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Optimizing design of spring using genetic algorithm

Abstract:
This paper deals with the elaborate designed optimization technique
of coil spring sets. Attention is focused reducing the weight and
stresses are calculated keeping in to considerations the various
critical points. Graphical optimization the various critical points
graphical optimization technique is used for non-linear programming
.Maximum endurance shear stresses spring constant etc.. are taken as
the objective function also we have mainly discuss about the
application and problem formulation using genetic algorithm which is
one of nontraditional methods to optimizes weight of coils spring.
INTRODUCTION TO GA:-
Over a few years, a number of search and optimization
techniques, drastically different on principle from classical methods,
are getting increasing more alternation. These methods mimic a
particular natural phenomenon to solve as optimization problem.

With the development of mathematical programming
techniques for optimization and rapid advances made in computer
hardware and software technologies, it is now possible to formulate
engineering design problems as an optimization problem
With the objective of minimizing the cost or weight subject to
satisfaction of all the conditions of design.

The evolution strategies like Genetic algorithm,
simulated annealing, fuzzy sets, neural networks are major techniques
of which genetic algorithms are the present topic of discussion.
GA is a population- based search and optimization
technique . It is an interactive optimization procedure. Instead of
working with a single solution, in each iteration, a GA works with a
number of solutions.

GA is search algorithms that simulate Darwinian evolutionary
generating a population of potential solutions to the problem and then
manipulating those solutions using genetic operations. The solutions
are typically represented as finite sequences drawn from a finite
alphabet of characters. Through selection, crossover and mutation
operations, better solutions are generated out of current population of
potential solutions. This process continues until an acceptable
solutions is found.
BRIEF DETAILS OF GA:-
A genetic algorithmapplies the principles of evolution found in nature
to the problem of finding an optimal solution to a solver problem. In
a genetic algorithm, the problem is encoded in a series of bit
strings that are manipulated by the algorithm; in an genetic
algorithm, the decision variables and problem functions are used
directly. Most commercial solver problems are based on genetic
algorithms. A genetic algorithm for optimization is different from
classical optimization methods in several ways:
Random Versus Deterministic Operation
Population Versus Single Best Solution
Creating New Solutions Through Mutation
Combining Solutions Through Crossover
Selecting Solutions via Survival Of The
Fittest
Drawbacks of Genetic Algorithms
Randomness: It release in part on random sampling. This makes it a
nondeterministic method, which may yield somewhat different
solutions in different runs. even if you havenâ„¢t changed your model.
In contrast, the linear, nonlinear and integer solvers also included in
the premium solver are deterministic methods-they always yield the same
Solution if you start with the same values in the decision variable
cells.
Population: where most classical optimization methods maintain a single
best solution found so for, a genetic algorithm maintains a population
of candidate solution. Only one of these is best but the other
members of the population are sample points in other reasons of the
search space, where a better solution may later be found. The use of a
population of solution helps the genetic algorithm avoid become
trapped at a local optimum, when an even better optimum may be found
outside the vicinity of the current solution.
Mutation: genetic algorithm periodically makes random or mutations in
one or more member of the current population, yielding a new candidate
solution .There are many possible ways to perform a mutation and the
generic solver actually employs three different mutation strategies.
The result of a mutation may be an infeasible solution, and the generic
solver attempts to repair such a solution to make it feasible; this
is sometimes, but not always, successful.
Crossover: an generic algorithm attempts to combine elements of
existing solutions in order to create a new solution ,with some of
the features of each parent the element of existing solution are
combined in a crossover operation , inspired by the crossover strands
that occurs in as with mutation ,there are many possible ways to
perform a crossover operation some much better than there and the
generic solver actually employs multiple variations of two different
crossover strategies.
Selection: Inspired by the role of natural selection in evolution an
generic algorithm performs a selection process in which the most fit
members of the population survive,
And the least fit members are eliminated .In a constrained
optimization problem, the notion of fitness depends partly on whether
a solution an is feasible and party on its object function value .the
selection process is the step that guides the generic algorithms
towards ever better solutions.
Drawbacks: A drawback of any generic algorithm is that a solution is
better only in comparison to other, presently known solution: such an
algorithm actually has no concepts of an optimal solution, or any
way to best whether a solution is optimal. This also means that an
generic algorithm never knows for certain when to stop, aside from the
length of time or the number of iteration or candidate solutions, that
you wish t allow it to explore.

CONVENTIONAL METHODS AND THEIR PROBLEMS:

The use of machine learning technique is design processes has been
hampered by a number of problems. There are three main types of search
methods (1) calculus - based (2) Enumerative (3) Random.
(1) CALCULUS _ BASED
These are again divided in to two

INDIRECT METHOD:
The indirect methods which seek local extra by solving the usually non
-linear set of equation. for their given a smooth , unconstrained
function, finding a possible peak starts by restricting search to
those points with slopes of zero in all directions
DIRECT METHOD:
This is simply the notion of hill climbing in a direction related to
the local gradient i.e. to find the local best, climb the function in
the steepest permissible direction.
(2)) Enumeration:
Is a very human kind of search when the number of possibilities is
small. Such schemes must ultimately be discounted in the robustness
race of simple reason: lack of efficiency.
(3) Random:
walks and random schemes that search and save the best must also be
discounted because of efficiency requirements, Random search in the
long run, can be expected to do no better than enumertlative schemes.,
PROBLEM SOLVED BY GA:

Design variables:
The following are the design variables in this problem
Diameter of coil spring (d)
Mean diameter of coil spring (D)
Number of active coils (N)
Design constraints:
The constraints represents some functional relationships
among the design variable and other design parameters satisfying
certain physical phenomenon and certain resource limitation in this
problem the following are the design constraints.
Maximum endurance shear stress in an coil
2* ta
_______________
(1/n-((tm-ta)/ty)<=ten
Out side diameter D+d <=Do
Inside diameter D-d<=di
Bounds limits
Dmin <= d<= dmax
Dmin <= D <= d max
Nmin <= N <= Nmax
Maximum deflection allowable (8* pmax D3N)
------------------
-<=0
G*d4
Stress factor K=(4*D-d)/(4*D-d4-d)+0.615-d/D.
Mean shear stress tm =(8*k*pm*D)/3.14*d3


IMPORTANCE OF SPRINGS:

A spring is defined as an elastic body, whose function is to
distort when loaded and to recover its original shape when load is
removed. Springs are simple machine elements that play important role
in the operations of many mechanical and electrical devices. Their
primary function, unlike that at most other components is to introduce
controlled flexibility by deflecting under applied loads. The springs
detection in machine design is utilized to absorb the energy of
suddenly applied loads and to store energy for subsequent release.
Among primary functions of springs the following are perhaps the most
important.
1. TO ABSORB ENERGY AND MITIGATE SHOCK:
In order energy with out exclusive peak loads, the springs
must deflect by a considerable amount .A common example of the use of a
spring to mitigate shock due to track irregularities is freight-car
track springs E.g.:- Automobiles, toys and watches.
2. TO APPLY A DEFINITE FORCE:-
An automobile valve springs supplies the necessary holding force for
the valve follower against the can the main springs of watch supplying
recovery force Eg:- Brakes
3. TO SUPPORT MOVING MASSSES OR ISOLATED VIBRATIONS:-
The usual purpose of springs used to support moving or vibrating
moves is to eliminate or reduces vibration or impact. The springs used
in automobile suspension not only tend to mitigate shock but also
prevent transmission to the car body of objectionable vibration caused
by regular waves in the road contours.
4. TO INDICATE OR CONTROL LOAD TORQUE:-
One of the most important function of springs is that of
tourishable a flexible member, will deflect by considerable amount when
subject to load or torque Eg:- Common spring scales.
ADVANTAGES OF GA OVER CONVENTIONAL METHODS:
1. The first and for most advantages of ga is that they aim for global
optimization where as conventional methods aim at local optimization.
2. Instead of working with a single solution, in each iteration, a ga
works with a number of solutions.
3. These algorithm are computationally simple yet powerful in their
search for improvement.
4. These are not fundamentally limited by restrictive assumptions about
the search space.
5. GA use pay off information, not derivatives or other auxiliary
knowledge.
6. GA use probabilistic transition rules, not determistic rules.
CONCLUSION:
We conclude that weight of spring is optimized by using GA which is one
of the non traditional methods. so it is advisable that application of
GA in optimization of various design parameters. When compared with
other traditional method.

BIBLOGRAPHY:

G.J.DOUKIDIS &R.J.PAUL (Eds) ARTIFICIAL INTELLIGENCE IN OPERATIONAL
RESEARCH.
r.D.MACHREDIE,R.J.PAUL,R.ANKETERL,B.LEHAANEY&S.WARWICK[Eds]