Pareto Optimization of Temporal Decisions

Abstract

The focus of this paper is on constrained optimization problems where the objective is to maximize a set of local preferences for times at which events occur. Previous work by the same authors has resulted in a reformulation of a subclass of these problems into a generalization of Temporal Constraint Satisfaction Problems, using a semi-ring as the underlying structure for reasoning about preferences. A tractable strategy for combining and comparing preferences was proposed, wherein computing global preferences consists of taking the minimum of the component preference values. This strategy, which we here dub the “weakest link optimization” (WLO) strategy, is a coarse method for comparing solutions, and therefore can easily be demonstrated to have drawbacks. To formalize this observation, we show here that the optimal solutions generated by WLO are not in general Pareto optimal. To compensate for these limitations, we make WLO more robust by combining it with a process that involves iteratively committing to temporal values in the set of optimal solutions, concomitantly fixing the preference value for the projection of the solution to the local preference. The intuition is simple: by applying WLO iteratively to reduced problems, WLO might be able to improve the preference values of the remaining temporal variables. We demonstrate the improvement gained from applying this technique on examples from Mars Rover planning domain, and prove that the combined strategy results in solutions that are in the set of Pareto optimal solutions.