Moco: A Learnable Meta Optimizer for Combinatorial Optimization

Relevant combinatorial optimization problems (COPs) are often NP-hard. While they have been tackled mainly via handcrafted heuristics in the past, advances in neural networks have motivated the development of general methods to learn heuristics from data. Many approaches utilize a neural network to directly construct a solution, but are limited in further improving based on already constructed solutions at inference time. Our approach, Moco, learns a graph neural network that updates the solution construction procedure based on features extracted from the current search state. This meta training procedure targets the overall best solution found during the search procedure given information such as the search budget. This allows Moco to adapt to varying circumstances such as different computational budgets. Moco is a fully learnable meta optimizer that does not utilize any problem specific local search or decomposition. We test Moco on the Traveling Salesman Problem (TSP) and Maximum Independent Set (MIS) and show that it outperforms other approaches on MIS and is overall competitive on the TSP, especially outperforming related approaches, partially even if they use additional local search.