# Solving the Urban Transit Routing Problem Using a Cat Swarm Optimization-Based Algorithm
## 4 Computational Results
### Considering the Provider's Operational Cost  
The provider's operational cost is considered in this section by investigating to what extent the total length of all routes affects it. Of course, the smaller the total length of all routes, the bigger the profit for transport companies. As mentioned (see Section 1), [PERSON] and [PERSON] (2018) proposed a method of balancing costs between the customer and the provider, admitting a fourth term \(F_{\delta}(r)\) in the evaluation function (Equation (8)). In this contribution, we adopt the same method using the same values for the coefficients for calculating the term \(F_{\delta}(r)\) (see Table 3). Score \(F_{\delta}(r)\) is summed in an analogous way to the rest of the \(F_{i}\) scores (\(FIT(r)=\ \omega_{1}\cdot F_{1}(r)+\ \omega_{2}\cdot F_{2}(r)+\ \omega_{3}\cdot F_{3}(r)+ \omega_{4}\cdot F_{4}(r)\)). The \(\omega_{4}\) weight is set equal to 1. As seen in Section 3.1.3, the \(K_{i}\) values are the maximum values that the respective \(F_{i}\) scores can obtain. Thus, we can modify \(K_{i}\) values to put analogous emphasis on a specific score. We can reach the same goal by changing the values of weights \(\omega_{i}\) too. When considering score \(F_{\delta}(r)\), one can clearly realize the multi-objective nature of the applied algorithm. As mentioned above, score \(F_{\delta}(r)\) is mainly affected by the total length of the entire route set, which clearly affects operational costs, for example, average fuel consumption, and introduces in the evaluation function the service provider's point of view. Since the value of \(F_{\delta}(r)\) increases as the total route set length decreases,\(F_{\delta}(r)\) is competing with the other \(F_{i}\) scores. Computational experiments show that if the algorithm's parameter values are properly chosen, the algorithm can succeed in constructing route sets that balance the conflicting goals (passenger's demands vs. operational costs). In order to obtain optimal results from the passengers' scope and be able to have a fair comparison of the algorithm's performance with other methods reported in the literature, the weight value of \(F_{\delta}(r)\) was set to 0 (operational cost not taken into account) in all experimental results presented in Sections 4.1 and 4.2. In Tables 17 and 18, the evaluation and comparison of route sets constructed by the proposed CSO algorithm and the approach by [PERSON] and [PERSON] (2018) is made considering the following criteria (in order of significance):  
1. Total length (\(L_{tot}\)) in minutes of each route set, which should be as small as possible. 2. Unsatisfied travel requirements (\(d_{unsatt}\)), which should be as small as possible and ideally 0%. 3. Average travelling time per user (\(att\)), which should be as small as possible. 4. Percentage of travels with zero transfers (\(d_{0}\)), which should be as large as possible and ideally 100%. Note that in this case, the agents that remain active during the execution of the algorithm were initially picked according to their fitness value (see Section 3.2), and the refinement phase (see Section 3.2) is not activated. In the first set of experiments, parameter \(K_{\delta}\) was set to 10, while \(x_{\delta m}\) varies from 20 to 200 min. In Table 17, we present the average values of all evaluation criteria. Both algorithms were executed for 100 Monte Carlo runs, the number of routes equals 4, and the maximum number of nodes is restricted to 8. As can be seen from Table 17, the approach of the CSO algorithm produces in all cases better results according to the criteria set forth above. The cost for the transmission system provider is about 72.9% on average when compared to the corresponding costs generated by the approach of (2018). The volatility of \(L_{tot}\) values is much smaller than the corresponding volatility displayed at (2018). This means that we