# Multi-Source Data-Driven Terrestrial Multi-Algorithm Fusion Path Planning Technology
## 3 Multi-Objective Path Planning
### Optimization Objectives  
In this study, the weighted sum method (WSM) is adopted as the core multi-criteria decision-making (MCDM) approach for multi-objective route planning. WSM offers a clear structure and ease of implementation, along with strong robustness to fluctuations in weight assignments, making it well-suited for the demands of dynamically changing traffic scenarios. In contrast, other mainstream MCDM methods, such as the multiplicative aggregation method, may introduce distortions due to nonlinear interactions among objectives. Similarly, while the technique for order preference by similarity to an ideal solution (TOPSIS) performs well in ranking alternatives, it suffers from high computational complexity and normalization bias in high-dimensional dynamic path optimization problems. Considering algorithmic efficiency, controllability, and adaptability to real-world applications, WSM remains the most suitable choice for this research. The multi-objective route planning problem formulated in this study seeks to minimize a composite optimization function \(F_{\text{total}}(p)\), which consists of a set of weighted objective functions. A route \(p\) is defined as a sequential path of nodes \(p=(n_{1},n_{2},\dots,n_{k})\) from the origin to the destination, where each pair of adjacent nodes \((n_{i},n_{i+1})\) is connected by an edge in the graph \(G\). The objective function is composed of multiple weight factors and normalized objective metrics. Each weight dynamically varies according to the travel scenario to reflect the diversity and adaptability of user requirements. To ensure comparability among different objectives, all terms are normalized using a common formula. The final mathematical formulation of the optimization objective is expressed as follows:  
\[ \begin{split}\min_{p}\ F_{\text{total}}(p)&=\alpha(t )\cdot f_{\text{length}}(p)+\beta(t)\cdot f_{\text{congestion}}(p)+\gamma(t) \cdot f_{\text{time}}(p)\\ &\quad+\epsilon(t)\cdot f_{\text{risk}}(p)+\eta(t)\cdot f_{\text {avoidance}}(p)\end{split}  \tag{3}\]  
As summarized in Table 2, the objective functions and their descriptions are as follows:  
To ensure the feasibility and safety of the generated routes, the following formulation defines the set of constraints for the optimization problem: \begin{table}
\begin{tabular}{l l} \hline \hline
**Objective Function** & **Description** \\ \hline \(f_{\text{length}}(p)\) & Total Travel Distance \\ \(f_{\text{congestion}}(p)\) & Cumulative Length of Congested Segments \\ \(f_{\text{time}}(p)\) & Total Travel Time \\ \(f_{\text{risk}}(p)\) & Cumulative Risk Value of the Route \\ \(f_{\text{avoidance}}(p)\) & Degree of Route Penetration into Avoidance Zones \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Objective functions and their corresponding descriptions. \[ \begin{split} f_{\text{time}}(p)\leq T_{\text{max}}\\ f_{\text{congestion}}(p)\leq C_{\text{max}}\\ f_{\text{risk}}(p)\leq R_{\text{max}}\\ f_{\text{avoidzone}}(p)\leq A_{\text{max}}\end{split}  \tag{4}\]  
Here, \(T_{\text{max}}\), \(C_{\text{max}}\), \(R_{\text{max}}\), \(A_{\text{max}}\) denote the maximum tolerable thresholds for travel time, congestion, risk, and avoidance zone exposure, respectively. These thresholds are imposed to prevent the selected route from deviating beyond the bounds of safety and feasibility: In addition, the constraints on the decision variables within the optimization problem are defined as follows:  
\[\forall i\in\{1,2,\ldots,k-1\},\ (n_{i},n_{i+1})\in E \tag{5}\]  
That is, each pair of adjacent nodes in the route must be connected by a valid edge in the graph \(G\) to ensure the physical accessibility of the path within the actual road network. This study selects five key optimization objectives: total distance, congested distance, travel time, risk index, and avoidance zone. These objectives collectively reflect the multi-dimensional performance of travel routes in terms of efficiency, safety, and driving preferences.