length23.73 | 31 | |
| Maximum Independent Set | SATLIB | MIS Size423.3 | 23 | |
| Traveling Salesman Problem | TSP 1000 | Objective Value23.69 | 20 | |
| Traveling Salesman Problem | TSP-10000 (test) | Solution Length74.06 | 17 | |
| Traveling Salesperson Problem | TSP N=1000 Generalization (128 instances) | Optimality Gap17.69 | 14 |