Algorithm

Computer science

Mathematical optimization

Reinforcement learning

Mathematics

Travelling salesman problem

Artificial intelligence

Heuristic

Deep learning

Optimization problem

Machine learning

Combinatorial optimization

Knowledge-Based Systems

Traveling salesman and vehicle routing problems with their variants, as classic combinatorial optimization problems, have attracted considerable attention for decades of their theoretical and practical value. Many classic algorithms have been proposed, for example, exact algorithms, heuristic algorithms, solution solvers, etc. Still, due to their complexity, even the most advanced traditional methods require too much computational time or are not well-defined mathematically; algorithm-based decision-making is no exception. Also, these methods cannot be generalized to a larger scale or other similar problems. With the latest developments in machine and deep learning, people believe it is feasible to apply reinforcement learning and other technologies in the decision-making or heuristic for learning combinatorial optimization. In this paper, we first gave an overview on how combinate deep reinforcement learning for the NP-hard combinatorial optimization, emphasizing general optimization problems as data points and exploring the relevant distribution of data used for learning in a given task. We next reviewed state-of-the-art learning techniques related to combinational optimization problems on graphs. Then, we summarized the experimental methods of using reinforcement learning to solve combinatorial optimization problems and analyzed the performance comparison of different algorithms. Lastly, we sorted out the challenges encountered by deep reinforcement learning in solving combinatorial optimization problems and future research directions.

Deep reinforcement learning for transportation network combinatorial optimization: A survey