I was curious if there were any new developments in solving the traveling salesman problem using something like a Hopfield recurrent neural network. I feel like I saw something about recent research getting a breakthrough in this, but I can't find the academic papers anywhere. Is anyone aware of any new, novel developments in this area?
This Medium post lists the latest (not a full list of course) studies in the combinatorial optimization domain. All three papers use Deep Reinforcement Learning, which does not need any training set but learns completely from its own experience.
I have been working on the first paper for some time and inference time is on milliseconds level. According to their experiments, the approximation ratio (a metric they use to benchmark their own method) on 1000-1200 test cases reaches to 1.11.
there are many papers on using artificial neural networks to solve TSP including recurrent and Hopfield networks, and they "succeed" in a rough sense, but so far there does not seem to be any evidence that the techniques are in any way (strongly?) superior to other algorithmic approaches, so its something more like a research curiosity at the moment. the use of ANNs for this problem is indeed counterintuitive from the pov of combinatorial algorithmics and the mechanisms by which the problem inputs/ outputs are encoded are novel and tend to vary, and maybe are not yet so standardized. the authors seem maybe more interested in demonstrating "proof of concept" and a comparison with other algorithm types seems more rare (there is some in the last paper). see eg
Traveling salesman problem using neural network techniques / Abdel-Moetty
Comparison of Neural Networks for Solving the Travelling Salesman Problem / La Maire, Mladenov
A Recurrent Neural Network to Traveling Salesman Problem / Siqueira, Scheer, Steiner
I commented this on another answer, but I think it deserves its own answer. Some Google Brain fellows presented a method for solving TSP using an architecture reminiscent of seq2seq in the 2017 paper NEURAL COMBINATORIAL OPTIMIZATION WITH REINFORCEMENT LEARNING. In the introduction, they call out a (1985) paper that uses Hopfield networks to solve TSP. So that idea has been around for a while.
Another answer mentioned the 2015 "Pointer Networks" paper. It did something similar to this paper, but it was a supervised algorithm - it needed labeled data. The 2017 paper doesn't require this (by using negative tour length as a reward signal in a reinforcement learning algorithm).
The heuristic "always bet on neural nets" hasn't let me down (but then again, I've never been through an AI winter).
I don't see any reason to expect Hopfield recurrent neural networks to help with the traveling salesman problem.
Neural networks are a form of machine learning, and they are effective when we have a labelled training set: a bunch of instances, where for each we know the input (the feature vector) and the correct label/classification/output. Machine learning is often useful for finding patterns when we're not sure exactly how to define what the right output is; "we know it when we see it".
In contrast, the traveling salesman problem is a combinatorial problem: we want to know the shortest route through a graph. There's no issue in defining or specifying what the right output is: it's a well-defined mathematical problem. There's no obvious reason to think machine learning would be useful for the traveling salesman problem.