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Introduction
Genetic algorithms abbreviated as GAs , are among fast growing stochastic simulation techniques of recent times. T
These belong to the class of broadly applicable, general-purpose, generate-and-test optimization methods with underlying evolution principles of biological systems and the genetic operators having adaptive mechanisms.
These principles help in escaping from local extremes without supervision during a simulation and as a result, they have become global optimization methods. Despite their simplicity, GAs can solve complex systems that other techniques might not have ability to accomplish.
These have been applied successfully to real-world problems and in many cases, have shown better search efficiency compared with traditional optimization algorithms.
Genetic algorithms are being used in a number of diverse applications such as function optimization, system identification and control, image processing, combinatorial problems, neural networks, fuzzy systems, robotics, and many other areas of science and engineering. The growing trend of applications indicates the robustness of the search method and the flexibility of the formulation.
The first attempts to combine numerical solution of models and evolution theory started in late 1950s with the mutation as a base to generate new combinations of a set of solutions at a given time. During 1960s I. Rechenberg started introducing " Evolution strategies " to optimize real-valued parameters for airfoils. His ideas were further developed by Schwefel (1977). In early 1960s, Hans J. Bremermann of university of California at Berkeley added an operation of mating where new solution was a sum of two genes of parent solutions. In same period, Fogel, Owens and Walsh (1966) developed “evolutionary programming in which mutating transition diagram would keep evolving the system for fittest selections. These were limited procedures and covered only a small part of the search space for solution. By middle of 1960s, the conventional Genetic Algorithms (GAs) came into light by detailed work of John Holland who developed a systematic approach using both mating and mutation.
Concepts of Biology Used in Genetic Algorithms
All living organisms consist of cells. In each cell there is the
same set of chromosomes.
Chromosomes are strings of DNA and serves as a model
for the whole organism. A chromosome consists of genes,
the building blocks of DNA with a particular protein
encoded by each gene.
Basically each gene encodes a trait, or physical property for
example color of eyes and possible settings for a trait (e.g.
blue, brown) are called alleles. Each gene has its own
position in the chromosome termed as locus.
A complete set of genetic material is known as genome and
a particular set of genes in genome is genotype.
The genotype is responsible for later developments of
organism's phenotype, which identifies its physical and
mental properties.
In the process of reproduction first a recombination (or
crossover ) occurs and genes from parents form a new
chromosome.
The new created offspring can then be mutated. Mutation
means, that the elements of DNA are a bit changed.
These changes are mainly caused by errors in copying
genes from parents.
The fitness of an organism is measured by success of the
organism in its life.
Search Space
Consider a simple problem of traveling salesperson
between N cities with distance between each pair of
cities ( i & j ) known.
can be completely or partially known to a solver during the process of evolving a solution.
In general, only a few solution points with large errors
may be known and the evolution process refines the
solution to a best fitness. When an algorithm has a
capability to start from very low fitness value solutions
and access any region of the space, the search will
eventually evolve to the valley of suitable solutions. Then
such an algorithm will be termed as ergodic.
0
20
40
60
80
Percentage Difference
Y Axis
X Axis
Figure 10.1 An example of a search space with various extremes and a valley of suitable solutions.
Multimodal Object Function
Optimization models are based on search for highest points in a multi- dimensional state space that may have a complex landscape. It can be viewed as a minimization or maximization problem. Figure 10.2 shows a two-dimensional state space having multiple maxima or multimodal form. For such spaces the investigation becomes global optimization of multimodal object function.
Figure 10.2 shows a two-dimensional object function having following mathematical form:
1
2 2
2 2
1
B(x y )
cosw(x y ) g(x,y) A (10.3)
It is a multimodal function with global maximum at _(x, y) = (0, 0)_** and g(0, 0) = A +1****. We can restrict search in state space to small portion M by defining the region:
M ( x,y) ^2 |Q(x,y) 0 (10.4a)
where, Q(x, y) is given as
, otherwise.
, if|x| aand|y| b Q( x,y) 1
(10.4b)
This function sets the g(x, y) and the search area as the phenotype fitness.
-10 -8^ -6^ -^
-2 0 2 4
6 8 10
0
2 4 6
8 10
Figure 10. 2 An example of a multimodal state space.
