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python 實(shí)現(xiàn)A*算法的示例代碼

2020-01-04 14:56:35
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A*作為最常用的路徑搜索算法,值得我們?nèi)ド羁痰难芯?。路徑?guī)劃項(xiàng)目。先看一下維基百科給的算法解釋:https://en.wikipedia.org/wiki/A*_search_algorithm

A *是最佳優(yōu)先搜索它通過在解決方案的所有可能路徑(目標(biāo))中搜索導(dǎo)致成本最?。ㄐ羞M(jìn)距離最短,時(shí)間最短等)的問題來解決問題。 ),并且在這些路徑中,它首先考慮那些似乎最快速地引導(dǎo)到解決方案的路徑。它是根據(jù)加權(quán)圖制定的:從圖的特定節(jié)點(diǎn)開始,它構(gòu)造從該節(jié)點(diǎn)開始的路徑樹,一次一步地?cái)U(kuò)展路徑,直到其一個(gè)路徑在預(yù)定目標(biāo)節(jié)點(diǎn)處結(jié)束。

在其主循環(huán)的每次迭代中,A *需要確定將其部分路徑中的哪些擴(kuò)展為一個(gè)或多個(gè)更長的路徑。它是基于成本(總重量)的估計(jì)仍然到達(dá)目標(biāo)節(jié)點(diǎn)。具體而言,A *選擇最小化的路徑

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

其中n是路徑上的最后一個(gè)節(jié)點(diǎn),g(n)是從起始節(jié)點(diǎn)到n的路徑的開銷,h(n)是一個(gè)啟發(fā)式,用于估計(jì)從n到目標(biāo)的最便宜路徑的開銷。啟發(fā)式是特定于問題的。為了找到實(shí)際最短路徑的算法,啟發(fā)函數(shù)必須是可接受的,這意味著它永遠(yuǎn)不會(huì)高估實(shí)際成本到達(dá)最近的目標(biāo)節(jié)點(diǎn)。

維基百科給出的偽代碼:

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 failurefunction 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課程中路徑規(guī)劃項(xiàng)目,結(jié)合上面的偽代碼,用python 實(shí)現(xiàn)A* 

import mathdef 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("已到達(dá)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?jī)?nèi)容,希望對(duì)大家的學(xué)習(xí)有所幫助,也希望大家多多支持VEVB武林網(wǎng)。


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