Multi-haul quasi network flow model for vertical alignment optimization

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.

A 3D Model for Optimizing Infrastructure Costs in Road Design

“…We present below an approximation of the earthwork obtained from the central axis of the road (useful for approaching the optimal alignment) and a more accurate computation, using the parameterization of the road surface given in Section . In both cases, we have not considered material transportation costs (these costs are deeply studied, for example, in Hare et al., or Beiranvand et al., ).…”

“…The design variables depend on the specific problem and on the mathematical (geometric) model. In this sense, works published so far can be classified into three main groups: those focusing on the horizontal alignment (Casal et al., ; Easa and Mehmood, ; Lee et al., ; Mondal et al., ), those centering their attention into the vertical alignment (see Fwa et al., ; Hare et al., , ; Beiranvand et al., ), and those studying both alignments simultaneously (Bosurgi et al., ; Chew et al., ; Hirpa et al., ; Jong and Schonfeld, ; Li et al., ; Shafahi and Bagherian, ). For each of them, the chosen variables depend on the geometric model used to define the layout: within the horizontal alignment it is possible to consider, only main axes (Lee et al., ), axes and circular curves (Hirpa et al., ; Mondal et al., ; Jong and Schonfeld, ; Shafahi and Bagherian, ), or axes, circular curves, and transition curves (Casal et al., ; Kang et al., ); within the vertical alignment, vertical curves may be considered (Jong and Schonfeld, ; Shafahi and Bagherian, ), or may not (Hirpa et al., ).…”

Mountain railway alignment optimization considering geological impacts: A cost‐hazard bi‐objective model

“…In the literature, alignment optimization studies can be classified into horizontal alignment optimizations (e.g., Casal, Santamarina, & Vázquez‐Méndez, 2017; Easa & Mehmood, 2008; Jong, Jha, & Schonfeld, 2000; Mondal, Lucet, & Hare, 2015), vertical alignment optimizations (e.g., Bababeik & Monajjem, 2012; Beiranvand, Hare, Lucet, & Hossain, 2017; Easa, 1988; Monnet, Hare, & Lucet, 2019; Revelle, Whitlach, & Wright, 1996; Xin et al., 2014) and 3‐D alignment optimizations (e.g., Chiou & Yen, 2018; de Smith, 2006; Jha, Schonfeld, & Samanta, 2007; Kang, Schonfeld, & Yang, 2009; E. Kim, Jha, & Son, 2005; Maji & Jha, 2009, 2017; Pushak, Hare, & Lucet, 2016; Um, Choi, & Yang, 2011). Among these, most studies focus on optimizing alignments with cost functions as their objectives.…”

Bi‐objective mountain railway alignment optimization incorporating seismic risk assessment

“…To overcome these problems, researchers have invested considerable efforts into automated alignment optimization methods. Corresponding state‐of‐the‐art studies can be classified into (a) horizontal alignment optimizations, for example: Jong, Jha, and Schonfeld (2000) integrate a geography information system with a genetic algorithm (GA) to solve preliminary highway design problems; Mondal, Lucet, and Hare (2015) solve a horizontal alignment optimization model using two derivative‐free optimization algorithms; Sushma and Maji (2020) propose an algorithm based on customized motion‐planning, which performs flexibly in finding appropriate horizontal alignments; (b) vertical alignment optimizations, for example: Bababeik and Monajjem (2012) use a GA to optimize construction and operating costs of vertical alignments; Beiranvand, Hare, Lucet, and Hossain (2017) design a multihaul quasi‐network flow model to improve the accuracy of vertical alignment optimization processes; Monnet, Hare, and Lucet (2019) extend a mixed integer linear program for modeling the vertical alignment design; and (c) 3D alignment optimizations, for example: de Smith (2006) first applies a distance transform to solve constrained 3D alignment optimizations; Pushak, Hare, and Lucet (2016) compare five discrete algorithms in finding 3D alternative paths to generate potential corridors for railways and roads. Although the effectiveness of these studies in solving their problems has been verified, most of them focus on optimizing alignments in relatively flat regions.…”