For three decades, many mathematical programming methods have been developed to solve optimization problems. However, until now, there has not been a single totally efficient and robust method to coverall optimization problems that arise in the different engineering fields.Most engineering application design problems involve the choice of design variable values that better describe the behaviour of a system.At the same time, those results should cover the requirements and specifications imposed by the norms for that system. This last condition leads to predicting what the entrance parameter values should be whose design results comply with the norms and also present good performance, which describes the inverse problem.Generally, in design problems the variables are discreet from the mathematical point of view. However, most mathematical optimization applications are focused and developed for continuous variables. Presently, there are many research articles about optimization methods; the typical ones are based on calculus,numerical methods, and random methods.
The calculus-based methods have been intensely studied and are subdivided in two main classes: 1) the direct search methods find a local maximum moving a function over the relative local gradient directions and 2) the indirect methods usually find the local ends solving a set of non-linear equations, resultant of equating the gradient from the object function to zero, i.e., by means of multidimensional generalization of the notion of the function’s extreme points from elementary calculus given smooth function without restrictions to find a possible maximum which is to be restricted to those points whose slope is zero in all directions. The real world has many discontinuities and noisy spaces, which is why it is not surprising that the methods depending upon the restrictive requirements of continuity and existence of a derivative, are unsuitable for all, but a very limited problem domain. A number of schemes have been applied in many forms and sizes. The idea is quite direct inside a finite search space or a discrete infinite search space, where the algorithms can locate the object function values in each space point one at a time. The simplicity of this kind of algorithm is very attractive when the numbers of possibilities are very small. Nevertheless, these outlines are often inefficient, since they do not complete the requirements of robustness in big or highly-dimensional spaces, making it quite a hard task to find the optimal values. Given the shortcomings of the calculus-based techniques and the numerical ones the random methods have increased their popularity.
2. OPTIMIZATION
It’s a procedure to make a system or
design as effective, especially involving the
mathematical techniques.
To minimize the cost of production or to
maximize the efficiency of production.
3. GENETIC ALGORITHM
A genetic algorithm (or short GA) is a
search technique used in computing to
find true or approximate solutions to
optimization and search problems.
Genetic algorithms are categorized as
global search heuristics.
Genetic algorithms are a particular class
of evolutionary algorithms.
4. HISTORY
Based on the mechanics of biological
evolution
Initially developed by John Holland,
University of Michigan (1970’s)
These algorithms are now used by a
majority of Fortune 500 companies to
solve difficult scheduling, data fitting,
trend spotting and budgeting problems,
and virtually any other type of
combinatorial optimization problem.
7. G A PROCEDURE
A typical genetic algorithm requires two
things to be defined:
a genetic representation of the solution
domain.
a fitness function to evaluate the solution
domain.
8. PROBLEM DOMAINS
Problems which appear to be particularly
appropriate for solution by genetic
algorithms include timetabling and
scheduling problems, and many scheduling
software packages are based on GAs. GAs
have also been applied to engineering
Genetic algorithms are often applied as an
approach to solve global optimization
problems.
As a general rule of thumb genetic
algorithms might be useful in problem
domains that have a complex fitness
landscape as recombination is designed to
move the population away from local optima
that a traditional hill climbing algorithm might
get stuck in.
9. What Do We Mean By Genetic
Algorithm?
It is started with a set of randomly
generated solutions and recombine pairs
of them at random to produce offspring.
Only the best offspring and parents are
kept to produce the next generation.
11. Applications :
Automated design of mechatronic
systems using bond graphs and genetic
programming (NSF).
Code-breaking, using the GA to search
large solution spaces of ciphers for the
one correct decryption.
Design of water distribution systems.
Distributed computer network
topologies.
Electronic circuit design, known as
12. Application : continue.
Software engineering.
Traveling Salesman Problem.
Mobile communications infrastructure
optimization.
Electronic circuit design, known as
Evolvable hardware.
14. -
As with the human race,
the weakest candidates
are eliminated from the
gene pool, and each
successive generation of
individuals contains
stronger and stronger
characteristics. It’s
survival of the fittest, and
the unique processes of
crossover and mutation
conspire to keep the
species as strong as
possible.
15. Advantages :
A GA has a number of advantages.
It can quickly scan a vast solution set.
Bad proposals do not effect the end
solution negatively as they are simply
discarded.
The inductive nature of the GA means that it
doesn't have to know any rules of the
problem - it works by its own internal rules.
This is very useful for complex or loosely
defined problems.
16. Disadvantages :
A practical disadvantage of the genetic
algorithm involves longer running times
on the computer. Fortunately, this
disadvantage continues to be minimized
by the ever-increasing processing speeds
of today's computers.
17. Conclusion
:
Evolutionary algorithms have been around since
the early sixties. They apply the rules of nature:
evolution through selection of the fittest
individuals, the individuals representing solutions
to a mathematical problem.
Genetic algorithms are so far generally the best
and most robust kind of evolutionary algorithms.
18. References:
A.D. Channon, and R.I. Damper, "Towards the
Evolutionary Emergence of Increasingly Complex
Advantageous Behaviours". International Journal of
Systems Science, 31(7), pp. 843-860, 2000.
C.A. Balanis, Antenna Theory Analysis and Design
John Wiley & Sons, 2nd ed., 1997.
Chakraborty .R .C, Fundamentals of Genetic
Algorithms, AI Course Lecture 39-40, June 01,2010.