#AI Search
Explore heuristic search.
##File structure
In go.py:
Main program, and generic search.
In fringe.py:
Fringe defintion and Fringe specific definition for each algorithm.
In puzzle.py:
State definition, and specific puzzle state definition for 8-Puzzle
particularly. Definition of heuristics for 8-puzzle.
Note: The name of the heuritics defined below, match the one found in
puzzle.py
##Usage
python go.py
[-h]
[-a {astar,best,bfs,dfs}]
[-t {manhattan,displaced,invalid,max, linear}]
[--start START START START START START START START START START]
[-d {easy,medium,hard,worst}] [-b BENCHMARK] [-v]
optional arguments:
-h, --help
show this help message and exit
-a {astar,best,bfs,dfs}
Select the algorithm you want to run. Chose between
astar, best, bfs or dfs.
-t {manhattan,displaced,invalid,max, linear}
Select the heuristic you want to apply. Chose between
manhattan, displaced, invalid, linear or max.
-d {easy,medium,hard,worst}
Select a predifined start state with specific
difficulty. Chose between easy, medium, hard or worst.
Note: if this option is selected, --start will be
ignored, also goal state is set to:
1 2 3
8 4
7 6 5
--start START START START START START START START START START
Write the 8-Puzzle start state you would like to
solve. Integers between 1 and 8, blank represented
with B. Default start state:
1 2 3
4 5
7 6 8
-b BENCHMARK, --benchmark BENCHMARK
Select the number of loops, you want to average on. It
will run all algorithms, and output results to a file.
-v, --verbose
Increase output verbosity. Will show the path to the
goal.
Test Runs
Start state is: (5, 6, 7, 4, 8, B, 3, 2, 1)
Goal state is: (1, 2, 3, 8, 4, B, 7, 6, 5)
| Algorithm | Heuristic | Avg. Time (s) | Node to goal | Node visited |
|---|---|---|---|---|
| astar | manhattan | 0.9343 | 31 | 52495 |
| astar | displaced | 4.2816 | 31 | 162764 |
| astar | max | 1.0431 | 31 | 52504 |
| astar | linear | 4.4095 | 31 | 125207 |
| astar | invalid | 5.3976 | 31 | 166829 |
| best | manhattan | 0.0016 | 45 | 129 |
| best | displaced | 0.0007 | 31 | 79 |
| best | max | 0.0020 | 45 | 129 |
| best | linear | 0.0107 | 77 | 441 |
| best | invalid | 0.0051 | 39 | 203 |
| dfs | N/A | 0.9809 | 64835 | 149154 |
| bfs | N/A | 1.6932 | 31 | 181438 |
Note: We chose specific start and goal state to have significant differences in terms of time, node to goal and node visited between the different Algorithms and Heuristics.
Note: Test runs used was possible using --benchmark 500 parameter.
Note: To determine the Average time, each row in the table were ran 500
times. In total, 12 * 500 = 6000 experiments ran to get theses results.
It took 4:25:58, to finish these experiments, on a remote machine.
Analysis and Explanation
We see that A*, no matter the heuristic chosen is always finding
the optimal path. But, we see that A* takes in general the most time compared
to all other Algorithms, and visits more node then Best-First Search.
Best-First Search only finds the optimal path when given the displace tiles
heuristic. We see that Best-First Search takes the least amount of time, no
matter the heuristic chosen.
Depth-First Search is definitly far from the optimal path, it visits a lot of
nodes. But is faster then A* or Breadth-First Search.
Breadth-First Search finds the optimal path, but is the one that visits the
most node.
Regarding heuristics, for Manhattan and displaced tiles, the results are
quite unexpected. Best-First Search performs at its best using displaced
tiles, while A* is performing really poorly using the same heuristic. Its
time to execute and the number of visited node is really poor. We see that
A* performs the best using the Maximum heuristic (combination of
Manhattan and displaced tiles).
The invalid heuristic is not very conclusive in this case, other that, it is
A* worst heuristic. And Best-First Search gets its second best result in
terms of node to goal.
Sample run using provided goal state
Solving using: astar
Using Heuristic: manhattan
Start state is: (1, 2, 3, 4, 0, 5, 7, 6, 8)
Goal state is: (1, 2, 3, 8, 0, 4, 7, 6, 5)
astar - Solved in 0.0025 seconds
1.
1 | 2 | 3
4 | B | 5
7 | 6 | 8
cost: 8 total_cost: 0
2.
1 | 2 | 3
B | 4 | 5
7 | 6 | 8
cost: 8 total_cost: 8
3.
1 | 2 | 3
7 | 4 | 5
B | 6 | 8
cost: 9 total_cost: 17
4.
1 | 2 | 3
7 | 4 | 5
6 | B | 8
cost: 10 total_cost: 27
5.
1 | 2 | 3
7 | 4 | 5
6 | 8 | B
cost: 9 total_cost: 36
6.
1 | 2 | 3
7 | 4 | B
6 | 8 | 5
cost: 8 total_cost: 44
7.
1 | 2 | 3
7 | B | 4
6 | 8 | 5
cost: 4 total_cost: 48
8.
1 | 2 | 3
7 | 8 | 4
6 | B | 5
cost: 10 total_cost: 58
9.
1 | 2 | 3
7 | 8 | 4
B | 6 | 5
cost: 9 total_cost: 67
10.
1 | 2 | 3
B | 8 | 4
7 | 6 | 5
cost: 8 total_cost: 75
11.
1 | 2 | 3
8 | B | 4
7 | 6 | 5
cost: 0 total_cost: 75
Total nodes to goal: 11
Total nodes visited: 186