

![0_image_0.png](0_image_0.png)

It is weaker during the first generations in the anisotropic case then it becomes slightly stronger, to finally fill the grid at the same takeover time.

## 5. Anisotropic Selection And Niching

Many real optimization problems require the coexistence of diverse solutions during the search. In this section we show how the anisotropic selection is able to promote niching.

## 5.1 Niching Methods

Niching methods have been proposed in the field of genetic algorithms to preserve population diversity and to allow the GA to investigate many peaks in parallel. As a side effect, niching prevents the GA from being trapped in local optima.

Niching methods are inspired from nature where species specialize themselves to different ecological niches in order to decrease the selective pressure they undergo. Niching GA's tend to achieve a natural emergence of niches in the search space. A niche is commonly referred to as an optimum of the domain, the fitness representing the resources of that

![0_image_1.png](0_image_1.png) 

niche [12]. Niching methods are used to solve multimodal problems, and also in dynamic optimization [4]. For such problems a GA must maintain a diverse population that can adapt to the changing landscape and locate better solutions dynamically. There are different niching GA for panmictic population: sharing, crowding, etc. These methods are based on the concept of distance: sharing [7] decreases the fitness according to the number of similar individuals in the population, and with crowding, replacement is performed considering the distance between solutions.

## 5.2 Experimental Results

To show up to what extent anisotropic selection promotes niching, we have conducted experiments where two solutions with the best fitness (here 1) are placed on a 64 × 64 square grid at the initial generation. These solutions are farther from each other in the least favored direction (here oriented horizontally). Figure 5.2 shows some snapshots of the spreading of the two bests over generations for different anisotropic degrees. Cells in light grey (resp. dark grey) are copies of the first best (resp. the second best), and all white cells have a null fitness value. Generations grow from top to bottom, and the anisotropic parameter α **increases from**
left to right. The left-hand row (α **= 0) represents standard**
binary tournament schema ; we observe that standard selection is not able to maintain niches, after 1000 generations the grid is a mixture of the two optima. On the other hand, as α **increases, two stable frontiers between niches emerge.**
Hence AS increases cohesion in each cells lineages.