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2. 2 Problem Description & Assumption Metric model in Sapa planner:  f(p) = w * time(p) + (1-w) * cost(p).  Assuming that the trade-off value w is given. In reality, it's hard to extract the user preference model exactly  It's easier for them to say: “Yes, I'm interested in time and cost of the travel plan. Let me see some plans, I will choose” (no trade-off preference)‏ “Hmm, I don't have much money.” (prefer plans with cheap cost)‏ “I want plans not too expensive, and not too slow as well”. (compromised time and cost)‏

3. 3 Problem Description & Assumption Our work's assumption:  User concerns about time, cost of executing a plan.  User preference model is convex combination between two objectives f(p) = w * time(p) + (1-w) * cost(p)‏ One of the most frequently used model.  The trade-off between time, cost is unknown. But the distribution of w is given. Problem:  Find a set of plans such that the user can select one satisfying their hidden trade-off.

4. 4 Solution Approach Integrated Convex Preference (ICP) measure to evaluate the quality of a set of plan X.  If ICP(X1) < ICP(X2) then X1 is better than X2 in supporting the user: Given a trade-off value w of the user, X1 is more likely contains better quality plan than X2. Extend the A* search procedure of Sapa:  Consider 2 objectives: Multi-objective A*.  Put heuristic on top of Multi-objective A*: To select the most promising node

5. 5 Multi-objective A* with ICP measure

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7. 7 How well the set can be?

8. 8 How to test the approach? Sapa with sampling:  Generate set of N w values, based on the distribution: {w1,..., wN}  For each w_i, invoke Sapa to find a plan p(w_i).  P={p(w1),..., p(wN)}. Time: t1. Our approach: Q = {q1,..., qM}. Time: t2. Comparison:  Simulating T transactions.  For each transaction t, generate w based on distribution.  Compare 2 optimal plans w.r.t w in P and Q.  Compare t1, t2.

9. 9 Future works (though current work is on-going ;-)‏ Qualitative preference model  On trajectory / behavior of the plans. For instance: prefer United Airline to American Airline; would like to visit some places during the trip,... Our work as Over-subscription planning:  Utility is fixed: all goals are achievable.  Cost is more general.  Natural extension: utility as an objective to maximize.

10. 10 Thank you! Q &A