Why Optimization? (cont.)
Ease of use - even simple heuristics can work well.
But what of nondeterminism in hybrid systems? ? Game Theory, AI game-tree search extended to transition games
Is this in competition with control synthesis techniques which use game theory to back-propagate constraints? ? No!
So one of the appeals of an optimization approach is its ease of use. It's surprising that simple heuristics can work well. I also expect that engineers who use heuristic means to design will find it most natural to use heuristics to try to break their designs.
One might argue that some problems may require a heuristic function which encodes deep understanding of the system. It's a problem shared with some deductive approaches: Sometimes the difficulty of choosing the right invariant to prove is the primary barrier to their use.
I expect that automatic construction of heuristic will arise out of the good research of others I see here. For example, Mark Greenstreet and Ian Mitchell's conservative reachability analysis may generate false negatives. That is, unsafe regions marked reachable may or may not be. Regardless, these regions and the ones which reach it can be used to construct a powerful heuristic for searching for a failure scenario. [worked example]