$\begingroup$ You used bad sample, TSP is hard to approximate, so there is no PTAS for TSP also there is no 2 approximation for TSP is easy to show if there is polynomial time 2-approximation for TSP there is polynomial time algorithm for solving hamiltonian cycle problem, I think you mean metric TSP which is special case but still there is no PTAS in this case (and …

Heuristics are shortcuts to solutions. The idea of heuristic methods in AI is based on cognitive science, or the study of how humans think. Indeed, humans use heuristics to make decisions and ...

The closer the heuristic gets to the shortest path the better it is. But if a heuristic overestimates then the node with the optimal path may get pushed down the queue and a less optimal path will get selected. For a grid with only the 4 cardinal directions (and no obstacles) the optimal heuristic is the manhattan distance (option 4).

If the heuristic function is not admissible, than we can have an estimation that is bigger than the actual path cost from some node to a goal node. If this higher path cost estimation is on the least cost path (that we are searching for), the algorithm will not explore it and it may find another (not least cost) path to the goal.

Heuristic Algorithm: The Heuristics algorithm can be defined as the technique of solving a problem when traditional algorithms fail to achieve the...

Algorithm is proof-able, the complexity, the correctness, etc. But I wonder how can one proof heuristic? Indeed I wonder is "proof" a correct term / action correlate to heuristic, but how about say, proof the heuristic can give sub-optimal answer (like at most 10% worst than the optimal) for 90% out of all possible input?

Oct 9, 2014 · If the heuristic only underestimates by a little bit, maybe some of those routes will turn out to be useful. On the other hand, if the heuristic overestimates, A* can think that the alternatives to the route already has are all terrible, so it won't bother to look at them. But the heuristic overestimates so they might be much better than they seem.

Mar 9, 2017 · Designing a heuristic is a creative act, so one can't really give advice on how to do it. Ideally, though, the heuristic should give a good estimate of the true cost. The purpose of the heuristic is to guide the search and a search that receives accurate guidance will terminate faster than one that receives poor guidance.

In my theoretical computer science class and we were covering "Heuristics". In it we covered "Greedy Heuristics" for the "Vertex Cover Problem", "Interval Scheduling" and the "Traveling Salesperson

Obviously, $17 \gt 2$ and therefore the heuristic is not admissible. However, after having implemented the algorithm and tested it, it seems that it is able to find the optimal solution each time. Trying to alter the heuristic function only makes it worse than optimal.