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python 实现A*算法的示例代码

2018-08-13 14:17 1261 查看

A*作为最常用的路径搜索算法，值得我们去深刻的研究。路径规划项目。先看一下维基百科给的算法解释：https://en.wikipedia.org/wiki/A*_search_algorithm

A *是最佳优先搜索它通过在解决方案的所有可能路径（目标）中搜索导致成本最小（行进距离最短，时间最短等）的问题来解决问题。），并且在这些路径中，它首先考虑那些似乎最快速地引导到解决方案的路径。它是根据加权图制定的：从图的特定节点开始，它构造从该节点开始的路径树，一次一步地扩展路径，直到其一个路径在预定目标节点处结束。

在其主循环的每次迭代中，A *需要确定将其部分路径中的哪些扩展为一个或多个更长的路径。它是基于成本（总重量）的估计仍然到达目标节点。具体而言，A *选择最小化的路径

F（N）= G（N）+ H（n）

其中n是路径上的最后一个节点，g（n）是从起始节点到n的路径的开销，h（n）是一个启发式，用于估计从n到目标的最便宜路径的开销。启发式是特定于问题的。为了找到实际最短路径的算法，启发函数必须是可接受的，这意味着它永远不会高估实际成本到达最近的目标节点。

维基百科给出的伪代码：

function A*(start, goal)
// The set of nodes already evaluated
closedSet := {}
// The set of currently discovered nodes that are not evaluated yet.
// Initially, only the start node is known.
openSet := {start}
// For each node, which node it can most efficiently be reached from.
// If a node can be reached from many nodes, cameFrom will eventually contain the
// most efficient previous step.
cameFrom := an empty map
// For each node, the cost of getting from the start node to that node.
gScore := map with default value of Infinity
// The cost of going from start to start is zero.
gScore[start] := 0
// For each node, the total cost of getting from the start node to the goal
// by passing by that node. That value is partly known, partly heuristic.
fScore := map with default value of Infinity
// For the first node, that value is completely heuristic.
fScore[start] := heuristic_cost_estimate(start, goal)
while openSet is not empty
current := the node in openSet having the lowest fScore[] value
if current = goal
return reconstruct_path(cameFrom, current)
openSet.Remove(current)
closedSet.Add(current)
for each neighbor of current
if neighbor in closedSet
continue // Ignore the neighbor which is already evaluated.
if neighbor not in openSet // Discover a new node
openSet.Add(neighbor)
// The distance from start to a neighbor
//the "dist_between" function may vary as per the solution requirements.
tentative_gScore := gScore[current] + dist_between(current, neighbor)
if tentative_gScore >= gScore[neighbor]
continue // This is not a better path.
// This path is the best until now. Record it!
cameFrom[neighbor] := current
gScore[neighbor] := tentative_gScore
fScore[neighbor] := gScore[neighbor] + heuristic_cost_estimate(neighbor, goal)
return failure
function reconstruct_path(cameFrom, current)
total_path := {current}
while current in cameFrom.Keys:
current := cameFrom[current]
total_path.append(current)
return total_path

下面是UDACITY课程中路径规划项目，结合上面的伪代码，用python 实现A*

import math
def shortest_path(M,start,goal):
sx=M.intersections[start][0]
sy=M.intersections[start][1]
gx=M.intersections[goal][0]
gy=M.intersections[goal][1]
h=math.sqrt((sx-gx)*(sx-gx)+(sy-gy)*(sy-gy))
closedSet=set()
openSet=set()
openSet.add(start)
gScore={}
gScore[start]=0
fScore={}
fScore[start]=h
cameFrom={}
sumg=0
NEW=0
BOOL=False
while len(openSet)!=0:
MAX=1000
for new in openSet:
print("new",new)
if fScore[new]<MAX:
MAX=fScore[new]
#print("MAX=",MAX)
NEW=new
current=NEW
print("current=",current)
if current==goal:
return reconstruct_path(cameFrom,current)
openSet.remove(current)
closedSet.add(current)
#dafult=M.roads(current)
for neighbor in M.roads[current]:
BOOL=False
print("key=",neighbor)
a={neighbor}
if len(a&closedSet)>0:
continue
print("key is not in closeSet")
if len(a&openSet)==0:
openSet.add(neighbor)
else:
BOOL=True
x= M.intersections[current][0]
y= M.intersections[current][1]
x1=M.intersections[neighbor][0]
y1=M.intersections[neighbor][1]
g=math.sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1))
h=math.sqrt((x1-gx)*(x1-gx)+(y1-gy)*(y1-gy))
new_gScore=gScore[current]+g
if BOOL==True:
if new_gScore>=gScore[neighbor]:
continue
print("new_gScore",new_gScore)
cameFrom[neighbor]=current
gScore[neighbor]=new_gScore
fScore[neighbor] = new_gScore+h
print("fScore",neighbor,"is",new_gScore+h)
print("fScore=",new_gScore+h)
print("__________++--------------++_________")
def reconstruct_path(cameFrom,current):
print("已到达lllll")
total_path=[]
total_path.append(current)
for key,value in cameFrom.items():
print("key",key,":","value",value)
while current in cameFrom.keys():
current=cameFrom[current]
total_path.append(current)
total_path=list(reversed(total_path))
return total_path

以上就是本文的全部内容，希望对大家的学习有所帮助，也希望大家多多支持脚本之家。

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