# Multi-Source Data-Driven Terrestrial Multi-Algorithm Fusion Path Planning Technology
## 3 Multi-Objective Path Planning
### Optimization Objectives
They enable dynamic weight adjustment and personalized route planning based on the actual needs of the user and the environment. The definitions and calculation methods for each optimization objective are as follows:  
1. **Path Length** To determine the optimal vehicle route from origin to destination, the total distance of the path serves as a fundamental optimization metric. Given a sequence of path nodes \(p=\{n_{1},n_{2},\ldots,n_{k}\}\), the total path length \(f_{\text{length}}(p)\) is computed as \[f_{\text{length}}(p)=\sum_{i=1}^{k-1}d(n_{i},n_{i+1})\] (6) where \(d(n_{i},n_{i+1})\) denotes the Euclidean or actual road distance between consecutive nodes. This metric forms a core component of the overall cost function used to evaluate and optimize paths. After determining a feasible sequence of waypoints, a genetic algorithm is applied to perform global optimization, aiming to minimize path length while also considering additional criteria such as smoothness and safety. The process involves the following steps:  
* **Population Initialization**: Randomly generate an initial population of \(N\) candidate paths, each representing a full traversal through the predefined waypoints. * **Fitness Evaluation**: Evaluate each path using a composite cost function that integrates the total path length \(f_{\text{length}}(p)\), path smoothness, and proximity to obstacles (safety margin). * **Selection operation**: Retain the top 20% of elite individuals based on fitness scores, and select the remaining 80% via roulette wheel selection to maintain genetic diversity. * **Crossover and Mutation**:
* _Two-point crossover_: Exchange middle segments between pairs of parent paths to create offspring. * _Gaussian mutation_: Apply perturbations to waypoint coordinates with a probability of 5%, promoting the exploration of the solution space. * **Iterative Convergence**: Repeat the evaluation, selection, and variation steps for up to 100 generations or until the fitness standard deviation across the population drops below 0.1%. * **Optimal Solution Output**: The individual with the highest fitness in the final generation is selected as the globally optimized path. By integrating path length as a primary component of the fitness function and employing evolutionary strategies, this approach effectively searches for routes that are not only short, but also smooth and safe for vehicle traversal. 2. **Congestion Length**  
Congested distance is used to measure the length of congested segments along the route, reflecting the traffic flow pressure. The congestion state of each road segment is determined by its congestion label, and the calculation formula is as follows:  
\[f_{\text{congestion}}(p)=\sum_{i=1}^{k-1} \begin{cases}d(n_{i},n_{i+1})&\text{ if congestion}(n_{i},n_{i+1})>0\\ 0&\text{otherwise}\end{cases}  \tag{7}\]  
Here, congestion\((n_{i},n_{i+1})\) represents the congestion label of the edge. A non-zero value indicates that the segment is congested. 3. **Travel Time**  
Total travel time refers to the cumulative time required for the vehicle to complete the entire route, taking into account the traffic speed limits and real-time traffic conditions. Let \(t(n_{i},n_{i+1})\) represent the estimated travel time between nodes \(n_{i}\) and \(n_{i+1}\), then  
\[f_{\text{time}}(p)=\sum_{i=1}^{k-1}\,t(n_{i},n_{i+1  
The risk index is used to measure the potential safety risks along the route, considering factors such as historical accidents, night-time lighting, weather conditions, and public security. The total risk index for the route is calculated as follows:  
\[f_{\text{risk}}(p)=\sum_{i=1}^{k-1}r(n_{i},n_{i+1}) \tag{9}\]  
Here, \(r(n_{i},n_{i+1})\) represents the risk factor value of the edge. A higher value indicates greater safety risk. 5. **Avoidance Zone**  
The avoidance zone index reflects the extent to which the route traverses specific sensitive areas, such as construction zones, accident-prone areas, and restricted zones.