How can I find the shortest path between 100 moving targets? (Live demo included.)

Question

Background

This picture illustrates the problem:

I can cont

Answer 1

Greedy method

One approach suggested in the comments is to go to the closest target first.

I've put up a version of the demo which includes the cost calculated via this greedy method here.

The code is:

function greedyMethod(start_x,start_y) {
  var still_to_visit = (1<

For 10 targets it is around twice the optimal distance, but sometimes much more (e.g. *4) and occasionally even hits the optimum.

This approach is very efficient so I can afford some cycles to improve the answer.

Next I'm considering using ant colony methods to see if they can explore the solution space effectively.

Ant colony method

An Ant colony method seems to work remarkable well for this problem. The link in this answer now compares the results when using both greedy and ant colony method.

The idea is that ants choose their route probabilistically based on the current level of pheromone. After every 10 trials, we deposit additional pheromone along the shortest trail they found.

function antMethod(start_x,start_y) {
  // First establish a baseline based on greedy
  var L = greedyMethod(start_x,start_y);
  var n = pts.length;
  var m = 10; // number of ants
  var numrepeats = 100;
  var alpha = 0.1;
  var q = 0.9;
  var t0 = 1/(n*L);

  pheromone=new Array(n+1); // entry n used for starting position
  for(i=0;i<=n;i++) {
    pheromone[i] = new Array(n);
    for(j=0;jbestc) {
              besti = i;
              bestc = c;
            }
          }
        }
        if (Math.random()>0.9) {
          thresh = totalh*Math.random();
          for(i=0;i

Results

This ant colony method using 100 repeats of 10 ants is still very fast (37ms for 16 targets compared to 3700ms for the exhaustive search) and seems very accurate.

The table below shows the results for 10 trials using 16 targets:

   Greedy   Ant     Optimal
   46       29      29
   91       38      37
  103       30      30
   86       29      29
   75       26      22
  182       38      36
  120       31      28
  106       38      30
   93       30      30
  129       39      38

The ant method seems significantly better than greedy and often very close to optimal.