## 4 A Strategy Based on a Segmentation of the Search Domain's
### Problem Description  
The present section refers to point 2 of the introduction. It describes the procedure introduced in Part B-2 in Figure 1. Figure 5 presents the corresponding pseudocode. The illustration again divides the algorithm into two parts. Part C corresponds to the dimensionality reduction steps, while Part D describes the Distribution tasks. Numbers also mark the beginning positions of the operation groups. It is worth mentioning here that Part D-4 decides the particle type based on the generation order: the females compose the first segment of the distribution, the sage males, the second, and the intrepid males, the last. Since the segment order in the distribution does not change during the iterations, it tags the particles with their precise types. The proposed technique divides the domain into \(S\) regular segments along each \(D\) dimension. The procedure first uniformly apportions the particles to the resulting \(S^{D}\) subdomains. Then, it uniformly distributes them over each subdivision (Part A in Figure 1). Depending on the number of particles and the domain dimensions, the distribution process may produce some remaining individuals. Thus, at the end of the process, these remainders are individually assigned to random positions of the landscape. While this uniform distribution operation may significantly help the scan evolution, it remains insufficient to guarantee an always fully successful search. Rather, it serves as the first step in the preparation of the initial distribution of the individuals over the landscape. Moreover, in practice, any augmentation of the probed domain dimensionality will strongly affect this strategy. The authors of Ref. [19] faced a similar situation with the automatic niching ability of their algorithm. To solve the problem, the authors of [19] first reduced the domain dimensionality via a Principal Component Analysis (PCA). Since the domain segmentation introduced herein and defined by the \(S^{D}\) subdomains would rapidly require unmanageable numbers of particles, the second step (Part C in Figure 5) aims to reduce the problem dimensionality. It should reduce the number of dimensions considered during the segmentation from \(D\) to \(D^{*}\). Therefore, instead of \(S^{D}\), the operation will involve \(S^{D^{*}}\) subdomains. Based on the Ref. [19] suggestion, the maximal value for \(D^{*}\) here is three. Thus, if \(D\leq 3\), then \(D^{*}=D\), otherwise \(D^{*}=3\). The third step (Part D in Figure 5) aims at apportioning the particles to the \(S^{D^{*}}\) subdomains more efficiently, or, more specifically, apportioning the particles based on biased decisions established during pre-evaluations of the potential of the subdomains. The first uniform particle distributions made over each subdomain allow pre-probing of their worth. The evaluation of the potential of a zone is ultimately similar to the optimization process itself. Given its role, the pre-probing step must thus offer a rough but reliable description at the lowest possible computation cost. When observing landscapes such as the 2D Vincent function (36 minima) illustrated in Figure 6a, it appears that the potential of a zone to contain multiple optima can be depicted and evaluated by its jaggedness. On the other hand, when looking at the 2D Himmelblau function (4 minima) presented in Figure 6b, it seems clear that in the context of minimization, the jaggedness aspect has no bearing and cannot serve in a pre-probing strategy. In fact, a comparison of the function local or subdomain means to the overall average would be preferable to pre-identifying the zones closer to the four minima. On the  
Figure 5: Pseudocode of the weighted generation of the particle distribution. contrary, the means of the subdivisions would provide no valid insights into the nature of the Vincent function, since it essentially combines sine functions.