Deep learning-driven scheduling algorithm for a single machine problem
  minimizing the total tardiness
Michal Bouška Přemysl Šůcha Antonín Novák Zdeněk Hanzálek
In this paper, we investigate the use of the deep learning method for solving
a well-known NP-hard single machine scheduling problem with the objective of
minimizing the total tardiness. We propose a deep neural network that acts as a
polynomial-time estimator of the criterion value used in a single-pass
scheduling algorithm based on Lawler's decomposition and symmetric
decomposition proposed by Della Croce et al. Essentially, the neural network
guides the algorithm by estimating the best splitting of the problem into
subproblems. The paper also describes a new method for generating the training
data set, which speeds up the training dataset generation and reduces the
average optimality gap of solutions. The experimental results show that our
machine learning-driven approach can efficiently generalize information from
the training phase to significantly larger instances. Even though the instances
used in the training phase have from 75 to 100 jobs, the average optimality gap
on instances with up to 800 jobs is 0.26%, which is almost five times less than
the gap of the state-of-the-art heuristic.