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POAnt colony simulation - optimizing the path
 

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    <p>I am trying to build a simple ant colony simulation. The world is grid of squares; each one of them can consist of some level of pheromone and any number of ants. There are 2 types of pheromone: food pheromone and nest pheromone. Ants know nothing about the environment, but ants that return to nest follow nest pheromone (in the sense that they almost always choose to move to the cell with the maximum pheromone level, among all nearby cells) and leave food pheromone, and vice versa.</p> <p>From time to time the ants make random moves not in the direction of maximum pheromone. Each tick of the simulation the ant checks the level of the pheromone in 8 nearby cells, and if the pheromone level in the current cell is less then the maximum of pheromone level in all nearby cell, it adds some pheromone. </p> <p>The current simulation works pretty well, but the path found is not the optimal one. I have 2 problems that I don't know how to solve:</p> <ol> <li>How do I simulate the fact that the diagonal move is longer than the non-diagonal move (up,down left or right)?</li> </ol> <p><img src="https://i.stack.imgur.com/1Hal9.jpg" alt="In the current situation, black path and blue path are equal in length. In realty, however, blue path is shorter."></p> <ol> <li>How should I simulate the diffusion of the pheromone? Right now, the pheromone evaporates over time but there is no diffusion. I have tried to transfer some amount of the pheromone from each cell, each tick of the simulation, to the 8 nearby cells, but the result was a total mess - the whole environment was full with pheromone - I think it was because of the mechanism the ants use to adjust the pheromone level.</li> </ol>
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    1. COWhy the diagonal move is longer than the non-diagonal one? What do you mean?
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    2. COOn my current simulation, ants can move to either one of 8 neighbour cells, with same "speed". In this situation, ant can move from nest to food in straight line, or in zigzag path, and the distance (=number of cells it passed on, and therefore the period of each cycle from nest to food) will be the same. In realty, of course, zigzag path (north-east, north-west, south-east, south-west) is longer then straight path (north,south, east and west). I added an illustration.
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    3. COHave you tried to add some penalty to diagonal corners, when looping through 8 neighbor cells? This will prevent in case of equality to choose a diagonal move. You can try and adjust the penalty value.
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