# GIS-Based Multi-Objective Routing Approach for Street-Based Sporting-Event Routing
## 2 Methodology
### Routing Framework  
We explored the optimal route of the event track using road-network data built using GIS software. We wrote the path-search algorithm in the C# language in the Grasshopper environment, which is an application-programming interface (API) of Rhinoceros 3D. The framework of the routing and optimization processes according to the order of data processing was as follows:  
1. If the width of the road was less than or equal to the required width of the track, we deleted the data from the route list. 2. If the classification of the road route was bridge or tunnel, we deleted the data from the route list. 3. If there was only one road adjacent to the avoidance facility defined in Section 3.2, we deleted the data from the route list. 4. We deleted completely discontinuous and dead-end roads that did not meet the criteria from the route list. Section 4 outlines the definitions of fully discontinuous and dead-end roads where the criteria were not met. 5. The user inputs a node as the primary base. The event track is a closed path. Hence, a path that starts from the node and returns to it is searched. A routing algorithm randomly explores the path between all pairs of vertices in an edge-weighted directed graph and builds a regression path. If the width of the road exceeded twice the required width of the track, it was recognized as a turnaround route. However, it was not selected as a path if the turn radius of the turn node was not satisfied. 6. We entered all studied regression routes into the GA process. The GAs apply genetic operations, such as population representation, selection, crossover, and mutation, to find optimal results for complex problems [48]. In order to define the optimal outcome, we evaluated the route by entering the weight for each parameter stated in Section 3.2. We then subjected the evaluated routes to genetic operations to create new offspring and find more optimized solutions. 7. The derived optimal-route list was returned in the form of a closed curve. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Category** & **Weight** & **Parameter** & **Value** & **Unit** \\ \hline \multirow{6}{*}{**Level 01**: Route variables—I} & 1.0 & Width of the road (min.) & 12 & M \\ \cline{2-5}  & 1.0 & Pass through intersections & Y & - \\ \cline{2-5}  & 0.0 & Pass through bridges & No & - \\ \cline{2-5}  & 0.0 & Pass through tunnel & No & - \\ \cline{2-5}  & 1.0 & Height obstacle (min.) & 4.5 & M \\ \hline \multirow{6}{*}{**Level 02**: Route variables—II} & 0.5 & Track length & 2.4 & KM \\ \cline{2-5}  & 0.6 & Tolerance range of track length & \(\pm 0.3\) & KM \\ \cline{2-5}  & 0.3 & Number of turns (min.) & 14 & Turns \\ \cline{2-5}  & 0.3 & Number of turns (max.) & 22 & Turns \\ \cline{2-5}  & 0.8 & Radius of turning (min.) & 12 & M \\ \cline{2-5}  & 0.7 & Radius of turning (max.) & 120 & M \\ \cline{2-5}  & 0.7 & Buffer interval length (min.) & 180 & M \\ \hline \multirow{6}{*}{**Level 03**: Environmental variables} & 0.9 & Educational-institution avoidance & \\ \cline{2-5}  & 0.8 & Child- and geriatric-welfare-institution avoidance & \\ \cline{1-1} \cline{2-5}  & 0.8 & Public-institution avoidance & \\ \cline{1-1} \cline{2-5}  & 0.9 & Medical-facility avoidance & \\ \cline{1-1} \cline{2-5}  & 0.9 & Transportation-facility avoidance & \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Priorities for routing. The following are the main formulas of path-search used in this study, and Table 4 presents the symbols used in the formula and their explanations. \(f1\) (Route variables--I) [24]: \(f1\) determines whether the condition is met. If the condition is not met, the route is deleted, and if the condition is met, the route is output as an available route.