Fiber-to-Object Assignment Problem (FOAP) comes from Astronomy. This geometrical and combinatorial problem is to arrange the maximum of segments – or rectangles – in the plane without crossovers. To solve this problem, we have recursively built a series of heuristic algorithms that converge on a maximal solution. Anyway the first elements of the series give good results quickly. They can be improved by post-optimization heuristics based on the same heuristics. Our results show that these heuristics are able to reach the best solution within a few minutes.