# Road Passenger Load Probability Prediction and Path Optimization Based on Taxi Trajectory Big Data
## 4 Methods and Models
### Taxi Passenger-Seeking Route Recommendation Model  
Based on the known node and route information, a reasonable customer-seeking scheme is developed while satisfying the regional supply-demand ratio and the maximum distance of customer-seeking. The following assumptions are also made in this study when developing the passenger search program:  
**Assumption 1**. : _If a passenger is encountered on the road during the process of passenger-seeking, it will go to the passenger's destination and will no longer go to the passenger-carrying hotspot._  
**Assumption 2**. : _The speed of the taxi remains unchanged during the passenger-seeking process, ignoring traffic jams, bad weather, and other situations. Since the research object of this paper is cruising taxis, the waiting time window problem is not considered._  
**Assumption 3**. : _The hotspot nodes in the passenger search program have known location coordinates before passenger search, and the passage time and road conditions of the roads at each node are known._  
**Assumption 4**. : _The passenger search scheme does not consider the case of carpooling, i.e., the successful passenger search immediately goes to the designated destination of the passenger._  
**Assumption 5**. : _Taxi drivers have the qualification of transport hubs to carry passengers and can go to the city's transport hubs to carry passengers at any time._  
**Assumption 6**. : _Taxi passenger-seeking recommended locations for straight-line distances of 20 km from the taxi, which are effective. However, straight-line distances of more than 20 km for taxis do not have a significant recommended passenger-seeking effect._  
**Assumption 7**. : _Taxis visit each passenger-seeking hotspot 1 time and do not need to go back to the starting point, looking for passengers during one cruise from the starting point to the end point._  
Figure 6: Prediction model of road passenger load probability based on _BiLSTM_ model. In the process of passenger searching, the primary goal of taxi drivers is to increase the probability of finding passengers and reduce empty running time, with the secondary goal being the shortest path distance [35; 36]. Therefore, when optimizing the path for passenger searching, it is not sufficient to simply consider time, distance, or cost. Instead, it is necessary to comprehensively consider factors such as the probability of finding passengers on the roads and the time required to make a reasonable decision for taxi drivers' passenger searching paths. Therefore, this paper takes the probability of finding passengers as the primary objective for path optimization and considers the shortest distance as the secondary objective. The following passenger searching path optimization model is established in this paper:  
\[Z_{1}=\max\sum_{i,j\in V}w_{ij}q_{ij} \tag{7}\]  
\[Z_{2}=\min\sum_{i,j\in V}w_{ij}d_{ij} \tag{8}\]  
\[\sum_{j=1}^{n}d_{ij}-\sum_{j=1}^{n}d_{ji}=0 \tag{9}\]  
\[\sum_{j=1}^{n}w_{ij}-\sum_{j=1}^{n}w_{ji}=0 \tag{10}\]  
\[\sum_{i=1}^{n}y_{ij}=1,\forall i,j\in V \tag{11}\]  
\[w_{ij}=0 or1 \tag{12}\]  
\[d_{ij}\leq 48 \tag{13}\]  
where the taxi driver passenger-seeking path optimization problem can be represented as a complete graph \(G=(V,A)\); \(V=\{1,2,3\cdots n\}\) denotes the set of passenger-carrying hotspot nodes; and \(A=\{i,j\|i,j\in V,i\
eq j\}\) denotes the set of arcs. \(d_{ij}\) denotes the Manhattan distance between hotspots, and \(q_{ij}\) denotes the probability of carrying a passenger. Manhattan distance [37] is a path between two location points from the start point to the end point with only two directions and non-opposite directions. The objective function (1) represents maximizing the probability of a taxi driver carrying a passenger on the road; the objective function (2) represents the passenger-seeking distance from the starting point to the end point.