Joint travel problem in space–time multi-state supernetworks

Abstract

Joint travel problem (JTP) is an extension of the classic shortest path problem and relevant to shared mobility. A pioneering endeavor via supernetwork framework has been put forward to model two-person JTP. However, it was only addressed in the static context and with the assumption of zero waiting disutility, which resulted in no or weak synchronization among the travelers. This paper proposes a space-time multi-state supernetwork framework to address JTP for conducting one joint activity in the timedependent context. Space-time synchronization and various choice facets related to joint travel are captured systematically. Two-person JTP is first discussed in a uni-modal transport network, and further extended to incorporate multi-modal and multi-person respectively. Stage-wise recursive formulations are proposed to find the optimal joint paths. It is found that JTP is a variant of Steiner tree problem by reduction and the number of meeting/departing points has no impact on the run-time complexity in space-time multistate supernetworks.

Space–time prism bounds of activity programs: a goal-directed search in multi-state supernetworks

“…Pioneering efforts have been dedicated to the STPs of multimodal public transport (e.g. O'Sullivan et al 2000) and multiple persons (e. g. Neutens et al 2008, Liao et al 2013b, 2017b. Relying on the extendibility of multi-state supernetworks, activity-travel choice facets related to private-public trip chains, ICT use, and household interactions can be readily embodied, which enhances the behavioral realism of STP models.…”

A household optimum utility approach for modeling joint activity-travel choices in congested road networks

“…For instance, Meister et al (2005) propose a genetic algorithm to generate household daily schedules. Liao et al (2013b); Liao (2019) use a multistate supernetwork approach, which converts the activity-travel scheduling problem into a shortest path-inding problem, to model joint travel decisions in a multi-modal system. Their proposed supernetwork for modeling joint travel is lied on the earlier comprehensive work of the same authors on scheduling individual activitytravel choices (see e.g., Liao et al (2013a); Liao (2016)).…”

Tolerance-based strategies for extending the column generation algorithm to the bounded rational dynamic user equilibrium problem

“…In the dynamic context, time-dependent paths with the minimum disutility can be found by dynamic programming ( Dean, 2004;Liao, 2017 ). When the newly generated path p with disutility c rs p ( k, f n ) satisfying Eq.…”