## 4 Case Study: The Disposal in Finland
The solution r2q1 captures the reference point well since they coincide with respect to other objectives than the objectives (1) and (5) which are better than the reference values. Thus, the decision maker is willing to continue with the solution r2q1 as the current solution \(\mathbf{f}_{2}\). Iteration 3. The long operation time of the encapsulation facility (the objective (6)) is still under the microscope at the third iteration but the decision-maker is tempted by the short central tunnel appeared in the previous iteration and combines the long operation time with small disposal facility area. Like the first reference point, also this is unachievable. The solution obtained by using \(q=2\) (r3q2) is shown in green and the solution obtained with \(q=8\) (r3q8) is shown in orange in Figure 3(a). Figure 3(b) illustrates that the solution r3q2 yields a schedule with an early starting date and the disposal takes the longest time while the solution r3q8 starts the disposal later but it is performed faster as seen in Figure 3(c). The solution r3q8 yields almost ideal value for the costs, and we can deduce that in order to achieve lower costs we have to give up in the objectives related to the storage capacity and times. Moreover, the disposal ends rather late. For the current solution \(\mathbf{f}_{3}\) the decision-maker selects the solution r3q8 due to the low costs and small disposal facility area. Figure 2: Results for the iteration 1. Since one motivation for this research was to take into account more goals than just the costs, we are eager to see what happens if we omit the costs and solve the problem with only the first eight objectives (1)-(8). The reference point 3' is similar to the reference point 3 without the value for the costs. The results with \(q=2\) (r3'q2) and \(q=8\) (r3'q8) are given in Figure 5. Note that since there  
Figure 4: Results for the iteration 3. Figure 3: Results for the iteration 2.  
are now only eight objectives, the scalarized function is different than in the case of nine objectives. The solutions in Figure 5 are quite similar and there is less variation than in the solutions in Figure 3(a). Iteration 4. The current solution \(f_{3}\) has high interim storage capacity and a small amount of canisters. At the fourth iteration, the decision maker is interested in to see if the opposite is possible, namely a solution with small interim storage capacity with allowing the higher number of canisters. Again, the reference point is unachievable. In Figure 5(a), the reference point 4 and the solutions with \(q=4\) (r4q4) and \(q=9\) (r4q9) are illustrated. The solutions are shown in green and orange, respectively. Again, the corresponding disposal schedules are given in Figures 5(b),c. As we see, the solution r4q4 satisfies the wishes towards the interim storage capacity as well as the utilization of the empty canister positions quite well. Additionally, the better values than the reference are obtained in the repository area related goals and the costs. The solution r4q9 express this as well, but the original wishes towards the interim storage capacity are not satisfied. Since the solution r4q4 captures better the ideas of the decision-maker, it is selected for the current solution \(f_{4}\). Figure 5: The objective values corresponding the selected solutions \(q=2\) and \(q=8\) for the modified reference point 3 with objectives (1)–(8). Figure 6: Results for the iteration 4. Eventually, the decision maker is ready to make the final choice. During the solution process, we have learned that the solutions obtained from 4 different reference points can be split broadly into two main groups. The first group includes solutions where the disposal starts early while the other group includes the solutions with late starting. The most striking fact is that the solutions of the first group are obtained with smaller values of \(q\) and the solutions of the second group with the larger values of \(q\). This phenomenon is repeated with all of four reference points.