Crow search algorithm

1. Crow Search Algorithm
DR. AHMED FOUAD ALI
FACULTY OF COMPUTERS AND INFORMATICS
SUEZ CANAL UNIVERSITY

2. Outline
 Crow search algorithm (History and main idea)
 Social behavior and inspiration.
 Crow search algorithm implementation.
 Crow search algorithm.
 References.

3. Crow search algorithm (History and main idea)
 Crow search algorithm (CSA) is a nature-
inspired algorithm, proposed by A. Askarzadeh
in 2016 .
 CSA is a population based method.
 CSA mimics the behavior of crow birds and
their social interaction.

4. Social behavior and inspiration
 Crows are intelligent birds which have large
brain relative to their body size.
 They are living in group (flock).
 They hide their foods in hiding places.
 They can memorize these places and retrieve
the hidden foods even after several months.

5. Social behavior and inspiration (Cont.)
 Crows can do thievery by following the other
crows in order to watch their food's hiding
places and steal the hidden food.
 If a crow feels that another one is following it,
it moves to another place far away form the
food's hiding place in order to fool a thief.

6. Crow search algorithm implementation.
 The crow search algorithm (CSA) mimics the
social behavior of the crow birds as shown in
the following items.
 {Initialization}. The crows in the group
represent the search agent (solution) in the
population, the search space represents the
environment.
 The population contains N solutions.
 The position of each crow i at iteration t is
represented by a vector xt
i ,
where xt
i = [xt
i1, xt
i2, ..., xt
id] and d is a problem
dimension.

7. Crow search algorithm implementation (Cont.)
 The whole population of size N with dimension
d at iteration t can be represented as follow

8. Crow search algorithm implementation (Cont.)
 {Memory Initialization.} The memory M of all
crows (population) at iteration t for dimension d
are initialized as follow.

9. Crow search algorithm implementation (Cont.)
 {Solution evaluation.} Each solution in the
population is evaluated by calculating its fitness
by using the fitness function (objective function)
f(xi
(t+1) ).
 {Position update.} The crow (solution) i can
update its position based on the position of
crow j (a random selected solution in the
population) in order to discover its food's
hiding place.
 During the movement of crow i toward crow j
two stats can happen.

10. Crow search algorithm implementation (Cont.)
 State 1: If crow j does not watch crow i when it follow
it, crow i will discover the food's hiding place of crow j
and the crow i will update its position as follow.
Where ri is random number in the interval [0,1], fli
(t) is the
flight length and mj
(t) is the memory of crow j.
The value of fl is responsible for the exploration and
exploitation processes, if fl < 1, it means the crow i will
move toward crow j which lead to local search while if
fl > 1 it means the crow i will move far from crow j which
leads to global search.

11. Crow search algorithm implementation (Cont.)
 State 2: The another state is happened when the crow j
knows that crow i is watching it and it discovered its
food's hiding place.
 At this case the crow j move random to fool crow i.
 The two states are based on the awareness probability
Apt
i of each crow in the population as follow.
Where Apt
i is the awareness probability.
The CSA balancing between exploration and
exploitation processes according to the value of Apt
i .
Increasing the value of Apt
i leads to global search while
decreasing the value of Apt
i leads to local search.

12. Crow search algorithm implementation (Cont.)
 {Memory update.} Each crow (solution) updates its
memory according to fitness value.
 If the fitness value of the new crow's position is better
than the current memory's value then it updates its
memory otherwise the memory will not changed.
 The process of updating memory is shown as follow.

13. Crow search algorithm.

14. Crow search algorithm (Cont.)
 {Parameters initialization.} At the beginning, we set the initial values for the
flight length fl, awareness probability AP parameters, the population size N and
the maximum number of iterations maxitr.
 {Iteration counter initialization.} we set the initial iteration's counter, where t = 0.
 { Population initialization.} we generate the initial population randomly, each
solution in the population is vector where xi
(t) ∈ [L,U] randomly, i = 1,…,N.
 { Solution evaluation.} Each solution in the population is evaluated by calculating
it fitness function.
 { Memory initialization.} The initial memory for each solution in the population
is a vector m (t) and it is assigned after calculating its fitness function.

15. Crow search algorithm (Cont.)
 {Solution update.} The main loop of the algorithm is repeated until the termination
criteria are satisfied.
 Each solution in the population is updated according to the value of the awareness
probability as shown in Equations 1 and 2.
 {Solution feasibility.} The solution's new position is accepted if its value is feasible,
otherwise its rejected and the current solution is kept.
 {Memory update.} In Equation 3, the memory of each solution is updated
according to the fitness of it.
 If the fitness value of each solution is better than the current solution's memory
value then the memory is updated otherwise the memory is not updated.
 {Best solution produced.} Once the termination criteria are satisfied, the overall
best solution is produced.

16. References
 A. Askarzadeh. A novel meta-heuristic method for solving constrained
engineering optimization problems: crow search algorithm. Computers &
Structures, 169, 1-12, 2016.