Python实现A*路径搜索算法详解

一颗松果
一颗松果
发布时间:2026-10-13| 4人浏览过
原创

本文深入解析A*路径搜索算法,结合UDACITY课程项目,展示如何使用Python实现该算法。文章涵盖A*的核心原理、F(N)=G(N)+H(N)公式含义、可接受启发函数的要求,并提供完整的Python代码实现与伪代码对照,帮助开发者掌握最优路径搜索技术。

A*算法作为目前应用最广泛的路径搜索算法之一,值得进行深入研究与探讨。在路径规划项目中,我们可以参考维基百科提供的算法解释:https://en.wikipedia.org/wiki/A*_search_algorithm

A*属于最佳优先搜索算法,其核心思想是通过搜索所有可能通向目标的路径,找出成本最小(如行进距离最短、耗时最少等)的方案。在这些路径中,算法优先考虑那些看似能最快引导至解决方案的路径。该算法基于加权图构建:从图的特定起始节点出发,逐步扩展路径树,直到某条路径到达预设的目标节点为止。

在主循环的每次迭代中,A*需要判断将部分路径中的哪些节点扩展为一个或多个更长的路径。这一决策基于对到达目标节点剩余成本的估计。具体而言,A*选择使下式值最小的路径进行扩展:

F(N)= G(N)+ H(n)

其中n代表路径上的最后一个节点,g(n)表示从起始节点到节点n的实际路径开销,h(n)是一个启发式函数,用于估计从节点n到目标节点的最便宜路径开销。该启发式函数需针对具体问题定制。为了确保算法能找到实际最短路径,启发函数必须具备“可接受性”,即它永远不能高估到达最近目标节点的实际成本。

以下是维基百科提供的算法伪代码:

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

结合上述伪代码,下面是UDACITY课程中路径规划项目的Python实现示例,展示了A*算法的具体应用。

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本站。

相关标签:

免责声明:本文内容仅供参考,不代表本站观点。转载或引用请注明出处。

Python 相关产品和应用

全部下载
Selenium

Selenium

4.51.0 · Windows

用于浏览器自动化和 Web 测试的 Python 工具。

scikit-learn

scikit-learn

1.9.1 · Windows

常用 Python 机器学习算法与模型评估工具库。

Black

Black

26.10.1 · Windows

强调一致性的 Python 自动代码格式化工具。

Ruff

Ruff

0.17.1 · macOS

由 Rust 编写的高速 Python 代码检查和格式化工具。

pytest

pytest

9.1.1 · Windows

简洁而强大的 Python 自动化测试框架。

FastAPI

FastAPI

0.146.0 · Windows

高性能 Python API 框架,支持类型提示和自动接口文档。

Flask

Flask

3.1.3 · Windows

轻量灵活的 Python Web 应用框架。

Django

Django

6.1.2 · Windows

成熟的 Python Web 框架,适合构建内容站点和业务系统。

Spyder

Spyder

6.1.7 · Windows

面向科学计算与数据分析的 Python 集成开发环境。

SciPy

SciPy

1.18.1 · Windows

面向科学、工程和技术计算的 Python 算法库。