This will be a relatively short post, following on specifically from Part 2, and Part 3 where we moved away from a static grid and instead had coordinates and available neighbours.

Through playing around with the code and algorithm I found various things that I wanted to change, mainly for the purpose of optimisation. With a small 'map' it appears to find paths very fast, but as you increase the search space this can exponentially increase the search time - and we need ways to make it as fast as possible.

1. Use a dictionary rather than looking up in the pandas DataFrame.

Instead of using the available neighbours function we can pre-process our neighbours into a dictionary with the origin coordinate as the key and a list of neighbours as the value. We can then call these neighbours directly in the astar function using:

neighbours = coord_dict.get(current)

For a large map, this will make an immense difference to the search speed. I found somewhere in the range of 100x for a use case I was investiagating but it will obviously depend on map size.

2. This one is a minor change - but in the heuristic function...

def heuristic(a, b):

return np.sqrt((b[0] - a[0]) ** 2 + (b[1] - a[1]) ** 2 + (b[2] - a[2]) ** 2)

...we're taking the square root. That is correct if you want to know the precise distance, but all we want is a way to compare each neighbour regarding how far they are from the destination. As this calculation is happening for every neighbour, even small time costs will add up

3. If the neighbour is in the closed loop, skip

In the logic used in previous parts, we were actually only skipping a neighbour if it was in the closed list and it had a g-score higher than the current neighbour. I've found this logic actually means we're checking nodes multiple times, which can be unnecessary and very inefficient. This is a trade-off however, the original logic is slow but allows the algorithm to re-consider a possible path and in general it will always find the shortest path. The new logic is much faster and will find a very similar path but not always the absolute shortest.

If you want to implement the change, this code:

tentative_g_score = gscore[current] + heuristic(current, neighbour)

if neighbour in close_set and tentative_g_score >= gscore.get(neighbour, 0):

continue

if tentative_g_score < gscore.get(neighbour, 0) or neighbour not in [i[1]for i in oheap]:

came_from[neighbour] = current

gscore[neighbour] = tentative_g_score

fscore[neighbour] = tentative_g_score + heuristic(neighbour, goal)

heapq.heappush(oheap, (fscore[neighbour], neighbour))

Becomes:

if (gscore[current] + heuristic(current, neighbour)) < gscore.get(neighbour, 0) or neighbour not in [i[1]for i in open_heap]:

came_from[neighbour] = current

gscore[neighbour] = gscore[current] + heuristic(current, neighbour)

fscore[neighbour] = gscore[neighbour] + heuristic(neighbour, goal)

heapq.heappush(open_heap, (fscore[neighbour], neighbour))

This should have a large impact on run time:

4. Another minor one, but I was using a line of code that didn't need to be there:

for x, y, z in neighbours:

neighbour = x, y, z

Can just be:

for neighbour in neighbours:

FULL CODE:

def heuristic(current, destination):

return (destination[0] - current[0]) ** 2 + (destination[1] - current[1]) ** 2 + (destination[2] - current[2]) ** 2

def astar(start, goal):

close_set = set() # closed list

came_from = {} # parent node dict

gscore = {start:0} # g-score dict

fscore = {start:heuristic(start, goal)} #f score dict

open_heap = [] #open list

heapq.heappush(open_heap, (fscore[start], start)) # put start node into open list

while open_heap:

current = heapq.heappop(open_heap)[1] # extract current node

if current == goal: # if the current is the goal, compile the path back to the origin (from the parent list)

data = []

while current in came_from:

data.append(current)

current = came_from[current]

return data

neighbours = coord_dict.get(current) # find available neighbours

if neighbours == None:

neighbours = []

close_set.add(current) # add current node to closed list

for neighbour in neighbours: # iterate through neighbours

if neighbour in close_set: # if neighbour is in closed set, don't consider

continue

if (gscore[current] + heuristic(current, neighbour)) < gscore.get(neighbour, 0) or neighbour not in [i[1]for i in open_heap]: # if neighbour has lower g score OR isn't on the open list already

came_from[neighbour] = current # add to parent dict

gscore[neighbour] = gscore[current] + heuristic(current, neighbour) # calculate g score

fscore[neighbour] = gscore[neighbour] + heuristic(neighbour, goal) # calculate f score (g+h)

heapq.heappush(open_heap, (fscore[neighbour], neighbour)) # add to open list

return []