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Inverse optimization with endogenous arrival time constraints to calibrate the household activity pattern problem

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  • Chow, Joseph Y.J.
  • Recker, Will W.

Abstract

A parameter estimation method is proposed for calibrating the household activity pattern problem so that it can be used as a disaggregate, activity-based analog of the traffic assignment problem for activity-based travel forecasting. Inverse optimization is proposed for estimating parameters of the household activity pattern problem such that the observed behavior is optimal, the patterns can be replicated, and the distribution of the parameters is consistent. In order to fit the model to both the sequencing of activities and the arrival times to those activities, an inverse problem is formulated as a mixed integer linear programming problem such that coefficients of the objectives are jointly estimated along with the goal arrival times to the activities. The formulation is designed to be structurally similar to the equivalent problems defined by Ahuja and Orlin and can be solved exactly with a cutting plane algorithm. The concept of a unique invariant common prior is used to regularize the estimation method, and proven to converge using the Method of Successive Averages. The inverse model is tested on sample households from the 2001 California Household Travel Survey and results indicate a significant improvement over the standard inverse problem in the literature as well as baseline prescriptive models that do not make use of sample data for calibration. Although, not unexpectedly, the estimated optimization model by itself is a relatively poor forecasting model, it may be used in determining responses of a population to spatio-temporal scenarios where revealed preference data is absent.

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  • Chow, Joseph Y.J. & Recker, Will W., 2012. "Inverse optimization with endogenous arrival time constraints to calibrate the household activity pattern problem," Transportation Research Part B: Methodological, Elsevier, vol. 46(3), pages 463-479.
    • Handle: RePEc:eee:transb:v:46:y:2012:i:3:p:463-479
    DOI: 10.1016/j.trb.2011.11.005
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    2. Chan, Timothy C.Y. & Lee, Taewoo, 2018. "Trade-off preservation in inverse multi-objective convex optimization," European Journal of Operational Research, Elsevier, vol. 270(1), pages 25-39.
    3. Hong, Sung-Pil & Kim, Kyung min & Byeon, Geunyeong & Min, Yun-Hong, 2017. "A method to directly derive taste heterogeneity of travellers’ route choice in public transport from observed routes," Transportation Research Part B: Methodological, Elsevier, vol. 95(C), pages 41-52.
    4. Ghobadi, Kimia & Mahmoudzadeh, Houra, 2021. "Inferring linear feasible regions using inverse optimization," European Journal of Operational Research, Elsevier, vol. 290(3), pages 829-843.
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    6. Xiao Fu & William H. K. Lam, 2018. "Modelling joint activity-travel pattern scheduling problem in multi-modal transit networks," Transportation, Springer, vol. 45(1), pages 23-49, January.
    7. Xu, Zhiheng & Kang, Jee Eun & Chen, Roger, 2018. "A random utility based estimation framework for the household activity pattern problem," Transportation Research Part A: Policy and Practice, Elsevier, vol. 114(PB), pages 321-337.
    8. He, Brian Yueshuai & Zhou, Jinkai & Ma, Ziyi & Wang, Ding & Sha, Di & Lee, Mina & Chow, Joseph Y.J. & Ozbay, Kaan, 2021. "A validated multi-agent simulation test bed to evaluate congestion pricing policies on population segments by time-of-day in New York City," Transport Policy, Elsevier, vol. 101(C), pages 145-161.
    9. Mahmoud Javanmardi & Mehran Fasihozaman Langerudi & Ramin Shabanpour & Abolfazl Mohammadian, 2016. "An optimization approach to resolve activity scheduling conflicts in ADAPTS activity-based model," Transportation, Springer, vol. 43(6), pages 1023-1039, November.
    10. Yashar Khayati & Jee Eun Kang & Mark Karwan & Chase Murray, 2021. "Household Activity Pattern Problem with Autonomous Vehicles," Networks and Spatial Economics, Springer, vol. 21(3), pages 609-637, September.
    11. Jee Eun Kang & Will Recker, 2015. "Strategic Hydrogen Refueling Station Locations with Scheduling and Routing Considerations of Individual Vehicles," Transportation Science, INFORMS, vol. 49(4), pages 767-783, November.
    12. Kang, Jee Eun & Chow, Joseph Y.J. & Recker, Will W., 2013. "On activity-based network design problems," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 398-418.
    13. Li Ping Gan & Will Recker, 2013. "Stochastic Preplanned Household Activity Pattern Problem with Uncertain Activity Participation (SHAPP)," Transportation Science, INFORMS, vol. 47(3), pages 439-454, August.
    14. Liu, Xintao & Yan, Wai Yeung & Chow, Joseph Y.J., 2015. "Time-geographic relationships between vector fields of activity patterns and transport systems," Journal of Transport Geography, Elsevier, vol. 42(C), pages 22-33.
    15. Susan Jia Xu & Mehdi Nourinejad & Xuebo Lai & Joseph Y. J. Chow, 2018. "Network Learning via Multiagent Inverse Transportation Problems," Service Science, INFORMS, vol. 52(6), pages 1347-1364, December.
    16. Chow, Joseph Y.J. & Ritchie, Stephen G. & Jeong, Kyungsoo, 2014. "Nonlinear inverse optimization for parameter estimation of commodity-vehicle-decoupled freight assignment," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 67(C), pages 71-91.
    17. Xiyuan Ren & Joseph Y. J. Chow & Prateek Bansal, 2023. "Estimating a k-modal nonparametric mixed logit model with market-level data," Papers 2309.13159, arXiv.org, revised Aug 2024.
    18. Chan, Timothy C.Y. & Kaw, Neal, 2020. "Inverse optimization for the recovery of constraint parameters," European Journal of Operational Research, Elsevier, vol. 282(2), pages 415-427.
    19. Ren, Xiyuan & Chow, Joseph Y.J., 2022. "A random-utility-consistent machine learning method to estimate agents’ joint activity scheduling choice from a ubiquitous data set," Transportation Research Part B: Methodological, Elsevier, vol. 166(C), pages 396-418.
    20. Timothy C. Y. Chan & Taewoo Lee & Daria Terekhov, 2019. "Inverse Optimization: Closed-Form Solutions, Geometry, and Goodness of Fit," Management Science, INFORMS, vol. 65(3), pages 1115-1135, March.

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