Title: Approximating meta-heuristics with homotopic recurrent neural networks,
Abstract: Much combinatorial optimisation problems constitute a non-polynomial (NP)
hard optimisation problem, i.e., they can not be solved in polynomial time. One
such problem is finding the shortest route between two nodes on a graph.
Meta-heuristic algorithms such as $A^{*}$ along with mixed-integer programming
(MIP) methods are often employed for these problems. Our work demonstrates that
it is possible to approximate solutions generated by a meta-heuristic algorithm
using a deep recurrent neural network. We compare different methodologies based
on reinforcement learning (RL) and recurrent neural networks (RNN) to gauge
their respective quality of approximation. We show the viability of recurrent
neural network solutions on a graph that has over 300 nodes and argue that a
sequence-to-sequence network rather than other recurrent networks has improved
approximation quality. Additionally, we argue that homotopy continuation --
that increases chances of hitting an extremum -- further improves the estimate
generated by a vanilla RNN.