Regret-based multi-objective route choice models and stochastic user equilibrium: a non-compensatory approach

ABSTRACT

Since regret theory has been introduced to model travellers’ route choices, various random regret minimization (RRM) models have been developed for the choice situation of multiple alternatives and multiple attributes. There are two approaches dealing with multi-objective optimisations: one is to combine different attributes into a single additive one and the other is to consider each attribute separately. The existing RRM models adopt the first approach to measure regret. However, travellers might not always trade off attributes in such a compensatory way. In this paper, under the assumption that travellers might consider attributes separately, we develop two new regret-based stochastic user equilibrium (SUE) models by incorporating the RRM model and the hybrid RUM-RRM model into a non-compensatory multi-objective framework. The majority of the second approaches dealing with multiple objectives generally provide a feasible solution set caused by conflicts among objectives. Different from that, the two new models provide probabilistic choice to each route, based on which a single SUE path flow pattern would be attained. Meanwhile, the compromise effect which is widely seen in consumer behaviour can be explained by the two new models. The equivalent variational inequality problems for the proposed models and a path-based algorithm using the method of successive averages have been given. Numerical examples are further conducted to illustrate the properties of the proposed models and the effectiveness of the algorithm.

KEYWORDS:

• Stochastic user equilibrium
• route choice
• regret theory
• multi-objective decision-making
• non-compensatory

Acknowledgements

The authors would like to thank Dr Judith Wang and Dr Hongbo Ye from Institute for Transport Studies, University of Leeds for their helpful comments and criticism. We would also like to thank three anonymous referees for their highly constructive criticism. Any errors or omissions remain the sole responsibility of the authors.

Disclosure statement

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

Notes

1 ‘NC’ represents ‘non-compensatory’, and ‘U’ represents ‘random utility maximisation’. The abbreviations represent the same in $Q_{iw}^{NC-U}$, $Q_{iw,m}^{NC-U}$, $P_{iw}^{NC-U}$ and $O_{iw}^{NC-U}$ to distinguish non-compensatory multi-objective models.

2 ‘R’ represents ‘random regret minimisation’. The abbreviation represents the same in $P_{iw}^{NC-R}$, $P_{iw,m}^{NC-R}$ and $O_{iw}^{NC-R}$.

3 ‘H’ represents ‘hybrid RUM and RRM’. The abbreviation represents the same in $P_{iw}^{NC-H}$ and $O_{iw}^{NC-H}$.

Additional information

Funding

The work described in this paper was jointly supported by research grants from the National Natural Science Foundation of China (grant numbers 71671087, 71571097, 71732003) and the humanities and social sciences project of Anhui, China (grant numbers SK2018A0025).