# Decision-Maker's Preference-Driven Dynamic Multi-Objective Optimization
## 3 Experimental Setup
### Statistical Analysis
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**PM** & **RESULTS** & **PPA** & **DPA** & **RSTFRA** \\ \hline acc & Wins & 69 & 83 & 63 \\ acc & Losses & 75 & 60 & 80 \\ acc & Diff & \(-6\) & 23 & \(-17\) \\ acc & Rank & 2 & \(\mathbf{1}\) & 3 \\ \hline stab & Wins & 23 & 23 & 32 \\ stab & Losses & 22 & 34 & 22 \\ stab & Diff & 1 & \(-11\) & 10 \\ stab & Rank & 2 & 2 & \(\mathbf{1}\) \\ \hline hvr & Wins & 82 & 94 & 40 \\ hvr & Losses & 62 & 50 & 104 \\ hvr & Diff & 20 & 44 & \(-64\) \\ hvr & Rank & 2 & \(\mathbf{1}\) & 3 \\ \hline react & Wins & 14 & 45 & 45 \\ react & Losses & 57 & 25 & 22 \\ react & Diff & \(-43\) & 20 & 23 \\ react & Rank & 3 & \(\mathbf{1}\) & \(\mathbf{1}\) \\ \hline nSVD & Wins & 91 & 65 & 39 \\ nSVD & Losses & 38 & 67 & 90 \\ nSVD & Diff & 53 & \(-2\) & \(-51\) \\ nSVD & Rank & \(\mathbf{1}\) & 2 & 3 \\ \hline sSVD & Wins & 67 & 87 & 47 \\ sSVD & Losses & 68 & 48 & 85 \\ sSVD & Diff & \(-1\) & 39 & \(-38\) \\ sSVD & Rank & 2 & \(\mathbf{1}\) & 3 \\ \hline nVD & Wins & 0 & 2 & 4 \\ nVD & Losses & 0 & 4 & 2 \\ nVD & Diff & 0 & \(-2\) & 2 \\ nVD & Rank & 3 & 2 & \(\mathbf{1}\) \\ \hline dVD & Wins & 0 & 4 & 4 \\ dVD & Losses & 0 & 4 & 4 \\ dVD & Diff & 0 & 0 & 0 \\ dVD & Rank & 3 & \(\mathbf{1}\) & \(\mathbf{1}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Overall Wins and Losses for various performance measures, and frequency and severity of change combinations, using wins-losses\({}_{B}\)[1]. Figures 2 and 3 present the objective space where the preferred objective vectors, or preferred outcomes, are contained in a DM's preference set. The preference set, or the bounding box, in these instances is a sphere whose defining properties are specified by a DM in the bootstrap procedure described in Algorithm 3. For the sphere specifications in Figures 2 and 3, the first three numbers represent the location of the center of the sphere, while the last number represents the radius of the sphere. Figures 2 and 3 are simply snapshots and are thus incapable of showing the dynamics of the preference set. They are, however, presented in this section to provide a one-time view into the state of the objective space during the optimization process. In all the snapshots presented by Figures 2 and 3, all the decisions in the archive are preferred by the DM, since all the objective vectors lie within the spheres representing the DM's preferences. This is a testament to the fact that the proposed algorithms are effective in finding optimal trade-off solutions/decisions that reflect a DM's preferences within the search space. DPA in Figure 2 had the highest number of preferred vectors/outcomes within its spheres, which is consistent with earlier results in this section, indicating its overall superiority over the other algorithms proposed in this study. As a matter of fact, it is ranked best for the experimental configuration represented by Figure 2, and RSTFRA is ranked the worst performing algorithm. In the experimental configuration represented by Figure 3, PPA ranked best, though only marginally better than DPA. Both algorithms effectively found the DM's preferred decisions, as none of the algorithms produced violating decisions.