7. What happens if the heuristic function is not admissible, but is still nonnegative? What can we...
Question:
7. What happens if the heuristic function is not admissible, but is still nonnegative? What can we say about the path found by A * if the heuristic function
(a) is less than 1 + ϵ times the least-cost path (e.g., is less than 10% greater than the cost of the least-cost path)
(b) is less than δ more than the least-cost path (e.g., is less than 10 units plus the cost of the optimal path)?
Develop a hypothesis about what would happen and show it empirically or prove your hypothesis. Does it change if multiple-path pruning is in effect or not?
Does loosening the heuristic in either of these ways improve efficiency? Try A * search where the heuristic is multiplied by a factor 1 + ϵ, or where a cost δ is added to the heuristic, for a number of graphs. Compare these on the time taken (or the number of nodes expanded)
and the cost of the solution found for a number of values of ϵ or δ.
Step by Step Answer:
Artificial Intelligence Foundations Of Computational Agents
ISBN: 9781107195394
2nd Edition
Authors: David L. Poole, Alan K. Mackworth