Scalable Solution of the Stochastic Multi-path Traveling Salesman Problem via Neural Networks

TL;DR

This paper introduces a neural network-based approach to efficiently solve the stochastic multi-path Traveling Salesman Problem, improving scalability and solution quality in vehicle routing under uncertainty.

Contribution

It proposes integrating neural network surrogate models into a two-stage stochastic programming framework for the multi-path TSP, enhancing computational efficiency.

Findings

Neural network surrogates reduce computation time.

The approach improves solution quality under stochastic travel costs.

Enhanced scalability demonstrated for complex routing problems.

Abstract

The multi-path Traveling Salesman Problem with stochastic travel costs arises in hybrid vehicle routing applications designed for Smart City and City Logistics, where multiple paths exist between each pair of locations. Travel times along these paths are typically affected by real-time traffic conditions and therefore modeled as stochastic. The objective of the problem is to determine a Hamiltonian tour that minimizes the expected total travel cost under uncertainty. In this work, we adopt a two-stage stochastic programming formulation. In the first stage, a predefined route specifying the sequence of locations to be visited is determined, while taking into consideration a second-stage recourse problem that selects the optimal path from the feasible set of alternative paths for each pair of locations, once real-time traffic conditions are realized. To reduce the computational burden imposed by the large number of scenarios required to capture travel time uncertainty, the innovation of this work is the integration of neural network-based surrogate models to approximate the expected value of the second-stage recourse problem. Different architectures and training strategies for the neural networks are proposed and analyzed, with performance evaluated in terms of computation time, solution quality, and generalization capability. Preliminary findings demonstrate the enhanced scalability and practical applicability of the approach for complex vehicle routing problems under uncertainty.