Efficient Active Search for Combinatorial Optimization Problems

André Hottung, Yeong-Dae Kwon, Kevin Tierney

Keywords: heuristic search, combinatorial optimization, learning to optimize, reinforcement learning, traveling salesperson problem, vehicle routing problem, job shop scheduling problem

Abstract: Recently numerous machine learning based methods for combinatorial optimization problems have been proposed that learn to construct solutions in a sequential decision process via reinforcement learning. While these methods can be easily combined with search strategies like sampling and beam search, it is not straightforward to integrate them into a high-level search procedure offering strong search guidance. Bello et al. (2016) propose active search, which adjusts the weights of a (trained) model with respect to a single instance at test time using reinforcement learning. While active search is simple to implement, it is not competitive with state-of-the-art methods because adjusting all model weights for each test instance is very time and memory intensive. Instead of updating all model weights, we propose and evaluate three efficient active search strategies that only update a subset of parameters during the search. The proposed methods offer a simple way to significantly improve the search performance of a given model and outperform state-of-the-art machine learning based methods on combinatorial problems, even surpassing the well-known heuristic solver LKH3 on the capacitated vehicle routing problem. Finally, we show that (efficient) active search enables learned models to effectively solve instances that are much larger than those seen during training.

One-sentence Summary: We propose active search approaches for combinatorial optimization problems that search for solutions by adjusting a subset of (model) parameters to a single instance at test time.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/arxiv:2106.05126/code)