Planning for Multiple Preferences versus Planning with No Preference

Many planning applications must address conflicting plan objectives, such as cost, risk, duration, and resource consumption and decision makers want to know the possible trade-offs. Traditionally, such problems are solved by invoking a single-objective algorithm (such as A*) on multiple, alternative preferences of the objectives to identify non-dominated plans. The less-popular alternative is to delay reasoning about preferences and directly optimize multiple plan objectives with a search algorithm like Multi-objective A* (MOA*). We notice that the relative performance of these two approaches hinges upon the number of f-values computed for individual search nodes. A* may revisit a node several times (once for each preference) and compute a different f-value each time. MOA* visits each node once and may compute some number of f-values (each estimating the value of a different non-dominated solution constructed from the node). While A* does not share f-values between searches for different solutions, MOA* can sometimes find multiple solutions while computing a single f-value per node. However, in doing so, MOA* is often ignorant of alternative solutions. We study several techniques for computing MOA* f-values that seek to lower the per node cost while also seeking multiple alternative solutions. The results of extensive empirical comparison show that i) the performance of multiple invocations of a single-objective A* versus a single invocation of MOA* is often worse in time and quality, and ii) that techniques for balancing per node cost and exploration are promising.