As far as I understand, the validity of the heuristic remains within the "actual cost of distance" for a given evaluated node. I had to develop some heuristics for finding A * solutions in state spaces and got a lot of positive efficiency using a heuristic that can sometimes return negative values, so that certain nodes are more “densely formed” with the goal that the state has a higher place on the border .
However, I worry that this is unacceptable, but I cannot find enough information on the Internet to verify this. I found this article from the University of Texas , which seems to be mentioned in one of the latest evidence that "... because heuristic functions are non-negative." Can anyone confirm this? I assume this is because you are returning a negative value, since your heuristic function will turn your g-cost negative (and therefore interfering with the default behavior of dijkstra-esque A *).
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