Efficient Method for Estimating Globally Optimal Simple Vertical Curves

This note discusses and details various methods for estimating simple vertical curves that optimally fit observed profile data that have been developed. In 1999, the author developed a linear programming (LP) method for estimating simple vertical curves using LINGO optimization software. To obtain the global optimal solution, the LP formulation was manually solved for different combinations of the 2 unknown nonlinear variables (5 m increments). In 2004, an improved method that automates the iterations using Visual-Basic in Excel Solver was published. The global optimal solution required 10 h for an increment of 0.1 m. This note presents an extension of the previously developed LP formulation that converges to the global optimal solution in 1 minute. The formulation involves no iterations of the nonlinear variables. Instead, the start and end points of the parabolic curve were modeled using 3 binary variables, and the resulting mixed-integer nonlinear model was solved using LINGO global option that has been recently developed. The proposed method, which is applicable to both crest and sag vertical curves, should be of interest to surveying professionals.

• Availability:
  • Find a library where document is available. Order URL: http://worldcat.org/issn/07339453
• Supplemental Notes:
  • Abstract reprinted with permission from ASCE
• Authors:
  • Easa, Said M
• Publication Date: 2008-2

Language

• English

Media Info

• Media Type: Print
• Features: Figures; References; Tables;
• Pagination: pp 33-37
• Serial:
  • Journal of Surveying Engineering
  • Volume: 134
  • Issue Number: 1
  • Publisher: American Society of Civil Engineers
  • ISSN: 0733-9453
  • Serial URL: http://ascelibrary.org/journal/jsued2

Subject/Index Terms

• TRT Terms: Cartography; Curvature; Geodetic surveying; Mapping; Optimization; Route choice; Route surveying; Surveying methods and processes
• Subject Areas: Design; Highways; I20: Design and Planning of Transport Infrastructure;

Filing Info

• Accession Number: 01088934
• Record Type: Publication
• Files: TRIS
• Created Date: Feb 25 2008 2:37PM