Whale Optimization Algorithm Dr. Ahmed Fouad Ali Faculty of Computers and Informatics Suez Canal University

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

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.

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.

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.

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

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.

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]

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.

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].

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]

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.

The WOA algorithm

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

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

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