To achieve high performance, autonomous systems, such as science explorers, should adapt to the environment to improve utility gained, as well as robustness. Flexibility during temporal plan execution has been explored extensively to improve robustness, where flexibility exists both in activity choices and schedules. These problems are framed as conditional constraint networks over temporal constraints. However, flexibility has been exploited in a limited form to improve utility. Prior work considers utility in choice or schedule, but not their coupling. To exploit fully flexibility, we introduce conditional simple temporal networks with preference (CSTNP), where preference is a function over both choice and schedule. Enumerating best solutions to a CSTNP is challenging due to the cost of scheduling a candidate STPP and the exponential number of candidates. Our contribution is an algorithm for enumerating solutions to CSTNPs efficiently, called A star with bounding conflicts (A*BC), and a novel variant of conflicts, called bounding conflicts, for learning heuristic functions. A*BC interleaves Generate, Test, and Bound. When A*BC bounds a candidate, by solving a STPP, it generates a bounding conflict, denoting neighboring candidates with similar bounds. A*BCs generator then uses these conflicts to steer away from sub-optimal candidates.
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