1. Multi-modal Demand Adjustment in EMME2 Yuri Teleshevsky URS Corporation, New York

2. Presentation Outline Adjustment of demand What is available in EMME2 Multi-class demand adjustment Example of application Efficiency of demand adjustment process Improved multi-class demand adjustment Advantages of this practical approach over “correct” gradient method

3. One-mode Trip Table Adjustment Available in EMME2 Macro:demadj22.mac Article:A gradient approach for the O-D matrix adjustment problem Author:Heinz Spiess Website:http://www.spiess.Ch/emme2/

4. One-mode Trip Table Adjustment Available in EMME2 Some important features of one-mode optimization with “demadj” in emme2: Adjustment based on both link and turn counts. Complete set of control options : Type of assignment Priorities of link count locations Priority of turn count locations Constraints (weights) on OD changes and more …

5. Multi-Modal Sequential Optimization Based on sequential use of standard “Demadj” procedure applied to every mode partial optimization Such sub-sequence of going through all modes comprise a cycle of multi-modal optimization Demadj: AUTO adjustment Demadj: TRUCK adjustment

6. Gradient And Sequential By-coordinate Optimization

7. Sequential By-coordinate Optimization

8. Bronx, NY

9. Study Area

10. Model Highway Network

12. Highway Network With Counts

13. Assigned Auto and Truck Volumes

14. Evaluation of Adjustment Results (1)

15. Evaluation of Adjustment Results (2)

16. Efficiency of Multi-modal Demand Adjustment (1) Major factors: Computer running time Ability to get close to optimum (close approximation to “correct” gradient method Level of deviation from original trip table Additional factor: Ability to control the optimization process

17. Efficiency of Multi-modal Demand Adjustment (2) Practical issues: One step on each one-mode intermediate optimization Run as few cycles as possible Have control outputs of intermediate results (trip tables of all modes and traffic volumes vs. counts by all modes) To address efficiency factors: Ability to get as close to optimum as gradient method Level of deviation from original trip table Ability to control the optimization process

18. Improved Sequential By-coordinate Optimization Within each cycle, do all one-mode optimizations from the same point -- keep the same traffic conditions through the whole cycle After trip tables have been updated for all modes within a cycle, they are all applied together in the next multi-modal assignment Results of the multi-modal assignment give a new starting point for the next cycle of multi- modal optimization This improvement changes a trajectory of sequential optimization (blue) to have both by-coordinate steps within one cycle (Auto and Truck demand updates) start from the same starting point The resultant one step multi-modal descent will be going closely matching a trajectory of “correct” gradient method

19. Balanced Sequential Optimization

20. Evaluation of Balanced Adjustment (1)

21. Evaluation of Adjustment Results (2)

22. Advantages of Sequential Optimization Vs. “Correct” Gradient Method (1) “Correct” multi-criteria optimization: min ga,gt {w a *A[a(g a ),t(g t )] + w a * T [a(g a ),t(g t )] } where A, T – criteria functions for Auto and Truck; w a, w t – coefficients a, t – traffic volumes of Auto and Truck g a, g t – Auto and Truck Demands

23. Advantages of Sequential Optimization Vs. “Correct” Gradient Method (2) “Correct” multi-criteria optimization:  - optimization of combined criterion – usually weighed sum  - the result of each individual criterion is not predictable  - weights do not represent “real” balance between Auto and Truck  - faster than Sequential Method

24. Advantages of Sequential Optimization Vs. “Correct” Gradient Method (3) Sequential by-coordinate optimization: At each cycle, optimization is by one variable only min ga {A[a(g a ), t fix ] } min gt {T[a fix, t(g t )] }

25. Advantages of Sequential Optimization Vs. “Correct” Gradient Method (4) Sequential by-coordinate optimization:  - optimization of each criterion individually  - full control of each criterion optimization  - possibility of minimizing a number of iterations by each criterion (decrease changes to initial trip table)  - slower than “Correct” Gradient Method

26. Advantages of Sequential Optimization Vs. “Correct” Gradient Method (5) Sequential by-coordinate optimization:  - is ready available based on standard EMME2 procedures and simple to implement – you can start using it today

27. THANK YOU