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Consider the following statements

S1: A heuristic is admissible if it never overestimates the cost to reach the goal

S2: A heuristic is monotonous if it follows triangle inequality property.

Which one of the following is true referencing the above statements?

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UGC NET Computer Science (Paper 2) Dec 2018 Paper
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  1. Statement S1 is true but statement S2 is false.
  2. Statement S1 is false but statement S2 is true.
  3. Neither of the statements S1 and S2 are true
  4. Both the statements S1 and S2 are true.

Answer (Detailed Solution Below)

Option 4 : Both the statements S1 and S2 are true.
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Detailed Solution

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S1: ​A heuristic is admissible if it never overestimates the cost to reach the goal        [correct]

A heuristic search carries the additional knowledge about the problem which helps in reaching the goal. A heuristic function is considered for finding the cost of the path. Cost is estimated if there is a path from a given node to goal node. When it reaches goal state, then at that instant cost will be zero. Heuristic search is admissible if it never overestimates the cost to reach the goal.

S2: ​A heuristic is monotonous if it follows triangle inequality property.              [Correct]

Heuristic search is a minimum cost solution to find the best path for a problem. A heuristic search is monotonous if it follows triangle inequality property. First, we visit a node to find an optimal path to it.  Triangle inequality problem: h(n1) <= c (n1 -> n2) + h(n2).
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