How do I implement genetic algorithm on placing 2 or more kinds of element with different (repeating)distances in a grid?
Please forgive me if I do not explain my question clearly in title. Here may I show you two pictures as my example:
my question is described as follows: I have 2 or more different objects(In the pictures, two objects: circle and cross), each one is placed repeatedly with a fixed row/column distance (In the pictures, the circle has a distance of 4 and cross has a distance of 2) into a grid.
In the first picture, each of the two objects are repeated correctly without any interruptions(here interruption means one object may occupy another one's position), but the arrangement in the first picture is ununiform distributed; on the contrary, in the second picture, the two objects may have interruptions (the circle object occupies cross objects' position) but the picture is uniformly distributed.
My target is to get the placement as uniform as possible (the objects are still placed with fixed distances but may allow some occupations). Is there a potential algorithm for this question? Or are there any similar questions?
I have some immature thinkings on this problem that: 1. occupation may relate to least common multiple; 2. how to define "uniformly distributed" mathematically? Maybe there's no genetic solution but is there a solution for some special cases? (for example, 3 objects with distance of multiple of 2, or multiple of 3?)
Uniformity can be measured as sum of squared inverse distances(or distances to equilibrium distances). Because it has squared relation, any single piece that approaches others will have big fitness penalty in system so that the system will not tolerate too close piece and prefer a better distribution.
If you do not use squared (or higher orders) distance but simple distance, then system starts tolerating even overlapped pieces.
If you want to manually compute uniformity, then compute the standard deviation of distances. You'd say its perfect with 1 distance and 0 deviation but small enough deviation also acceptable.
I tested this only on a problem to fit 106 circles in a square thats 10x the size of circle.
