In the basic technique for recombination of space images a mask for the secondary parent was used, which resembled on three sides the borders of the image. The fourth side described a curve, which defines an indistinct masquerade. So there a four kinds of masks, which fit to the image on the left, write upper or downer edge.
Image 1) Four mask classes
Also eccentric masks, which have an intersection on one side are covered by this definition.
Image 2) Eccentric 3 side mask
Further on generalization forms of the masks and joined with it, possibilities of positioning, will be discussed, which lead to different recombinations.
Instead of using three sides of an image as limitation of the image, one or two sides can be used as well.
Image 3) 2 Side masks and corresponding ROU
Image 4) 1 side mask and corresponding ROU
A mask or a ROU do not necessarily have contact to one side of the image. So free standing masks are produced, which are indistinct masked on all sides.
Image 5) Free standing masks and corresponding ROU
All described methods of recombination are based upon a two sexual recombination with exactly one mask of the secondary parent and with exactly one ROU of the primary parent. This is called in the evolutionary algorithms a one point recombination. This disposition can be extended by using more than one mask and one ROU which are coupled. From the given amount of masks a subset is derived, which shall be applied later on. Afterwards for every give mask a corresponding ROU is selected. If the amount of selected masks different from those of the selected ROUs, different techniques have to be applied. For example a generation of a ROUs subset. A special case occurs if less ROUs exist. A multiple usage of ROUs is not sensible, if the recombination is performed as an insertion operation. It is better, to reduce in such a case the a mount of masks. In the overall process the selection of recombination points are selected by a random number, which should be equal or less the amount of ROUs of the primary parent.
A multiple usage of masks for different ROUs is allowed. A recombination strategy can select the masks to a given ROU independent. In this recombination strategy the selection is driven by the primary parent.
Image 6) Recombination with two masks an a ROU
Another special case occurs, when overlapping ROUs are present. In such a case the sequence of the insertion operations are important. A recombination operation, which happens later, overwrites a part of the subset, which was created earlier by an insertion operation.
The amount of recombination parameters were regarded as parameters by a sexual recombination. Hence in a multiple sexual environment the distinction between secondary and primary parent should be held up. But now more than one secondary parent can be selected from the population and inserted into the parent population. Every secondary parent chooses a structure by one of his masks, which is later on inserted into the primary parent.
A control strategy is for the amount of ROUs of the primary parent is necessary. To define such a control strategy we start with a 1-mask recombination, every secondary parent is engaged in the generation of the offspring with exactly one mask. In such a case the primary parent is selected first from the population. Further, a subset of the ROU's are determined. The maximum amount is smaller or equal the amount of individuals in the rest population. Afterwards from the rest population as many secondary parents are selected as ROUs of the primary parents are selected. The selection should be performed sequential with or without putting back. Every ROU should be paired with a mask of the selected secondary parent. If there are no overlapping ROUs the sequence of the selection of the secondary parent from the rest population has non effect on the results.
Image 7) Multiple sexual recombination
Because of the analogy between ROIs and ROUs it is obvious to determine ROUs as rectangular. But this is not necessary. The form of ROUs of a primary parent could be solely defined by its central point. In the case of recombination those central point are paired with masks. The form of the masks is centered around the central point. This strategy would have the advantage that there is no need in applying any scaling even if the form of the mask and the ROUs differ.This would lead to an offspring with many errors. These could not be eliminated by post processings.
Image 8) ROU central point recombination
A significant divagating form of recombination occurs if the two pictures have different sizes or if a scaling operation is performed as part of a mutation (e.g. the secondary parent). Further on we shall discuss the case, that the secondary parent is enlarged and a 3 sides mask is used. In addition the primary parent shows an adequate 3 sides mask (image 9). In contrast to the other utilization of the two parents a non rectangular descendant arises - or an interim phase, from which the offspring is selected by an additional selection operation. It could be useful to chose along the middle axes a rectangular selection which laps over the borders of the primary parent. The left side of the descendant comes from the secondary parent. This can be seen in image 9), represented by a black surrounded rectangular. The difference between the basic recombination is, that parts of the secondary parent are enlarged and that the possibility exists to move the primary parent along the middle axes of both pictures up and down.
Image 9) Recombination strategy with strongly divergent scalings
