4

I have obtained all the possible paths of maze through image processing. Now, I want to use A* algorithm in order to find shortest path of maze. However, I am confused as to whether euclidean distance will be a better heuristic or manhattan distance. Does it depend upon maze type or is the choice of heuristic independent of maze type? Which distance (manhattan or euclidean) will be a good choice for the following possible paths and why? Please suggest.

PS. (Please add your reference too, if your have any. It will be helpful)

enter image description here

Curious
  • 127
  • 3
  • 11
  • I implemented shortest path finding using both euclidean and manhattan (separately) as heuristic in A*. However, none is giving good result. I want to self generate heuristic. What can be a possible option for that? Help will be appreciated. Please suggest. – Curious May 13 '17 at 17:20

2 Answers2

3

The objective of a Heuristic is to provide contextual information to the pathfinder. The more accurate this information is, the more efficient the pathfinder can be.

You have two contradicting requirements to get a good heuristic, which is good because it means there is a sweet spot. Here they are:

  • An Heuristic must be admissible, which means it shall never overestimate the distance. Otherwise, the algorithm will be broken and may return paths that are not even optimal.
  • An heuristic must return the largest distance possible. An heuristic that underestimates the remaining path from a cell, will favour that cell when another might have been better.

Of course the optimal Heuristic would return the exact, correct length (which generally is not achievable or defeats the purpose) because it cannot return a longer path without ceasing to be admissible.

In your case, it looks like you're dealing with 4-connected grids. In that case the manhattan distance will be a better metric than euclidian distance, because the Euclidian will under-estimate the cost of all displacements compared to Manhattan (due to the Pythagorean Theorem).

Whithout any further knowledge than 'the graph is a 4-connected Grid', there is no better metric than Manhattan. If however you manage to obtain more data (obstacle density, 'highways', etc.) then you might be able to devise a better heuristic - though keeping it admissible would be a very hard problem in itself.

EDIT Having a closer look, it looks like you have angled vertices in the bottom left. If that is so, you're not in a 4-connected graph, then you MUST use Euclidian distance, because Manhattan would not be admissible.

MrBrushy
  • 680
  • 3
  • 17
-4

Its not clear what moves are available to your hero. Does you graph make up a rectangular grid like chess board and can you go diagonally in one step like king in chess? If yes then Chebyshev distance is the best https://en.wikipedia.org/wiki/Chebyshev_distance. Otherwise use Euclidian distance. You cant use Manhattan here if you want an optimal path because Manhattan heuristic is not admissible on diagonal routes (it overestimates them) so it can lead to suboptimal pathes

Timur Nurmagambetov
  • 57
  • 2
  • 5