performance - How to speed up A* algorithm at large spatial scales?

Question

From http://ccl.northwestern.edu/netlogo/models/community/Astardemo, I coded an A* algorithm by using nodes in a network to define least-cost paths. The code seems to work but it is much too slow when I use it at large spatial scales.My landscape has an extent of 1000 patches x 1000 patches with 1 patch = 1 pixel. Even if I reduce it at 400 patches x 400 patches with 1 patch = 1 pixel, it is yet too slow (I can't modify my landscape below 400 patches x 400 patches). Here is the code:

to find-path [ source-node destination-node] 

let search-done? false
let search-path []
let current-node 0
set list-open []
set list-closed []  
let list-links-with-nodes-in-list-closed []
let list-links []

set list-open lput source-node list-open
while [ search-done? != true]
[    
ifelse length list-open != 0
[
  set list-open sort-by [[f] of ?1 < [f] of ?2] list-open 
  set current-node item 0 list-open 
  set list-open remove-item 0 list-open 
  set list-closed lput current-node list-closed
  ask current-node
  [  
    if parent-node != 0[
    set list-links-with-nodes-in-list-closed lput link-with parent-node list-links-with-nodes-in-list-closed 
    ]
    ifelse any? (nodes-on neighbors4) with [ (xcor = [ xcor ] of destination-node) and (ycor = [ycor] of destination-node)]
    [
      set search-done? true 
    ]
    [        
      ask (nodes-on neighbors4) with [ (not member? self list-closed) and (self != parent-node) ]  
      [  
        if not member? self list-open and self != source-node and self != destination-node
        [
          set list-open lput self list-open
          set parent-node current-node
          set list-links sentence (list-links-with-nodes-in-list-closed) (link-with parent-node)
          set g sum (map [ [link-cost] of ? ] list-links)
          set h distance destination-node 
          set f (g + h)
        ]
      ]
    ]
  ]
]

[
  user-message( "A path from the source to the destination does not exist." )
  report []
 ]
]
set search-path lput current-node search-path
let temp first search-path
while [ temp != source-node ]
[
 ask temp
[
  set color red
]
set search-path lput [parent-node] of temp search-path 
set temp [parent-node] of temp 
]
set search-path fput destination-node search-path
set search-path reverse search-path  
print search-path
end

Unfortunately, I don't know how to speed up this code. Is there a solution to calculate rapidly least-cost paths at large spatial scales ?

Thanks very much for your help.

Answer 1

Was curious so I tested mine A* and here is mine result

Maze 1280 x 800 x 32 bit pixels

• as you can see it took ~23ms
• no multithreading (AMD 3.2GHz)
• C++ 32bit app (BDS2006 Turbo C++ or Borland C++ builder 2006 if you like)
• the slowest path I found was ~44ms (fill almost whole map)

I think that is fast enough ...

Here is source for mine A* class:

//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
const DWORD A_star_space=0xFFFFFFFF;
const DWORD A_star_wall =0xFFFFFFFE;
//---------------------------------------------------------------------------
class A_star
    {
public:
    // variables
    DWORD **map;        // map[ys][xs]
    int xs,ys;          // map esolution   xs*ys<0xFFFFFFFE !!!
    int *px,*py,ps;     // output points px[ps],py[ps] after compute()

    // internals
    A_star();
    ~A_star();
    void _freemap();                                    // release map memory
    void _freepnt();                                    // release px,py memory

    // inteface
    void resize(int _xs,int _ys);                       // realloc map to new resolution
    void set(Graphics::TBitmap *bmp,DWORD col_wall);    // copy bitmap to map
    void get(Graphics::TBitmap *bmp);                   // draw map to bitmap for debuging
    void compute(int x0,int y0,int x1,int y1);          // compute path from x0,y0 to x1,y1 output to px,py
    };
//---------------------------------------------------------------------------
     A_star::A_star()   { map=NULL; xs=0; ys=0; px=NULL; py=NULL; ps=0; }
     A_star::~A_star()  { _freemap(); _freepnt(); }
void A_star::_freemap() { if (map) delete[] map; map=NULL; xs=0; ys=0; }
void A_star::_freepnt() { if (px) delete[] px; px=NULL; if (py) delete[] py; py=NULL; ps=0; }
//---------------------------------------------------------------------------
void A_star::resize(int _xs,int _ys)
    {
    if ((xs==_xs)&&(ys==_ys)) return;
    _freemap();
    xs=_xs; ys=_ys;
    map=new DWORD*[ys];
    for (int y=0;y<ys;y++)
     map[y]=new DWORD[xs];
    }
//---------------------------------------------------------------------------
void A_star::set(Graphics::TBitmap *bmp,DWORD col_wall)
    {
    int x,y;
    DWORD *p,c;
    resize(bmp->Width,bmp->Height);
    for (y=0;y<ys;y++)
     for (p=(DWORD*)bmp->ScanLine[y],x=0;x<xs;x++)
        {
        c=A_star_space;
        if (p[x]==col_wall) c=A_star_wall;
        map[y][x]=c;
        }
    }
//---------------------------------------------------------------------------
void A_star::get(Graphics::TBitmap *bmp)
    {
    int x,y;
    DWORD *p,c;
    bmp->SetSize(xs,ys);
    for (y=0;y<ys;y++)
     for (p=(DWORD*)bmp->ScanLine[y],x=0;x<xs;x++)
        {
        c=map[y][x];
             if (c==A_star_wall ) c=0x00000000;
        else if (c==A_star_space) c=0x00FFFFFF;
        else                      c=((c>>1)&0x7F)+0x00404040;
        p[x]=c;
        }
    }
//---------------------------------------------------------------------------
void A_star::compute(int x0,int y0,int x1,int y1)
    {
    int x,y,xmin,xmax,ymin,ymax,xx,yy;
    DWORD i,j,e;
    // [clear previous paths]
    for (y=0;y<ys;y++)
     for (x=0;x<xs;x++)
      if (map[y][x]!=A_star_wall)
       map[y][x]=A_star_space;
/*
    // [A* no-optimizatims]
    xmin=x0; xmax=x0; ymin=y0; ymax=y0;
    if (map[y0][x0]==A_star_space)
     for (i=0,j=1,e=1,map[y0][x0]=i;(e)&&(map[y1][x1]==A_star_space);i++,j++)
      for (e=0,y=ymin;y<=ymax;y++)
       for (   x=xmin;x<=xmax;x++)
        if (map[y][x]==i)
        {
        yy=y-1; xx=x; if ((yy>=0)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; if (ymin>yy) ymin=yy; }
        yy=y+1; xx=x; if ((yy<ys)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; if (ymax<yy) ymax=yy; }
        yy=y; xx=x-1; if ((xx>=0)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; if (xmin>xx) xmin=xx; }
        yy=y; xx=x+1; if ((xx<xs)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; if (xmax<xx) xmax=xx; }
        }
*/
    // [A* changed points list]
    // init space for 2 points list
    _freepnt();
    int i0=0,i1=xs*ys,n0=0,n1=0,ii;
    px=new int[i1*2];
    py=new int[i1*2];
    // if start is not on space then stop
    if (map[y0][x0]==A_star_space)
        {
        // init start position to first point list
        px[i0+n0]=x0; py[i0+n0]=y0; n0++; map[y0][x0]=0;
        // search until hit the destination (swap point lists after each iteration and clear the second one)
        for (j=1,e=1;(e)&&(map[y1][x1]==A_star_space);j++,ii=i0,i0=i1,i1=ii,n0=n1,n1=0)
         // test neibours of all points in first list and add valid new points to second one
         for (e=0,ii=i0;ii<i0+n0;ii++)
            {
            x=px[ii]; y=py[ii];
            yy=y-1; xx=x; if ((yy>=0)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; px[i1+n1]=xx; py[i1+n1]=yy; n1++; map[yy][xx]=j; }
            yy=y+1; xx=x; if ((yy<ys)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; px[i1+n1]=xx; py[i1+n1]=yy; n1++; map[yy][xx]=j; }
            yy=y; xx=x-1; if ((xx>=0)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; px[i1+n1]=xx; py[i1+n1]=yy; n1++; map[yy][xx]=j; }
            yy=y; xx=x+1; if ((xx<xs)&&(map[yy][xx]==A_star_space)){ map[yy][xx]=j; e=1; px[i1+n1]=xx; py[i1+n1]=yy; n1++; map[yy][xx]=j; }
            }
        }
    // [reconstruct path]
    _freepnt();
    if (map[y1][x1]==A_star_space) return;
    if (map[y1][x1]==A_star_wall) return;
    ps=map[y1][x1]+1;
    px=new int[ps];
    py=new int[ps];
    for (i=0;i<ps;i++) { px[i]=x0; py[i]=y0; }
    for (x=x1,y=y1,i=ps-1,j=i-1;i>=0;i--,j--)
        {
        px[i]=x;
        py[i]=y;
        if ((y>   0)&&(map[y-1][x]==j)) { y--; continue; }
        if ((y<ys-1)&&(map[y+1][x]==j)) { y++; continue; }
        if ((x>   1)&&(map[y][x-1]==j)) { x--; continue; }
        if ((x<xs-0)&&(map[y][x+1]==j)) { x++; continue; }
        break;
        }
    }
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------
//---------------------------------------------------------------------------

I know it is a bit too much code but it is complete. The important stuff is in member function compute so search for [A* changed points list]. The unoptimized A* (rem-ed) is about 100 times slower.

Code use bitmap from Borland VCL so if you do not have it ignore functions get,set and rewrite them to your input/output gfx style. They just load map from bitmap and draw computed map back to bitmap

Usage:

// init
A_star map;
Graphics::TBitmap *maze=new Graphics::TBitmap;
maze->LoadFromFile("maze.bmp");
maze->HandleType=bmDIB;
maze->PixelFormat=pf32bit;
map.set(maze,0); // walls are 0x00000000 (black)
// this can be called repetitive without another init
map.compute(x0,y0,x1,y1); // map.px[map.ps],map.py[map.ps] holds the path
map.get(maze,0); // this is just for drawing the result map back to bitmap for viewing

for more info about A* see Backtracking in A star