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• The rebalancing operations of bike sharing system are taken under the perspective of entire city. • The characteristics of rebalancing demand are found by using the realistic cycling trip data. • Multiple rebalancing vehicles and time-varying rental costs are considered in the proposed integer programming models. • A chance constraint programming model is proposed to solve the realistic problem. • Different evolutionary mechanisms are considered in our proposed genetic algorithms. Bike-sharing networks have become a carbon-emission and environmentally friendly form of transportation in recent years. However, the asymmetric demand patterns of user behaviour, both temporally and spatially, inevitably lead to an imbalance in the distribution of shared bikes in cities, thereby becoming the greatest obstacle to the networks' development. Based on the real-world data of cycling trips, we analyse the challenging problem of imbalanced bike distribution from the entire-city perspective, establishing that the static rebalancing demand for the whole city is a stochastic variable with multi-scenario characteristics. On this basis, we develop an integer programming model to consider multiple rebalancing vehicles with time-varying rental costs, to alleviate the imbalanced bike distribution, while also analysing the intrinsic properties of such a model. We further propose a chance constraint programming model, optimising a bike-sharing network through the implementation of various genetic algorithms that employ block crossover and variable mutation operators. We reveal the inability of deterministic models in addressing the real-world problem of rebalancing demands for operational bike-sharing. In the meantime, supported with stochastic simulation, we demonstrate that the proposed approach can resolve this problem both effectively and efficiently, ensuring the delivery of a high-level bike-sharing service across an entire metropolitan city. [ABSTRACT FROM AUTHOR]