Figure 11: The contribution into the common lower convex hull of plan sets in ZenoTravel domain with different distributions.

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## Relative Importance.

The sensitivity of plan sets to the distributions: All analysis having been done so far is to compare the effectiveness of approaches with respect to a particular distribution of the tradeoff value. In this part, we examine how sensitive the plan sets are with respect to different distributions. Optimizing high-priority feature: We first consider how plan sets are optimized on each feature (makespan and plan cost) by each approach with respect to two non-uniform distributions w02 and w08. Those are the distributions representing scenarios where the users have different priority on the features, and plan sets should be biased to optimizing the feature that has higher priority (i.e. larger value of weight). In particular, plans generated using the w08 distribution should have better (i.e. *smaller*) makespan values than those found with the w02 distribution (since in the makespan has higher priority in w08 than it is in w02); on the other hand, plan set returned with w02 should have better values of plan cost than those with w08.

Table 11 summarizes for each domain, approach and feature, the number of problems in which plan sets returned with one distribution (either w02 or w08) have better *median* value than with the other. We observe that for both features, the Sampling approach is very likely to
"push" plan sets to regions of the space of makespan and cost with better value of more interested feature. On the other hand, the Hybrid approach tends to be more sensitive to the distributions on both the features in ZenoTravel domain, and is more sensitive only on the makespan feature in DriverLog and Depots domain. Those results generally show that our approaches can bias the search towards optimizing features that are more desired by the user.

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