Els-y / a_star

applications of the A* algorithm

A* Algorithm

Two applications of the A* algorithm:

• N-Puzzle Game
• Traveling Salesman Problem, TSP

N-Puzzle Game

The code in puzzle.py has realized four heuristics:

1. Manhattan distance
2. The number of misplaced tiles
3. X-Y heuristics
4. Linear Conflict

The code can be used as follows, and you can replace the third argument of the class Puzzle instantiation to use different heuristics to estimate cost.

The four alternative values are [Puzzle.MANHATTAN, Puzzle.MISPLACED, Puzzle.XY_HEURISTICS, Puzzle.LINEAR_CONFLICT]

begin_node = PuzzleNode([5, 1, 5, 2, 7, 0, 4, 6, 3, 8])
end_node = PuzzleNode([9, 1, 2, 3, 4, 5, 6, 7, 8, 0])

print("Manhattan:")
p_manhattan = Puzzle(begin_node, end_node, Puzzle.MANHATTAN)
p_manhattan.a_star()
p_manhattan.print_result()

The list argument used in PuzzleNode instantiation represents the node state, in which the first element is the index of the empty tile. For the above node begin_node, it can be represents as follows,

1 5 2
7   4
6 3 8

Note: If you use X-Y heuristics, it may take a long time to get the results because of calling two bfs search to estimate cost. However, you can rewrite this code in C/C++, which will greatly reduce the execution time.

Traveling Salesman Problem, TSP

The heuristic function is derived from CSE 471/598 Project I

• Initial State: Agent in the start city and has not visited any other city
• Goal State: Agent has visited all the cities and reached the start city again
• Successor Function: Generates all cities that have not yet visited
• Edge-cost: distance between the cities represented by the nodes, use this cost to calculate g(n).
• h(n): distance to the nearest unvisited city from the current city + estimated distance to travel all the unvisited cities (MST heuristic used here) + nearest distance from an unvisited city to the start city.

The usage of the code tsp.py looks like this:

tsp = TSP()
problem = tsp.problem_generator(5)
graph = tsp.generate_graph(problem)

finish_state = tsp.a_star(problem, 0)

path = finish_state.get_path()
dist = finish_state.calc_path(path, graph)

print("Problem:")
print(problem)

print("\nDistance Graph:")
print_graph(graph)

print()
print("answer: " + str(path) + " " + str(dist))