## 2 Literature Review
### System Optimization  
Several topics are involved in system optimization: fleet size management, rebalance of shared resources, etc. [PERSON] et al. proposed a multi-periodic optimization formulation to determine the minimum bike fleet size by maximizing the total profits [35]. Sincethat the main topic of system optimization related to this work is rebalance/relocation of shared resources, we mainly review rebalance related literature in this section. Optimizing resource-sharing systems by relocation, which means relocating shared resources (e.g., cars and bikes) to solve the problem of imbalanced distribution of resources and try to make supply meet demand, is mainly discussed. Taking shared bikes as an example, a main principle is to move extra bikes from locations which have a surplus supply of bikes to locations which have a shortage of bikes. Relocation strategies have two primary types: operator-based relocation strategy (see [6; 8; 9; 10; 14; 15]) and user-based relocation strategy (see [1; 5; 7; 36; 37]). Some studies perform joint rebalance strategy by merging them together (see, e.g., [19]). An operator-based relocation strategy means relocation is driven by operators' behavior (e.g., reposition by trucks) and a user-based relocation strategy means relocation is directly driven by users (e.g., design appropriate incentives). In the early stage, the user-based relocation strategy may be sufficient to handle imbalance for the system. When user-based relocation is insufficient, operator-based relocation is applied by using a fleet of trucks to relocate bikes through well-designed routes. [PERSON] et al. solved a static relocation problem and minimized the weighted sum of three factors (inconvenience level of finding an available bike, lost demand and operational time) [38]. [PERSON] et al. proposed a stochastic-dynamic lookahead policy to cope with changing demand patterns [39]. [PERSON] used a Markov decision process to determine the priority of stations where bikes need to be relocated and minimizes the ratio of arrival rate of unsatisfied users who cannot find any bikes to determine the number of relocated bikes at appointed stations [40]. [PERSON] et al. adopted a user-based relocation strategy to increase usage in an electric vehicle sharing system [41]. [PERSON] et al. combined operator-based relocation with user-based relocation, which is called as a hybrid relocation strategy, in a dockless bike-sharing system [42]. Several factors affect the performance of relocation strategy, e.g., region partitioning policy, demand prediction, faulty bikes, etc. Many studies optimize the relocation strategy based on region partitioning, but, usually, the region partitioning results seems to be inefficient due to no well-predefined geographical zones. For example, for irregular areas, inefficient zone partitioning decisions may lead to very large errors in relocation stage. [PERSON] et al. [19] investigated the effects of geographical zone scale on the imbalance estimation of the dockless bike-sharing system and the relocation decisions. Besides, they developed a region decomposition approach to handle large scale instances based on appropriate scales. [PERSON] et al. [17] designed a recurrent neural networks-based real-time rental and return demand prediction approach, which can offer estimated demand information as input parameters for rebalance optimization model. Moreover, sometimes, faulty bikes will lead to infeasibility of relocation strategy [15]. More specificity, all the shared bikes in the system (including faulty ones) are assumed as available inventory if faulty bikes are not considered in the problem; this assumption makes operators fail to estimate the actual real-time supply information and is more likely to result in impractical rebalance decisions. [PERSON] et al. [15] formulated the bike rebalancing problem with faulty bikes and operator-based rebalance policy for dockless bike-sharing systems, where a fleet of heterogeneous trucks, multiple depots and multiple visiting are considered.