Joint design of transit and bike-sharing systems by multi-objective optimization considering stochastic user equilibrium

Abstract

In this study, we investigate the joint optimization design of transit and bike-sharing systems (JDTB) at the strategic planning level, where the transit network, operating frequencies of transit lines, bike-sharing parking locations, and associated bike deployment numbers are simultaneously determined. Considering that transit and bike-sharing systems are operated by different operators with various objectives, we propose a multi-objective bi-level optimization model to formulate the JDTB problem. The upper-level optimization has two competing objectives: namely, the transit objective to minimize overall costs for both users and the transit operator, and the bike-sharing objective to maximize bike-sharing profits. At the lower level, a stochastic user equilibrium (SUE) assignment model is proposed to capture users’ choice behaviors in integrated transit-bike systems. To achieve more realistic choice behaviors and provide practical and reliable JDTB solutions, this model considers various impact factors on users’ decision-making processes, including congestion and common-line issues in transit systems, bike availability and reuse, as well as multimode combination and transfers in trip chains. Moreover, a diagonalization method combined with an iterative balancing scheme as well as a meta-heuristic algorithm based on NSGA-II are developed to solve the SUE and JDTB problems, respectively. Numerical experiments demonstrate the efficacy of the proposed model and algorithm in achieving trade-off solutions between the interests of transit and bike-sharing operators.