Whale optimization algorithm

1. Whale Optimization Algorithm
DR. AHMED FOUAD ALI
FACULTY OF COMPUTERS AND INFORMATICS
SUEZ CANAL UNIVERSITY

2. Outline
 Whale Optimization Algorithm (WOA) (History and main idea)
 Inspiration and foraging behavior
 The basic concepts of the Whale optimization algorithm
 Encircling prey
 Exploitation phase: bubble-net attacking method
 Exploration phase: search for prey
 The WOA algorithm
 References

3. Whale Optimization Algorithm (WOA)
(History and main idea)
 The whale optimization algorithm
(WOA) is a novel meta- heuristics
algorithm proposed by Mirjalili at. el
 WOA is a population based method
 WOA simulate bubble-net attacking
method of the humpback whales when
they hunting their preys.

4. Inspiration and foraging behavior
 Whales are considered as the biggest mammals in
the world.
 They are intelligent due to the spindle cells in
their brain.
 The whales are living in groups and they are able
to develop their own dialect.
 There are 7 types of whales and the humpback
whale is one of these types.

5. Inspiration and foraging behavior (Cont.)
 It has a special hunting mechanism which is
called bubble-net feeding method.
 This foraging behavior is done by crating a
special bubbles in a spiral shape or (9 shape)
path.

6. The basic concepts of the Whale optimization
algorithm (Encircling prey)
 Humpback whales know the location of prey and
encircle them.
 They consider the current best candidate solution
is best obtained solution and near the optimal
solution.
 After assigning the best candidate solution, the
other agents try to update their positions towards
the best search agent as shown in the following
equation

7. The basic concepts of the Whale optimization
algorithm (Encircling prey) (Cont.)
Where t is the current iteration, A and C are
coefficient vectors, X* is the position vector of the
best solution, and X indicates the position vector of a
solution, | | is the absolute value.

8. The basic concepts of the Whale optimization
algorithm (Encircling prey) (Cont.)
The vectors A and C are calculated as follows:
Where components of a are linearly decreased from
2 to 0 over the course of iterations and r is random
vector in [0; 1]

9. Exploitation phase: bubble-net attacking method
 The humpback whales attack the prey with the
bubble-net mechanism.
 This mechanism is mathematical formulated as
follow:
 {Shrinking encircling mechanism:
In this mechanism, the value of A is a random
value in interval [-a, a] and the value of a is
decreased from 2 to 0 over the course of iterations
as shown in Eq. 9.

10. Exploitation phase: bubble-net attacking method
(Cont.)
 Spiral updating position mechanism
In this mechanism, the distance between the
whale location and the prey location is calculated
then the helix-shaped movement of humpback is
created as shown in the following equation
Where D’ =| X*(t) - X(t) | is the distance between
the prey (best solution) and the ith whale, b is a
constant, l is a random number in [-1; 1].

11. Exploitation phase: bubble-net attacking method
(Cont.)
 The humpback whales used the mentioned two
mechanisms when they swim around the prey.
 We set the mathematical model of these two
mechanisms, we assume that there is a
probability of 50% to chose between these two
mechanisms to update the position of whales as
follow
Where p is a random number in [0; 1]

12. Exploration phase: search for prey
In the exploration phase, the humpback whales
(search agents) search for prey (best solution)
randomly and change their positions according the
position of other whales.
In order to force the search agent to move far a way
from reference whale, we use the A with values > 1
or < 1
The mathematical model of the exploration phase is
as follows
Where Xrand is a random position vector chosen
from the current population.

13. The WOA algorithm

14. The WOA algorithm (Cont.)
Step 1. The standard whale optimization algorithm starts by setting the
initial values of the population size n, the parameter a, coefficients A and
C and the maximum number of iterations max_itr. line 1.
Step 2. Initialize the iteration counter t. lines 2.
Step 3. The initial population n is generated randomly and each search
agent Xi in the population is evaluated by calculating its fitness
function f(Xi). lines 3-6.
Step 4. Assign the best search agent X. line 7
Step 5. The following steps are repeated until the termination criterion
Satisfied. lines 9-30

15. The WOA algorithm (Cont.)
Step 5.1. The iteration counter is increasing t = t + 1. line 9
Step 5.2. All the parameters a,A, C, l and P are updated. line 11
Step 5.3. The exploration and exploitations are applied according to the
values of p and | A | line 12-27
Step 6. The best search agent X is updated. line 28
Step 7.The overall process is repeated until termination criteria satisfied.
line 29
Step8. Produce the best found search agent (solution) so far X. line 30

16. References
S. Mirjalili and A. Lewis, The Whale Optimization
Algorithm. Advances in Engineering Software, 95, (2016),
pp.51-67