Paintings, Polygons and Plant Propagation

It is possible to approximate artistic images from a limited number of stacked semi-transparent colored polygons. To match the tar- get image as closely as possible, the locations of the vertices, the drawing order of the polygons and the RGBA color values must be optimized for the entire set at once. Because of the vast combinatorial space, the rel- atively simple constraints and the well-defined objective function, these optimization problems appear to be well suited for nature-inspired opti- mization algorithms.
In this pioneering study, we start off with sets of randomized poly- gons and try to find optimal arrangements for several well-known paint- ings using three iterative optimization algorithms: stochastic hillclimb- ing, simulated annealing and the plant propagation algorithm. We discuss the performance of the algorithms, relate the found objective values to the polygonal invariants and supply a challenge to the community.