# Tag Info

### Is the summation of consistent heuristic functions also consistent?

No, it will not necessary be consistent or admissible. Consider this example, where $s$ is the start, $g$ is the goal, and the distance between them is 1. s --1-- g Assume that $h_0$ and $h_1$ are ...
• 361

### If an heuristic is not admissible, can it be consistent?

If a heuristic is not admissible, can it be consistent? No. Consistency implies admissibility. In other words, if a heuristic is consistent, it is also admissible. However, admissibility does not ...
• 33.7k

### If an heuristic is not admissible, can it be consistent?

For a heuristic to be admissible, it must never overestimate the distance from a state to the nearest goal state. For a heuristic to be consistent, the heuristic's value must be less than or equal to ...
• 8,865
Accepted

• 1,663
1 vote

### Is A* with an admissible but inconsistent heuristic optimal?

It depends on what you mean by optimal. A* will always find the optimal solution (that is, the algorithm is admissible) as long as the heuristic is admissible. (Note that the definition of admissible ...
• 361
1 vote

### If $h_i$ are consistent and admissible, are their sum, maximum, minimum and average also consistent and admissible?

The issue is that you must include assumptions about hopping into your heuristic. In particular, if you are considering individual cars then you must assume that they might be able to hop all of the ...
• 361

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