Question

Define a heuristic h for the problem above as h(n) = 15-n. (Clearly h(n) ��� 0, and h(G) = 0, where G, the goal, is 15). Suppose each operator costs 1 unit. a) Draw the search tree and show the order in which the nodes are visited using i) GBFS ii) A* iii) Hill-climbing. b) Is the heuristic admissible?

Answer 1

A heuristic is a problem-solving strategy that is a mental shortcut or general framework. It is different from an algorithm because it is not guaranteed to produce a correct result but is often used to save time and energy when making decisions. In this case, the heuristic function h(n) = 15-n is admissible.

Step-by-step explanation:

A heuristic is a problem-solving strategy that is a mental shortcut or general framework. It is different from an algorithm because it is not guaranteed to produce a correct result but is often used to save time and energy when making decisions.

In this case, a heuristic function h(n) = 15-n is defined for a problem. To determine if the heuristic is admissible, we need to check if it satisfies two conditions: it should never overestimate the true cost to the goal (h(G) = 0) and it should be optimistic, meaning it should always underestimate the true cost (h(n) ≤ d(n, G)). In this case, h(G) = 0, which satisfies the first condition. For the second condition, we need to check if h(n) ≤ d(n, G) for all nodes n. Since each operator costs 1 unit, the true cost to the goal is 15-n. So h(n) = 15-n is optimistic (h(n) ≤ d(n, G)) and therefore admissible.