-2

There are n vehicles on an n x n grid. At the start they are ordered in the top row 1. The vehicles have to get to the bottom row such that the vehicle at (1,n) must get to (n, n − i + 1). On each time step, each of the vehicles can move one square up, down, left or right, or it can stay put. If the vehicle stays put, one adjacent vehicle (but not more than one) can hop over it. Two vehicles cannot occupy the same square. Which of the following heuristics are admissible for the problem of moving all the vehicles to their destination?

i. sum from 1 to n (h1 ... hn)

ii. max(h1 ... hn)

iii. min(h1 ...hn)

I think that iii is the only correct one, but I'm not sure how to formulate my reasoning on why.

LeeAnn Ramsay
  • 1
  • 1
  • 1

1 Answers1

5

I am sure someone will come along with a very detailed answer, but as a favour to those who like me can be a bit overwhelmed by all things AI, an admissible heuristic is quite simply:

A heuristic that never overestimates the true cost of getting to the goal

Not to sound too uncharitable, but it sounds as if maybe the problems you've posted are from a homework problem or assignment. I wouldn't want to spoil your fun working out exactly which of those three heuristics are and aren't admissible - but hopefully that one sentence definition should help you along.

If you get confused, just remember: if once your vehicles have both reached their goals you find the actual cost was less than what the heuristic thought it would be then it's inadmissable.

lxt
  • 31,146
  • 5
  • 78
  • 83