Chicken swarm optimization (CSO)

A New Bio-inspired Algorithm Chicken Swarm Optimization
Xianbing Meng, Yu Liu, Xiaozhi Gao, and Hengzhen Zhang
Supervisor: Dr. Ahmed ElSawy
Presented by : Abdelrahman Alaa & Mohamed Wagih

Abstract
A new bio-inspired algorithm, Chicken Swarm Optimization (CSO), is proposed
for optimization applications. Mimicking the hierarchal order in the chicken
swarm and the behaviors of the chicken swarm, including roosters, hens and
chicks, CSO can efficiently extract the chickens’ swarm intelligence to optimize
problems. Experiments on twelve benchmark problems and a speed reducer
design were conducted to compare the performance of CSO with that of other
algorithms. The results show that CSO can achieve good optimization results in
terms of both optimization accuracy and robustness.
2

Agenda
 Introduction
 General Biology
 Chicken Swarm optimization (CSO)
 Movement of Chickens
 Parametric Analysis
 Validation and Comparison
 Benchmark Problems Optimization
 Speed Reducer Design
 Discussion
 References
3

Expectation
VS
Reality
4
Introduction

5
Introduction
Background
 Chickens are kept as food source and Live together in flocks
 Communicate using over 30 distinct sounds “clucks, cackles, chirps and cries”
including a lot of information “nesting, food discovery, mating and danger”
 Learn through trial, error and previous experience

6
Introduction
 CSO mimics the hierarchal order in the chicken swarm
and the behaviors of the chicken swarm.
Hierarchal order? Behaviors of the chicken swarm?

7
Introduction
 Chicken Swarm Hierarchal order

8
Introduction
Chicken swarm can be divided into several groups
each Group contains : 1 Rooster + many hens + many chicks
Competition between different chickens under specific order

9
General Biology
Hierarchal order
 A hierarchal order plays a significant role in the social lives of chickens
 The preponderant chickens will dominate the weak
 More dominant hens that remain near to the head roosters
 The More submissive chicken stand at the periphery of the group
 Removing or adding chickens from an existing group would causes
a temporary disruption to the social order until a specific hierarchal order
is established

10
General Biology
Hierarchal order
 The dominant individuals have priority for food access
 Roosters may call their group-mates to eat first when they find food
 Gracious behavior also exists in the hens when they raise their children.
 However, this is not the case existing for individuals from different groups.
Roosters would emit a loud call when other chickens from a different group
invade their territory

11
General Biology
Hierarchal order In General
 The chicken’s behaviors vary with Gender
 The head rooster would positively search for food, and fight with chickens
who invade the territory the group inhabits
 The dominant chickens would be nearly consistent with the head roosters
to forage for food
 The submissive ones, however, would reluctantly stand at the periphery of
the group to search for food. There exist competitions between different
chickens. As for the chicks, they search for the food around their mother

12
Chicken Swarm Optimization (CSO)
Chickens’ behaviors rules
1- Chicken swarm divided into groups
each Group=a dominant , a couple of and
2- Group division methodology. All depends on the fitness values
 Best fitness -> worst fitness and the rest are
 Each would be the head rooster in a group
 The hens randomly choose which group to live in.
 The mother-child relationship is also randomly established.

13
3- The hierarchal order, dominance relationship and mother-child relationship
in a group will remain unchanged. Only update every several (G) time steps
4- chicken follow their group-mate rooster to search for food While they
prevent the ones from eating their own food
 Assume chickens would randomly steal the good food already found
by others.
 The chicks search for food around their mother (hen)
 The dominant individuals have advantage in competition for food.
 RN “Roosters”, HN “hens”, CN “chicks” and MN “mother hens”
 The best RN chickens would be assumed to be roosters
 while the worst CN ones would be regarded as chicks
 The rest are treated as hens

14
All N virtual chickens, depicted by their positions
at time step t, search for food in a D-dimensional space.
In this work, the optimization problems are the minimal ones
Thus the best RN chickens -> the ones with RN minimal fitness values.

15
Chickens Movement (Roosters)
The roosters with better fitness values have priority for food access than the ones
with worse fitness values.
For simplicity, Roosters with better fitness values can search for food in
a wider range of places than that of the roosters with worse fitness values
 Randn (0, 𝝈 𝟐
) is a Gaussian distribution with mean 0 and standard deviation 𝝈 𝟐
 𝜀, which is used to avoid zero-division-error, is the smallest constant in the computer
 k, a rooster’s index, is randomly selected from the roosters group
 f is the fitness value of the corresponding x.

16
Chickens Movement (Hens)
Hens can follow their group-mate roosters to search for food.
They would also randomly steal the good food found by other chickens
Though they would be repressed by the other chickens.
The more dominant hens would have advantage in competing for food than the
more submissive ones
 Rand is a uniform random number over [0, 1]
 𝒓𝟏 ∈ [𝟏, … . . , 𝑵] index of the rooster, which is the ith hen’s group-mate
 𝒓𝟐 ∈ [𝟏, … . . , 𝑵] index of the chicken (rooster or hen ), which is randomly chosen 𝒓𝟏 ≠ 𝒓𝟐
S1= exp(
𝑓 𝑖−𝑓𝑟1
|𝑓 𝑖|+𝜀
) (4) S2= exp(𝑓𝑟2 − 𝑓𝑖) (5)

17
Obviously 𝑓𝑖 > 𝑓𝑟1 , 𝑓𝑖 > 𝑓𝑟2 , thus S2 <1< S1
Assume S1=0,
then the ith hen would forage for food just followed by other chickens.
The bigger the difference of the two chickens’ fitness values
the smaller S2 and the bigger the gap between the two chickens’ positions is.
Thus the hens would not easily steal the food found by other chickens.
S1 and S2 formulas differs because there exist competitions in a group.
the fitness values of the chickens relative to the fitness value of the rooster
are simulated as the competitions between chickens in a group.
S2= exp(𝑓𝑟2 − 𝑓𝑖) (5)

18
Suppose S2=0,
then the ith hen would search for food in their own territory.
For the specific group, the rooster’s fitness value is unique.
Thus the smaller the ith hen’s fitness value, the nearer S1 approximates to 1
and the smaller the gap between the positions of the ith hen and its group-mate rooster
Hence the more dominant hens
would be more likely than the more submissive ones to eat

19
Chickens Movement (Chicks)
The chicks move around their mother to forage for food. This is formulated below
𝒙 𝒎,𝒋
𝒕
stands for the position of the ith chick’s mother (𝒎 ∈ [𝟏, 𝑵])
𝑭𝑳(𝑭𝑳 ∈ 𝟎, 𝟐 ) parameter indicates that the chick would follow its mother to forage for food
Consider the individual differences, the FL of each chick would randomly choose between 0 and 2

20
Algorithm

21
Algorithm
• Individual of chicken swarm population are initialized by using the
following formula
• With lb and ub are lower bound and upper bound of the search
space.

22
Parametric Analysis
There exist six parameters in CSO.
 HN would be bigger than RN -> keeping hens is more beneficial for human because only
hens can lay eggs, which can also be the source of food
 HN is also bigger than MN -> not all hens would hatch their eggs simultaneously
Though each hen can raise more than one chick, we assume the population of adult chickens
would surpass that of the chicks, CN
 As for G, it should be set at an appropriate value, which is problem-based.
 If G is very big-> it's not conducive for the algorithm to converge to the global optimal quickly.
 If G is very small, the algorithm may trap into local optimal.
 After the preliminary test, G ∈ [2,20] may achieve good results for most problem.
 In practice, FL ∈ [0.4, 1] usually perform well.
 The formula of the chick’s movement can be associated with the corresponding part in DE
If we set RN and MN at 0, thus CSO essentially becomes the basic mutation scheme of DE.

23
Benchmark Problems Optimization
Twelve popular benchmark problems (shown in Table 1) are used to verify the
performance of the CSO compared with that of PSO, DE and BA.
The statistical results have been obtained, based on 100 independent trials, in all
the case studies. The number of iterations is 1,000 in each trial.
For a fair comparison, all of the common parameters of these methods, such as the
population size, dimensions and maximum number of generations, are set to be the
same. The related parameters of these algorithms are showed at Table 2
Validation and Comparison

24
Twelve popular benchmark problems (shown in Table 1)

25
The related parameters of these algorithms are showed at Table 2

26
The superiority of CSO over PSO, BA and DE should be the case.
If we set RN = CN = 0, and let S1, S2 be the parameters like c1 and c2 in PSO, thus
CSO will be similar to the standard PSO. Hence CSO can inherit many advantages
of PSO and DE.
Moreover, the chickens’ swarm intelligence can be efficiently extracted in CSO.
Given the diverse laws of the chickens' motions and cooperation between the
multigroups, the search space can be efficiently explored.
Under the specific hierarchal order, the whole chicken swarm may behave like a
team to forage for food, which can be associated with the objective problems to
be optimized. All of these merits enhance the performance of CSO.

27

28
Speed Reducer Design – design Gearbox

29
Speed Reducer Design – design Gearbox
Which can be rotated at its most efficient speed.
The gearbox is described by
 The face width 𝑏(𝑋1)
 Module of teeth 𝑚(𝑋2)
 Number of teeth in the pinion 𝑍 𝑋3
 Length of the first shaft between bearings ℎ1 𝑋4
 Length of the second shaft between bearings ℎ2 𝑋5
 Diameter of the first shaft 𝑑1 𝑋6
 Diameter of the first shaft 𝑑2 𝑋7
 Speed Reducer Design optimization is to minimize its total weight, subject
to constraints on bending stress of the gear teeth, surface stress, transverse
deflections of the shafts, and stresses in the shafts

30
Application - Speed Reducer Design – design Gearbox
This problem can be formulated as follows

31
Speed Reducer Design – Design Gearbox
the results achieved by CSO and other algorithms.
CSO’s results outperform all the results achieved by other methods
in terms of both optimization accuracy and robustness
which indicates that the solution is feasible.

32
Discussion
 The performance of CSO is compared with that of the PSO, DE and BA on twelve
benchmark problems.
 Experiments show that CSO outperforms the PSO, DE and BA in terms of both
optimization accuracy and robustness.
 Moreover, CSO can efficiently solve the speed reducer design, which endues the CSO
with a promising prospect of further studying.
 One of the reasons that CSO has very promising performance is that CSO inherits major
advantages of many algorithms. PSO and the mutation scheme of DE are the special
cases of the CSO under appropriate simplifications.
 What is more significant for the superiority of the CSO is that the chickens’ swarm
intelligence can be efficiently extracted to optimize problems.
 The chickens' diverse movements can be conducive for the algorithm to strike a good
balance between the randomness and determinacy for finding the optima.

33
Discussion
 The whole chicken swarm consists of several groups, namely multi-swarm. Through
integration of the hierarchal order, chickens of the different groups may behave as a team
and coordinate themselves to forage for food. Thus CSO can behave intelligently to
optimize problems efficiently.
 The innovation in this paper not only lies in efficiently extracting the chickens’ swarm
intelligence to optimize problems, but also making CSO innate multi-swarm method.
 Multi-swarm technique is usually used to enhance performance of the population-
based algorithm. As an innate multi-swarm algorithm, various multi-swarm techniques can
be used to develop the different variants of CSO. Thus CSO has good extensibility.
 Moreover, from the parametric analysis, the population of the hens is the biggest in the
swarm. Thus the performance of CSO largely depends on how the hens’ swarm
intelligence can be extracted to optimize problems.

34
Discussion
 The motion of the hens can be adaptively controlled according to the fitness value of
the problem itself.
 With the dynamical hierarchal order, the hens swarm can be updated. Hence CSO has
the self adaptive ability to solve the optimization problems.
 More comprehensive analyses on the CSO are still need to be investigated in the future.
 Moreover, we can consider there exist several roosters in a group and dynamically
adjust the population of the hens and chicks in each group.
 It’s also significant to tune the related parameters for enhancing the algorithm
performance, and design the variants of the CSO to solve many optimization applications.

35
References
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