# Multi-Haul Quasi Network Flow Model for Vertical Alignment Optimization

## TL;DR

This paper introduces the multi-haul quasi network flow (MH-QNF) model for vertical road alignment optimization, significantly improving accuracy, robustness, and computational efficiency over existing models.

## Contribution

The paper presents a novel MH-QNF model that enhances the accuracy and speed of vertical alignment optimization compared to previous models.

## Key findings

- MH-QNF solves over 93% of test problems with less than 1% error.
- MH-QNF is approximately 8 times faster than the CTG model.
- The model outperforms existing state-of-the-art models in robustness and efficiency.

## Abstract

The vertical alignment optimization problem for road design aims to generate a vertical alignment of a new road with a minimum cost, while satisfying safety and design constraints. We present a new model called multi-haul quasi network flow (MH-QNF) for vertical alignment optimization that improves the accuracy and reliability of previous mixed integer linear programming models. We evaluate the performance of the new model compared to two state-of-the-art models in the field: the complete transportation graph (CTG) and the quasi network flow (QNF) models. The numerical results show that, within a 1% relative error, the proposed model is robust and solves more than 93% of test problems compared to 82% for the CTG and none for the QNF. Moreover, the MH-QNF model solves the problems approximately 8 times faster than the CTG model.