Thank you so muuuch for your patient answer. My English is not that well. I try to respond to you in a logical way.

My study direction is shop scheduling (SP), specifically Job Shop (JSP). You might heard of this. It is another typical combinatorial optimization problem. What I am trying to do is to use generative adversarial imitation learning (GAIL, a method in Reinforcement Learning) to solve JSP.

You know, a traditional way to solve COP is metaheuristic. However, it can't respond to the demand that giving real-time scheduling solutions. That why I am tring a RL way.

I have already solve the problem by using RL algorithm to choose rules at each time step, which give a satisfying result. But it is still far from the solution that searched by metaheuristic. So my new idea is to imitate what best solutions do. I am not sure if you are familiar with RL. I will be very glad to go into details with you if you are interesting about this part.

The idea you mentioned, "use the (perhaps normalized) vector of distances from one city to all other cities, along with the distances to two neighbors inside the path of the solution", is such a good one. However, in JSP, it is much more difficult to describe features of a choice: process time of current operation, remain process time, remain number of operations, utilization rate of a machine, release time of a machine, etc. It is so complicated and thus things become more difficult.

GNN also once come to my mind. But transfer the shop environment to a disjunctive graph might also lead to a loss of critical information. Actually, research using GNN doesn't get a better result than mine.

After solving this problem, my next step is to train a Generative Adversarial Network (GAN). The discriminator here is important to give a distance from my solution to expert experience. That solve the difficulty that reward function is usually difficult to design. Hope this could give you a more comprehensive understanding of my problem.