Learning to Control Local Search for Combinatorial Optimization
This work addresses the problem of automating local search algorithm selection for combinatorial optimization, which is incremental as it builds on existing methods but introduces a learned controller.
The paper tackles the challenge of selecting appropriate local search variants for combinatorial optimization problems by formalizing the selection as a Markov Decision Process and training a deep graph neural network controller called NeuroLS. The result is that NeuroLS outperforms both traditional operations research controllers and recent machine learning approaches, as demonstrated by ample experimental evidence.
Combinatorial optimization problems are encountered in many practical contexts such as logistics and production, but exact solutions are particularly difficult to find and usually NP-hard for considerable problem sizes. To compute approximate solutions, a zoo of generic as well as problem-specific variants of local search is commonly used. However, which variant to apply to which particular problem is difficult to decide even for experts. In this paper we identify three independent algorithmic aspects of such local search algorithms and formalize their sequential selection over an optimization process as Markov Decision Process (MDP). We design a deep graph neural network as policy model for this MDP, yielding a learned controller for local search called NeuroLS. Ample experimental evidence shows that NeuroLS is able to outperform both, well-known general purpose local search controllers from Operations Research as well as latest machine learning-based approaches.