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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:
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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)
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.
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
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.
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.
