  There is a growing interest in integrating machine learning techniques and
optimization to solve challenging optimization problems. In this work, we
propose a deep reinforcement learning methodology for the job shop scheduling
problem (JSSP). The aim is to build up a greedy-like heuristic able to learn on
some distribution of JSSP instances, different in the number of jobs and
machines. The need for fast scheduling methods is well known, and it arises in
many areas, from transportation to healthcare. We model the JSSP as a Markov
Decision Process and then we exploit the efficacy of reinforcement learning to
solve the problem. We adopt an actor-critic scheme, where the action taken by
the agent is influenced by policy considerations on the state-value function.
The procedures are adapted to take into account the challenging nature of JSSP,
where the state and the action space change not only for every instance but
also after each decision. To tackle the variability in the number of jobs and
operations in the input, we modeled the agent using two incident LSTM models, a
special type of deep neural network. Experiments show the algorithm reaches
good solutions in a short time, proving that is possible to generate new greedy
heuristics just from learning-based methodologies. Benchmarks have been
generated in comparison with the commercial solver CPLEX. As expected, the
model can generalize, to some extent, to larger problems or instances
originated by a different distribution from the one used in training.
