BIOGEOGRAPHY-BASED OPTIMIZATION (BBO) ALGORITHM: A REVIEW
Manjeet Kaur*, Sakshi Sethi
Assistant Professor,
Amity University, Gurgaon, Haryana, India
Abstract - In this article we are presenting
review of an optimization technique
biogeography
based
optimization
algorithm. Although there are several
optimization techniques like genetic
algorithm, ant colony, and more yet BBO
algorithm is meta-heuristics search
optimization technique largely focus on
overall optimization. Here we review
various methods under BBO algorithm for
optimization.
Keywords- Optimization, BBO, Operators.
I.
Introduction:
Optimization is the act of achieving the best
possible result under various given
circumstances. The primary aim of the
optimization techniques is either to minimize
effort or to maximize benefit. The effort or the
benefit can be usually expressed as a function
of certain design variables. Hence,
optimization is the process of finding the
conditions that give the maximum or the
minimum value of a function. In this paper
we are trying to understand how biogeography
based optimization algorithm provides
solution for optimization problem. BBO is a
part of Evolutionary Algorithms that deals
with natural selection in the search space and
selects the best solution. The BBO works for
global optimization. Hence this paper
represents review of BBO algorithm for
optimization.
II.
Types of Optimization Techniques
Optimization problems are set of problems
that find the best result either by minimizing
the cost or maximizing the fitness. There are
wide ranges of application where optimization
is needed for speed and position control of
electric motors, travelling salesman problem,
root finding for system of linear and nonlinear
equations, tuning the controller parameters,
circuit and other. In general, what we have to
do is to reduce the cost or increase the profit.
Different Optimization techniques are:
Genetic Algorithm: Genetic algorithm is a
heuristic optimization technique inspired by
the mechanisms of natural selection. It starts
with an initial population containing a number
of chromosomes where each one represents a
solution of the problem in which its
performance is evaluated based on a fitness
function. Based on the fitness of each
individual and defined probability, a group of
chromosomes is selected to undergo three
common stages: crossover and mutation [10].
The application of these three basic operations
is to allow the creation of new individuals to
yield better solutions then the parents, leading
to the optimal solution.
Ant Colony: Ant colony method simulates the
behavior of ants living in colony. Initially all
ants start searching for food in arbitrary
manner. Once a path is found by one ant
which leads to food all other will follow that
path.
BBO: Biogeography is the study of the
geographic
distribution
of
biological
organisms. In BBO model, problem solutions
are represented as islands and the sharing
features between solutions are represented as
immigration and emigration between the
islands.
III. Basic Concept of BBO
Mathematical models of biogeography
describe migration, speciation, and extinction.
Islands that are well suited as habitats for
biological species are said to have a high
habitat suitability index (HSI). Features that
correspond with HSI include topographic
diversity, area, temperature, rainfall, etc. and
the
variables
which
specify
these
characteristics [2] are called suitability index
variables (SIVs). SIVs are independent
variables of the island, and HSI’s are
dependent variables.
Islands with high HSI tend to have a large
number of species, and those with low HSI
have a small number of species [3]. Islands
with a high HSI have many species that
emigrate to nearby islands because of the
accumulation of random effects on its large
populations. Emigration appears like animals
ride, flotsam fly or swim to other neighboring
islands. Biogeography-based optimization
(BBO) algorithm was first presented in [2] and
is an example of how a natural process can be
modeled to solve optimization problems.
Biogeography is the nature’s way of scattering
species, and is similar to general problem
solutions. A good solution is homologous to
an island with a high HSI, and a poor solution
is just like an island with a low HSI. High HSI
solutions have more capability to share their
features with other solutions, and low HSI are
more likely to share their features from other
solutions. This criterion to problem solving is
called
biogeography-based
optimization
(BBO). Fig.1 illustrates a model of species
abundance in an isolated island. The
emigration rate µ out of the island, and the
immigration rate λ into the island, are
functions of the number of species S on the
island. The maximum possible immigration
rate I occurs when there are zero species on
the island. As the number of species expands,
the islands become more crowded, fewer
species are able to successfully survive
immigration, and the immigration rate
decreases. The largest possible number of
species that the island can reinforce is Smax, at
which point immigration rate is zero.
If there are no species on the island
then the emigration rate is zero. As the
number of species increases, the islands
become more crowded, representative
individuals of species are more likely to leave
the island, and the emigration rate increases.
The maximum emigration rate E occurs when
the island contains the largest number of
species that it can support.
Emigration
Rate
E or I
Immigration
Smax
No. of species
Fig. 1 Distribution of Species in an Island
We have shown the immigration and
emigration curves in fig. 1 as straight lines,
but in general they might be nonlinear. This
model simply gives a general description of
the process of immigration and emigration.
IV.
Biogeography-based optimization
algorithm:
In a group of neighboring islands, species of
plants and animals will migrate over time
between the islands by various means, being
carried along by driftwood [2], fish, birds, and
the wind. Over evolutionary period of time,
some islands may tend to accumulate more
species than others because they possess
certain environmental features that are more
suitable to sustaining those species than
islands with fewer species. This ability to
sustain large number of species can be
associated with a fitness measure that we can
quantify by assigning a habitat suitability
index (HSI) to each island. The value of the
HSI depends on many features of islands. If a
value assigned to each feature, then the HSI is
the function of each feature. Each of these
values is represented by suitability index
variable (SIV).
These mappings are summarized as follows:
Island
(feature1, feature2,…, featuren)
(SIV1 SIV2,…,SIVn)
HSI
An island with a large number of species (a
high HSI) has an abundance of species which
can immigrate to other islands, so its rate of
emigration, denoted by µ, is correspondingly
large. The island is also less likely to able to
sustain further immigration of species because
of growing demand on its finite environmental
resources, so its immigration rate, denoted by
λ, is small. For many applications it suffices to
assume a linear relationship between an
island’s HSI and its immigration and
emigration rates and that these rates are the
same for all islands under consideration.
These relationships are depicted in fig. 2. One
can use the migration rates of each solution to
probabilistically share features between
islands. For each SIV in each island, it is
probabilistically decided whether or not to
immigrate.
Emigration
Rate
Immigration
E or I
S1
S2
Fitnes
E
or
Fig.2. Illustration of two candidate solutions to
s
some problem. S1 is poor solution and S2 is good
solution.
I
If immigration is [3] selected for a given SIV,
then the emigrating island is selected
probabilistically using Roulette wheel
selection normalized by µ. After the migration
operation,
a
mutation
operation
is
probabilistically applied to the island to
increase diversity in the population. This gives
the algorithm shown in fig. 3 as [4] a
conceptual description of one generation using
this approach (Single Immigration BBO
Algorithm). We use the notation yk (s) to
denote the sth feature of the kth island in a
population y of islands. Migration and
mutation of the entire population take place
before any of the solutions are replaced in the
population, which requires the use of the
temporary population Z [3].
Z
Y
For each island Zk
For each SIV s
Use λk to decide whether to immigrate to Zk(s)
If immigrating ting to Zk (s) then
Use µ to select the emigrating island yj
Zk(s)
yj (s)
End if
Probabilistically decide whether to mutate
Next SIV s+1
Next island Zk+1
Y
Z
Fig. 3 One generation of the BBO Algorithm
As with other population-based algorithms,
we often incorporate elitism in order to retain
the best solutions in the population from one
generation to the next. We use Z to denote the
no. of top individuals in the population that
have a zero probability of immigration [4].
If elitism is not used, then Z = 0 and
immigration rate λ is a linear function of
fitness and is positive for all fitness values. If
elitism is used, then Z > 0 and the immigration
probability is zero for the top Z individuals in
the search space.
fmin
fmax
fmin
fmax
fmax
a) Immigration rate
with no elitism (Z =
0). Immigration rate is
a function of fitness.
Table 1: Parameters used in BBO
Parameters of BBO
Probability of modification
Probability of mutation
Keep (Elitism parameter)
Values
1
0.005
2
VI. CONCLUSIONS & FUTURE WORK
λ
λ
V. Review
of
Selection
of
BBO
Parameters:
To start up with BBO, certain parameters need
to be defined. Selection of these parameters
decides to a great extent the ability of global
minimization. The migration operator affects
the ability of escaping from local optimization
and refining global optimization. Mutation
operator is used to obtain required diversity
among the population. Elitsm operator retains
the best solutions among the population.
Initializing the values of the parameters is as
per table.1.
b)Immigration rate with
elitism (Z ≠ 0). The
immigration rate λ is zero
for most fit Z individuals.
Fig. 4 Plot of fitness vs. immigration
probability (a) Without elitism, (b) With
elitism
We have successfully reviewed the BBO
algorithm for the optimization problem. It is
clearly understood from this paper how BBO
algorithm originated, the basic concepts and
the working of BBO algorithm. BBO
algorithm is one of the well-known
optimization techniques. Other technique like
genetic algorithm (GA), ant colony
optimization and particle swarm optimization
(PSO) are explained. In future we will design
modified version of BBO algorithm and run,
test it for various optimization problem. Also
we will compare BBO with other optimization
technique.
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