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

2026-05-14

AI Summary

This study addresses the multi-path traveling salesman problem with stochastic path costs in smart cities by proposing a two-stage stochastic programming approach. In the first stage, the sequence of node visits is determined; in the second stage, once traffic conditions are realized, the optimal path between each pair of consecutive nodes is selected. To mitigate the computational burden induced by a large number of scenarios, the method innovatively integrates neural network surrogate models—encompassing diverse architectures and training strategies—to efficiently approximate the expected second-stage path costs. This is further enhanced by scenario reduction and sample average approximation techniques. Experimental results demonstrate that the proposed framework substantially reduces computational overhead while preserving solution quality and generalization capability, thereby significantly improving the scalability and practical applicability of solving large-scale vehicle routing problems under uncertainty.

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.

Problem

• Stochastic Multi-path Traveling Salesman Problem
• Vehicle Routing
• Smart City
• Stochastic Programming
• Travel Time Uncertainty

Innovation

• neural network surrogate
• two-stage stochastic programming
• multi-path TSP
• stochastic vehicle routing
• scalable optimization