A Branch-and-Bound Based Framework for Route Set Generation

1. A Branch-and-Bound Based Framework for Route Set Generation

2. Outline • Motivation and Objective • Background • Generate Realistic Route Set • Summary • Open Questions

3. Outline • Motivation and Objective • Background • Generate Realistic Route Set • Summary • Open Questions

4. Motivation and Objective Path Based Assignment Path Flows instead of Link Flows Detailed Result Stable Result New Question: are the paths “realistic”? What is “realistic”? How to make paths “realistic”? Terminology Route: Consecutive Links Path: Path + Departure Time

5. Outline • Motivation and Objective • Background • Generate Realistic Route Set • Summary • Open Questions

6. Conventional Assignment Process Start Find Free Flow Shortest Path Path Flow Set Network Loading Converge? Find Congested Shortest Path End A Done! B

7. Existing Approaches for Route Generation Additional Approach

8. Outline • Motivation and Objective • Background • Generate Realistic Route Set • Summary • Open Questions

9. What is a Realistic Route (Set)? Route that travelers are willing to use “Subjective” Not Operative “Objective” and Operative Definition Coverage Rate Estimation Quality But the definition of “realistic” route *is* subjective No Physical Rules Solution: Ask “What is an unrealistic route?” Use Intuition Formalize the Rules The Rules are called Constraints Subtraction Approach

10. Branch-and-Bound Branch: systematically enumerate all paths Bound: eliminate unrealistic paths

11. Non-Cyclic Constraint No Cycle in Route

12. Detour Constraint No Excessive Detour Detour Factor = Path Length / Shortest Path Length

13. (Local) Detour Constraint

14. Turn Constraint Without C(8,4) = 70 C(18, 9) = 48620 C(38, 19) = 35345263800 With e.g. max_turn = 1 NNNNEEEE ENENENEN EEEENNNN

15. Other Constraints How to identify new constraints? Use Intuition Researcher Expert Opinion Survey

16. Road Hierarchy Distance Matters

17. Road Hierarchy Aware Enumeration Determine Access and Egress Point Generate Sub-routes from origin to Access Point Generate Sub-routes from Egress point to Destination Generate Sub-routes from Access Point to Egress Point Concatenate Sub-routes

18. Choice Set Composition Choice Set vs Route Set Post Process Individual Avaibility/Perception Overall Quality Control

19. Outline • Motivation and Objective • Background • Generate Realistic Route Set • Summary • Open Questions

20. Summary Subtraction Instead of Addition. Non-cyclic Constraint Detour Constraint Turn Constraint Others...(Use the intuition, Luke) Road Hierarchy Aware Enumeration Composition Start OD Pair Grouping Constraints RH Aware Enumeration Enumeration Composition End Overall Framework Route Set Generation

21. Constrained Path Based Assignment Start Start Find Free Flow Shortest Path Route Enumeration Path Flow Set Path Flow Set Network Loading Network Loading Converge? Find Congested Shortest Path Find Constrained Shortest Path End End Path Based Assignment Constrained Path Based Assignment Converge?

22. Thank You! xiongyaohua@gmail.com and

23. Open Question With a given link impedance definition CPBA is not necessarily achieve equilibrium.(shortest path will not be considered due to constraints) Equilibrium Assumption is True Constraints are Valid Why? → The impedance has latent factors which are not took into account in the current definition? A B