# Multi-Objective Routing and Categorization of Urban Network Segments for Cyclists
## 2 Materials and Methods
### Experiments  
#### 2.3.1 The Study Area  
This study solves a MOOP, finding the best cycling routes between an origin and a destination point in the center of Athens (see Figure 1). The A Posteriori method using multi-objective evolutionary algorithms (MOEAs), specifically the NSGA-II algorithm, is chosen to solve the specific problem. The point of origin (point A) is defined as the intersection between Eratosthenous Street and Vasileos Konstantinou Avenue, specifically the point at the pedestrian crossing on Eratosthenous Street in the direction of Vasileos Konstantinou Avenue. The destination point (point B) is the location of the monument to the Unknown Soldier on the forecourt of the Greek Parliament in Syntagma Square 600 m away from the point of origin.  
Around the points of origin and destination (points A and B), the study area with an area of approximately 430.000 m\({}^{2}\) is defined on the map with the boundaries indicated in Figure 2.  
Within these boundaries, a network is defined with all the elements that are accessible to bicycle users. This includes road segments such as boulevards (Vasileos Konstantinou, Vasilissis Olgas, Amalias, and Vasilissis Sofias) and one-way and two-way streets, pavements, park paths, and a single cycle lane. All of these segments are categorized into road elements, with coding r1 and r2 (which can be boulevards (Vasileos Konstantinou, Vasilissis Olgas, Amalias, and Vasilissis Sofias) and one-way and two-way streets), pavement and footpath elements (such as pavements, park paths, and zebra crossings) with coding p1 and p2 and bicycle lanes with coding b1. The decision points from which the user can move from one accessible element to another are also defined. In the NSGA-II literature, the decision points are called nodes (i, j) and the accessible elements are called links N\({}_{\text{ij,k}}\). Each element N\({}_{\text{ij,k}}\) has a start node i, an end node j, and an attribute code k.  
Figure 1: Points of origin (point A) and destination (point B). Source: Open Street Maps.  
Non-accessible elements are points within parks between designated paths (e.g., between trees and grass) and parks for which public access is not allowed (e.g., the Presidential Palace Garden). It is also worth noting that according to the AASHTO guideline for bicycle infrastructure, which is developed by the American Association of State Highway and Transportation Officials to provide guidance on roadway design and safety standards, a minimum bikeway width of 1.5 m is defined [36]. Therefore, sidewalks measured below the 1.5 m limit are excluded from the study. Figure 3 shows all the nodes (i,j) and links N\({}_{\text{i,j,k}}\).  
Note that the starting node in point A is node 1 and the ending node in point B is node 206. Additionally, in the case where two nodes i and j are connected by more than two links of the same classification (road, pedestrian element, and cycle track),  
p2). It is also noted that in this case, k1 corresponds to the right link in the direction i \(\rightarrow\) j where i < j, and, respectively, k2 corresponds to the left link in the direction i \(\rightarrow\) j where i < j.  
It is worth noting that a link can be used as i, j as well as j, i. For the National Garden, it should be mentioned that it becomes inaccessible after sunset (this is not included in the study). All the links N\({}_{\text{i,j,k}}\) are combined using the NSGA-II. The combinations form routes the number of which creates a set of discrete viable solutions.