Approximating meta-heuristics with homotopic recurrent neural networks

TL;DR

This paper demonstrates that deep recurrent neural networks, enhanced with homotopy continuation, can effectively approximate solutions to NP-hard combinatorial problems like shortest path routing, offering an alternative to traditional meta-heuristics.

Contribution

It introduces a novel approach using homotopic recurrent neural networks to approximate meta-heuristic solutions for complex combinatorial optimization problems.

Findings

Sequence-to-sequence RNNs outperform other RNN variants in approximation quality.

Homotopy continuation improves the accuracy of RNN-based solutions.

The method scales to graphs with over 300 nodes.

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.