Methods to enhance the quality of bi-level origin–destination matrix adjustment process

ABSTRACT

The quality of Origin–Destination matrix (OD) estimation depends on number of factors including the selection of appropriate upper-level function of bi-level formulation, constraints to the OD flows, and suitable solution algorithm. Addressing these aspects, the study first explored different upper-level formulations using two types of traffic information: traffic counts and sub-path flows. Second, it investigated the effects of OD constraints on the quality of solution. Third, it proposed modified genetic algorithm (MGA) to address the computational limitations of traditional genetic algorithm (GA). The study findings were as follows: a) Using symmetric mean absolute percentage error (SMAPE) to match traffic counts showed greater improvements in the OD quality; b) The estimates improved as more number of OD pairs were known to have a-priori knowledge about their flows with higher confidence levels; c) The MGA approach outperformed GA in terms of computational efficiency, and gradient descent (GD) in terms of solution quality.

KEYWORDS:

• OD matrix estimation
• bi-level optimization
• bluetooth
• sub-path flows
• genetic algorithm
• OD structure
• Brisbane

Acknowledgments

The authors are thankful to the Queensland Department of Transport and Main Roads (TMR) and the Queensland University of Technology for supporting this research. The conclusions of this paper reflect understandings of the authors, who are responsible for the accuracy of the research findings.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1. The objective ${\mathrm{c}}_1+\frac{1-\rho \left(\hat{\mathbf{s}},\mathbf{s}\right)}{2}$ in Equations (5)(5) $\underset{\mathbf{x}}{min}\mathrm{Z}\left(\mathbf{x}\right)=\underset{\mathbf{x}}{\mathrm{m}\mathrm{i}\mathrm{n}}\left(\left({\mathrm{c}}_1+\frac{1-\rho \left(\hat{\mathbf{s}},\mathbf{s}\right)}{2}\right)\ast \left({\mathrm{c}}_2+\frac{\mathrm{S}\mathrm{M}\mathrm{A}\mathrm{P}\mathrm{E}\left(\hat{\mathbf{y}},\mathbf{y}\right)}{2}\right)\right)$(5) and (6(6) $\underset{\mathbf{x}}{min}\mathrm{Z}\left(\mathbf{x}\right)=\underset{\mathbf{x}}{\mathrm{m}\mathrm{i}\mathrm{n}}\left(\left({\mathrm{c}}_1+\frac{1-\rho \left(\hat{\mathbf{s}},\mathbf{s}\right)}{2}\right)\ast ({\mathrm{c}}_2+\hat{\mathbf{y}}-\hspace{0.17em}\mathbf{y}\right))2$(6) ) considers any structural differences between the estimated/simulated and observed trip distribution from the perspective of sub-path flows. This acts as a scaling factor to the original traffic count-based objective.

2. Refer to (Behara, Bhaskar, and Chung 2020a)

3. The previous research by Behara, Bhaskar, and Chung (2020c) found that convergence was achieved within 100 iterations for the same study network. Since, Genetic Algorithm is a global search technique; we have considered the fixed number of iterations to be 10 times higher; that is, 1000. We believe for this study 1000 iteration is sufficient. However, for large-scale networks, the convergence criteria should be based on maximum relative change in the elements of estimated OD flows at successive iterations.