Gray Wolf Optimization
Gray wolf optimization is presented in the following subsections based on the work in [13].
1) Inspiration: Grey wolves are considered as apex predators, meaning that they are at the top of the food chain. Grey wolves mostly prefer to live in a pack. The group size is 512 on average.They have a very strict social dominant hierarchy.
The leaders are a male and a female, called alphas. The alpha is mostly responsible for making decisions about hunting, sleeping place, time to wake, and so on. The alphas decisions are dictated to the pack.
The second level in the hierarchy of grey wolves is beta. The betas are subordinate wolves that help the alpha in decisionmaking or other pack activities. The beta wolf can be either
male
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Omega wolves always have to submit to all the other dominant wolves. They are the last wolves that are allowed to eat.
The fourth class is called subordinate (or delta in some references). Delta wolves have to submit to alphas and betas, but they dominate the omega. Scouts, sentinels, elders, hunters, and caretakers belong to this category. Scouts are responsible for watching the boundaries of the territory and warning the pack in case of any danger. Sentinels protect and guarantee the safety of the pack. Elders are the experienced wolves who used to be alpha or beta. Hunters help the alphas and betas when hunting prey and providing food for the pack. Finally, the caretakers are responsible for caring for the weak, ill, and wounded wolves in the pack.
2) Mathematical model: In the mathematical model for the
GWO the fittest solution is called the alpha (α). The second and third best solutions are named beta (β) and delta (δ) respectively. The rest of the candidate solutions are assumed to be omega (ω). The hunting is guided by α, β, and δ and the ω follow these three candidates.
In order for the pack to hunt a prey they first encircling it. In order to mathematically model encircling behavior the following equations are used
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−→
D (11) where −→
D is as defined in 12 and t is the iteration number,
−→
A ,
−→
C are coefficient vectors,
−→
X p is the prey position, . is dot product and
−→
X is the gray wolf position.
−→
D = |
−→
C .
−→
X p
(t) −
−→
X (t)| (12)
The
−→
A ,
−→
C vectors are calculated as in equations 13 and
14
−→
A = 2
−→
A .
−→
r
1 −
−→
a (13)
−→
C = 2
−→
r
2 (14) where components of
−→
a are linearly decreased from 2 to 0 over the course of iterations and r
1
, r2 are random vectors in [0, 1]. The hunt is usually guided by the alpha. The beta and delta might also participate in hunting occasionally. In order to mathematically simulate the hunting behavior of grey wolves, the alpha (best candidate solution) beta, and delta are assumed to have better knowledge about the potential location of prey. The first three best solutions obtained so far and oblige the other search agents (including the omegas) to update their positions according to the position of the best search agents.
So the updating for the wolves positions is as in equations
15,16,17.
−→
Dα = |
−→
C1.
−→
Xα −
−→
X |,
−→
Dβ = |
−→
C2.
−→
Xβ −
−→
X |,
−→
Dδ = |
−→
C3.
−→
Xδ −
−→
X |
(15)
−→
X1 = |
−→
Xα−
−→
A1.
−→
Dα
|,
−→
X2 = |
−→
Xβ −
−→
A2.
−→
Dβ
|,
−→
X3 =
The human mind is very powerful, whether were trying to figure out what we don’t know, or trying to persuade others to fear the same as we do. With this fear mankind is set on a path of destruction. To conquer their fears humans often act out by violence. This violent outbreak doesn’t solve the problem but instead makes it worse. Wolves are examples of the ways humans handle their fears. Humans don’t understand the behaviors of wolves and that makes them believe that they are bad and should be feared. Mowats time researching the wolves has led him to believe that it isn’t the wolves who are the ones to blame, but the humans who were the cause of the main problem; the decrease in caribou. Mankind needs to realize that fear is a natural thing that occurs in everything, and we shouldn’t let our fears drive us to make bad decisions that we might regret later.
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During the night of April 19, 1989 a young woman was brutally raped and beaten while she went for a jog in Central Park. The rapist left her for dead lying in her own pool of blood. When she was found by a near Officer. The Central Parker Jogger went into a coma due to her severe injuries and was place on life support once she arrived to the hospital. Within a few hours after the crime six black and latino teenagers between the ages of 14-16 were picked up and questioned about their where about during the attack. The next day everyone found out about the horrifying news through the press the city went into an outrage and wanted justice for the victim. The city became divided between the whites and blacks and latinos communities.
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Generally, grey wolves want to live in a pack. The gathering size is from 5 to 12 by and large. They have extremely strict standards in the social predominant progressive system. As per \cite{GWO1} grey wolf pack comprises of the accompanying:
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