## 6 Results
Additionally, for a fair comparison between COA and other approaches from literature, one would have to also take into account the costs required for obtaining said information about the users. Therefore, comparing COA to other approaches from literature seems to be not possible without an extensive study on suitability values of users or a complex simulation of users based on various assumptions that can heavily influence the outcome of such a comparison. First, we want to show how the quality of incumbent solutions develops as the number of user interactions increases during a COA run. For this purpose, we calculate the optimality gap for a solution \(x\) obtained from COA as \(\text{gap}=100\%\cdot\left(f(x_{\text{opt}})-f(x)\right)/f(x_{\text{opt}})\). Figure 5 shows the average optimality gaps of solutions to each of our benchmark sets against the interaction levels \(\psi\). The results are grouped by \(\sigma_{v}\) and \(\sigma_{r}\) to additionally compare instances groups with similar user behavior. Recall that the number of attraction points is the same for all EVC and CSS instances. Therefore, for instances with a higher number of users, it is generally easier to find better solutions as there are more users that prefer the same locations. The plots show that, in all cases, solutions generally improve quickly with an increasing interaction level, and close to optimal solutions can be obtained well before identifying all the users' relevant locations. Specifically, at a user interaction level of 50%, the solutions generated by COA feature optimality gaps of 1.45% on average. An exception of this observation are the MAN instances with \(b=30\%\). For these, generated solutions do not reach an optimality gap below 1% before \(\psi=80\%\), on average. Moreover, the figure also shows that the solutions to MAN instances generally converge notably slower than the solutions to EVC and CSS instances. This behavior is likely caused by the weaker correlation of user preferences in  
Figure 5: Development of average optimality gaps with an increasing number of user interactions for each benchmark instance set. the MAN instances and the way that the FC generates scenarios presented to the users, specifically the aspect that locations important to the individual users are tried to be identified first. Locations important to individual users might not necessarily be the best locations to add to a solution, especially if there is a lower number of users with similar preferences. Consequently, the strategies based on which scenarios are generated may still have some room for improvement for such cases. Instead of primarily identifying locations important to users, targeting locations in relation to the current best solution with a higher emphasis might be a more expedient approach here. Note that an increased number of user interactions does not only imply a larger trainings set for the surrogate function but also results in better upper bounds \(w_{r,r}^{\text{UB}}\) for locations \(v\in V\) w.r.t. to an SPR \(r\in R\). Therefore, to gain a better understanding of how much the surrogate function actually contributes to finding an optimized solution, we study what happens when the learning surrogate suitability function \(\tilde{w}_{\Theta}\) is replaced by the naive function with no learning capabilities  
\[\tilde{w}_{\text{bl}}(r,v)= \begin{cases}w_{r,v}&\text{if }(r,v)\in K\\ 0&\text{else.}\end{cases}  \tag{21}\]  
In the following, we refer to our original COA implementation with the surrogate function \(\tilde{w}_{\Theta}\) as \(\text{COA}[\tilde{w}_{\Theta}]\) and denote the implementation with the naive function \(\tilde{w}_{\text{bl}}\) as \(\text{COA}[\tilde{w}_{\text{bl}}]\). A comparison between \(\text{COA}[\tilde{w}_{\Theta}]\) and \(\text{COA}[\tilde{w}_{\text{bl}}]\) is shown in Table 2. Each table cell shows the average optimality gaps of solutions to the respective instance group at the specified interaction levels \(\psi\).