Question

我的*算法并不总是采用最短的路径。

在此图像中，机器人必须遍历黑色方块，河流和树木是障碍物。黑线是它所采用的路径，显然不是最短的路径，因为它不应该下降。

这是我的*和我正在使用的启发式代码：

def HeuristicCostEstimate(start, goal):
    (x1, y1) = start
    (x2, y2) = goal
    return abs(x1 - x2) + abs(y1 - y2)

def AStar(grid, start, goal):
    entry = 1
    openSet = []
    heappush(openSet,(1, entry, start))
    cameFrom = {}
    currentCost = {}
    cameFrom[tuple(start)] = None
    currentCost[tuple(start)] = 0
    while not openSet == []:
        current = heappop(openSet)[2]
        print(current)
        if current == goal:
            break

        for next in grid.Neighbours(current):
            newCost = currentCost[tuple(current)] + grid.Cost(current, next)
            if tuple(next) not in currentCost or newCost < currentCost[tuple(next)]:
                currentCost[tuple(next)] = newCost
                priority = newCost + HeuristicCostEstimate(goal, next)
                entry +=1
                heappush(openSet,(priority, entry, next))
                cameFrom[tuple(next)] = current

    return cameFrom, current

http://pastebin.com/bEw8x0Lx

感谢您的帮助！随时请我澄清任何事情。

编辑：通过返回0删除启发式解决了这个问题。这表明问题在于我的启发式。有人会知道可能导致它的原因吗？

Answer 1

A* is not always guaranteed to find a shortest path. While it is true that without a heuristic (h(n) = 0), the shortest path will be found (it becomes Dijkstra's algorithm), this does not mean that with any heuristic the shortest path will be found. The heuristic is added to speed up this search and the trade off is that in some cases you will not find the shortest path.

To understand whats going on, remember that the heuristic is an estimation of the actual distance to target. If the prediction is perfect, the graph is essentially pre-calculated. Consider the following cases.

If your heuristic is lower than the actual cost, the shortest path will be found.
If the heuristic is equal to the actual cost, all shortest paths are essentially pre-calculated, and the shortest path will be found without any unnecessary exploring.
If the heuristic is sometimes greater than the actual cost, then A* is not guaranteed to find the shortest path, but search time may be faster than if the heuristic made underestimations.

It seems that your heuristic is underestimating the cost. It could also be that you have faulty neighbor generation or cost calculator.

For further reading: http://theory.stanford.edu/~amitp/GameProgramming/Heuristics.html

为什么我的a *算法不采用最短路径？

1 个答案: