Canis lupus

Blood samples from 256 dogs and seven Apennine wolves (Table 1) were collected following the European Rules for Animal Welfare when collected in Italy and approved National Human Genome Research Institute (NHGRI) Animal Care and Use Committee protocols when collected or received in the United States. The dog populations represent 23 breeds or varieties of historical Italian origin. The ENCI recognizes 13 of these populations as purebreeds and nine of which are also recognized by the AKC. Ten populations are termed “varieties,” and represent regional homogeneous populations, generally managed by informal registries and maintained by owners for specific behavioral applications. Three breeds, the Cane Corso, Italian Greyhound, and Neapolitan Mastiff, were sampled from Italian populations to compliment a preexisting collection of American populations of the same breeds. Animals selected for analysis were as distantly related as possible based on pedigree information from ENCI. DNA extraction was performed with the commercial Qiagen DNeasy Blood & Tissue Kit. Samples were genotyped on the Illumina CanineHD bead chip (Illumina, San Diego, CA, USA), which contains 172,115 potential markers, in the Ostrander laboratory at the National Human Genome Research Institute (NHGRI) of the National Institutes of Health (Bethesda, MD, USA) using manufacturer's recommended protocols.
Genotyped samples were merged with a larger dataset of 1,346 dogs representing 161 breeds (described in (Parker et al., 2017)) and publically available genotypes from five New Guinea Singing Dogs and three Catahoula Leopard Dogs (Hayward et al., 2016) to produce a dataset of 1,609 dogs representing 182 breeds, seven Apennine wolves, seven global Grey wolf representatives, and two Golden Jackals.

The gray wolf optimization algorithm (GWO) is a pack intelligence optimization algorithm designed by Mirjalili [54 (link)]. It was inspired by the social stratification characteristics and hunting and trapping behavior of wolves. It has the advantages of strong convergence performance, a simple structure, and easy implementation. There exist convergence factors with self-adaptive adjustment and information feedback mechanisms. Thus, a balance between local optimization and global optimization is achieved. For this reason, it has good problem-solving accuracy. Gray wolves are divided into four social classes: $\alpha ,\beta ,\delta ,\omega$ . After sorting according to the adaptation function, $\alpha$ wolves represent the optimal solutions. $\beta$ wolves and $\delta$ wolves represent the suboptimal solutions, with their role to assist $\alpha$ wolves in making decisions. The remaining candidate solutions are defined as $\omega$ wolves. Classes of $\alpha$ wolves, $\beta$ wolves, and $\delta$ wolves command the hunting behavior, and $\omega$ wolves follow the above-mentioned higher-level wolves in hunting. Since the position of the prey (the optimal solution) in the solution space is not known, it is assumed that the positions of wolf $\alpha$ , wolf, and wolf $\delta$ are closest to the prey.
As shown in Figure 8 [54 (link)], the hunting process of the gray wolf surrounding prey is represented by the following mathematical model: $$\overrightarrow{D}=\left|\overrightarrow{C}\cdot {\overrightarrow{X}}_P(t)-\overrightarrow{X}(t)\right|$$
$$\overrightarrow{X}(t+1)={\overrightarrow{X}}_p(t)-\overrightarrow{A}\cdot \overrightarrow{D}$$
where $\overrightarrow{C}$ and $\overrightarrow{A}$ are coefficient vectors determined by random values, $\overrightarrow{X_p}\left(t\right)$ and $\overrightarrow{X}\left(t\right)$ represent the position vector of the prey and the position vector of the gray wolf at iteration up to the t-th generation, respectively [54 (link)]. Since the location of the optimal solution in the solution space is not known, it is assumed that the locations of wolf $\alpha$ , wolf $\beta$ , and wolf $\delta$ are closest to the optimal solution. After recording the positions of these three wolves, the $\omega$ wolf is ordered to approach the $\alpha$ wolf, and the $\beta$ wolf is ordered to approach the $\delta$ wolf. During each iteration, the positions of the $\alpha$ wolf, the $\beta$ wolf, and the $\delta$ wolf are updated via the formulae shown in Equation (12) [54 (link)]: $${\overrightarrow{D}}_{\alpha }=\left|{\overrightarrow{C}}_1\cdot {\overrightarrow{X}}_{\alpha }-\overrightarrow{X}\right|{\overrightarrow{D}}_{\beta }=\left|{\overrightarrow{C}}_2\cdot {\overrightarrow{X}}_{\beta }-\overrightarrow{X}\right|D_{\delta }=\left|{\overrightarrow{C}}_3\cdot {\overrightarrow{X}}_{\delta }-\overrightarrow{X}\right|$$
$${\overrightarrow{X}}_1={\overrightarrow{X}}_{\alpha }-{\overrightarrow{A}}_1\cdot ({\overrightarrow{D}}_{\alpha }){\overrightarrow{X}}_2={\overrightarrow{X}}_{\beta }-{\overrightarrow{A}}_2\cdot ({\overrightarrow{D}}_{\beta }){\overrightarrow{X}}_3={\overrightarrow{X}}_{\delta }-{\overrightarrow{A}}_3\cdot ({\overrightarrow{D}}_{\delta })$$
Averaging the positions of the $\alpha$ wolf, the $\beta$ wolf, the $\delta$ wolf, and the result obtained is regarded as the final position after this iteration is updated. When $\left|\overrightarrow{A}\right|<1$ in Equation (12), the next generation of gray wolves can be located anywhere near the prey. The constant repetition of this behavior is to hunt the prey. It is worth mentioning that in order to prevent falling into local optimal solutions during the optimization process, the gray wolf chooses to move away from the prey when $\left|\overrightarrow{A}\right|>1$ .
To enable the gray wolf optimization algorithm to perform multi-objective optimization, Mirjalili provided two components [55 (link)]. One is a storage component responsible for storing non-dominated Pareto optimal solutions, which implements the storage function of several optimal solutions. The other is a leader-selection strategy component, which can obtain dominance relations with the help of the Pareto global optimum concept but cannot compare solutions that are not dominated by each other. This component selects a new leader in the uncrowded region of non-dominated solutions according to the roulette wheel method, marked as $\alpha ,\beta ,\delta$ , which is then archived.
In this study, two objective functions were chosen as constraints and the expressions are as shown in Equation (14): $$\begin{array}{l}Minimize:f_1(x)=-P\\ Minimize:f_2(x)=HIx={[x_1,x_2,\dots ,x_6]}^T,x\in (x_L,x_U)\end{array}$$
where P and HI represent the random forest HI prediction model and the random forest indentation pressure generation prediction model, respectively, $x_i\left(i=1,2,\dots ,6\right)$ represents the i-th design parameter, and $x_L$ and $x_U$ are the upper and lower bounds of each design parameter, respectively. All codes in this paper were written in the MATLAB environment, the number of populations in each iteration was set to 100, and the maximum number of external archives was chosen to be 100, for a total of 400 iterations, running on a PC with Inlet(R) Core(TM) i7-12700 k CPU 5.00 GHz 32 GB RAM.

The overall optimization process for the blood pump is divided into three parts (Figure 1). The first step is the creation of a random forest prediction model. First, the parameters and boundary values controlling the impeller shape are determined. Then, 240 sets of impeller parameters are randomly obtained using the Latin hypercube sampling method, and a 3D model is built and numerically simulated to obtain a database consisting of impeller parameters and pressure generation, and HI values. Thereafter, the random forest prediction model is trained. The second part is multi-objective optimization, using the multi-objective gray wolf optimizer (MOGWO) to calculate the Pareto front. This involves selecting three different optimized models in the Pareto front for modeling and performing the numerical simulation. In the third part, the internal flow differences between the baseline model and the optimized model are analyzed, and the model with the best-combined situation is selected. Each step is described carefully in the following section.