# Visualization of Emergency Evacuation Physical Behavior under Multi-Agent Decision-Making
## 3 Model Design Methodology
### Multi-Agent Design Based on Decision Theory
#### 3.2.2 Behavioral Decision-Making Model
Incremental search is the reuse of information from previous searches to achieve efficient search, significantly reducing the scope and time of the search, exemplified by the _LPA\({}^{*}\)_, \(D^{*}\)_Lite algorithms, etc. Among the traditional path planning algorithms, the implementation principles and application scope of the various algorithms vary considerably, as shown in Table 1 for a comparative distinction between five typical algorithms (_Dijkstra_, \(A^{*}\), _D\({}^{*}\), _LPA\({}^{*}\)_, _D\({}^{*}\)Lite_) in terms of search principles and application scope, etc. The positive and negative search directions are mostly related to the ability to handle dynamic planning; heuristic search offers an increase in time performance and avoids global blind search; incremental search represents a secondary use of iterative information and is mostly used to improve the efficiency of the algorithm. To this end, this study designed this behavior using the \(A^{*}\) algorithm to find the global path to the target point. The \(A^{*}\) algorithm searches for a minimum cost path in the discrete space, i.e., it calculates the position corresponding to the minimum value of the cost function \(F=G+H\) in each iteration. In the \(A^{*}\) algorithm, the estimation function \(H\) from the current position to the target position is crucial, and it directly affects whether the final path is optimal or not. To achieve the rapidity and path optimization of the algorithm, this study divides the estimation function into two parts: one is the shortest distance cost \(H_{D}\) for the current position of the intelligent body to reach the target, and the other is the choice preference cost \(H_{P}\) for the intelligence body, and the formula for \(H^{P}\) is Equation (10). \[H_{D}=\chi\times\sqrt{\left(x_{s}-x_{g}\right)^{2}+\left(y_{s}-y_{g}\right)^{2}} \tag{10}\]  
where \(\chi\) is the depletion per unit distance and (\(x_{s}\),\(y_{s}\)), (\(x_{g}\),\(y_{g}\)) are the starting and ending points of the intelligence, respectively. \(H_{D}\) can meet the requirements if there are no obstacles in the environment or the terrain is relatively simple. The crowd behavior is complex, however, and the environment in which the intelligent body is located, its behavior pattern, internal state, and walking direction should be considered in path selection. If the calculated path is far from the actual one by determining the evaluation function only, this study proposes the preference cost \(H_{P}\) for compensation. It can be expressed as Equation (11). \[H_{P}=\sum_{i=1}^{n}\gamma_{i}\times\omega_{i} \tag{11}\]  
where \(\gamma\) denotes the preference factor and \(\omega\) denotes the preference weight. Only the influence of current motion direction and previous direction, current direction and target direction, and channel width on the path cost function when passing through a narrow \begin{table}
\begin{tabular}{c c c c c} \hline
**Algorithm** & **Search Direction** & **Heuristic** & **Incremental** & **Scope of Application** \\ \hline Dijkstra & Positive Search & No & No & Global information known, static planning \\ \(A^{*}\) & Forward Search & Yes & No & Global information known, static planning \\ \(D^{*}\) & Reverse Search & No & Yes & Partial information known, dynamic planning \\ _LPA\({}^{*}\)_ & Forward Search & No & Yes & Some information is known, assume the rest \\  & & & & is free to access, dynamic planning \\ \(D^{*}\)_Lite_ & Reverse Search & Yes & Yes & Partial information known, assume remaining \\  & & & & free access, dynamic planning \\ \hline \end{tabular}
\end{table} 
Table 1: Comparison of five typical algorithms for path planning in terms of search principles and scope of application. channel are considered in this paper. The corresponding preference factors \(\gamma_{1}\), \(\gamma_{2}\), \(\gamma_{3}\) are calculated by Equations (12), (13), and (14), respectively.