Pareto routing and scheduling of dynamic urban rail transit services with multi-objective cross entropy method

Document Type

Journal Article

Publication Date


Subject Area

mode - rail, mode - tram/light rail, place - asia, place - urban, economics - operating costs, operations - scheduling, ridership - demand, planning - methods, planning - network design, planning - service improvement


Transit network, Energy consumption, Multi-objective optimization, Cross-entropy method, Pareto optimal


This paper presents a Pareto optimization framework for routing and scheduling dynamic rail transit network services. We first develop an event-based dynamic transit network model that can capture the evolution of passenger demand and service operations with incorporation of passengers’ transfers and recirculation of limited number of train vehicles over different service lines. A multi-objective optimizer is then built upon the transit model which seeks jointly the settings of service lines and schedules that could minimize passengers’ journey times, transfer rates, and operator’s cost. The problem is solved by a cross-entropy method (CEM) which samples potential solutions from statistically tractable distribution models with iterative updates via maximum likelihood. The operational constraints are explicitly incorporated in the solution process which enhances the feasibility of the sampled solutions and hence effectiveness of the computational process compared with other metaheuristics used in the literature. A CEM-based ranking algorithm is further developed for deriving the Pareto-frontiers for the multi-objective transit network routing and scheduling. The proposed framework is applied and tested on the Hong Kong Light Rail Transit (LRT) network using real world scenario data. The results reveal new insights on how the existing operational settings could be improved. The present study contributes to urban transit network service planning with advanced computational techniques.


Permission to publish the abstract has been given by Elsevier, copyright remains with them.


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