As Russel and Norvig point out in Artificial Intelligence: A Modern Approach (the most commonly used AI textbook) it is challenging to come up with a heuristic that is admissible but not consistent. Obviously, you can select values for nodes in a graph such that the heuristic they represent is admissible but not consistent. This … Read more
There were algorithms called A1 and A2. Later, it was proved that A2 was optimal and in fact also the best algorithm possible, so he gave it the name A* which symbolically includes all possible version numbers. Source: In 1964 Nils Nilsson invented a heuristic based approach to increase the speed of Dijkstra’s algorithm. This … Read more
As a heuristic, you could construct a graph where each node represents a set of contiguous, same-colour squares, and each node is connected to those it touches. (Each edge weighted as 1). You could then use a path-finding algorithm to calculate the “distance” from the top left to all other nodes. Then, by looking the … Read more
An easy optimization is to use sets instead of lists for the open and closed sets. openSet = set() closedSet = set() This will make all of the in and not in tests O(1) instead of O(n).
This article explains the basic implementation in length: The goal of this blog post is to show the fundamentals of A* through a really simple C# implementation. It also points to better implementations, more suitable for production use: As for ways to find better routes, there are plenty of C# examples around that are far … Read more
Well, I’ll add my comment here, since it is more optimal than the current highest-voted answer by @larsmans – but, I am convinced there must be something better (hence the bounty). If I multiply the heuristic with a constant, it’s no longer admissible The best I can come up with is (manhattenDistance/3)*6 + (manhattenDistance%3), where … Read more
The short answer is yes, there are situations in which A* is not the best algorithm to solve a problem. However, there are a number of ways to assess what constitutes the best algorithm for finding a solution. If you are considering best in terms of performance of multiple searches from a single source to … Read more
As Russel and Norvig point out in Artificial Intelligence: A Modern Approach (the most commonly used AI textbook) it is challenging to come up with a heuristic that is admissible but not consistent. Obviously, you can select values for nodes in a graph such that the heuristic they represent is admissible but not consistent. This … Read more
You should be able to make it much faster by trading off optimality. See Admissibility and optimality on wikipedia. The idea is to use an epsilon value which will lead to a solution no worse than 1 + epsilon times the optimal path, but which will cause fewer nodes to be considered by the algorithm. … Read more
Judging from the existing answers, there seems to be a lot of confusion about this concept. The Problem Is Always a Graph The distinction between tree search and graph search is not rooted in the fact whether the problem graph is a tree or a general graph. It is always assumed you’re dealing with a … Read more