Optimizing design of spring using genetic algorithm
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
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 algorithm”applies 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
haven’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
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
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
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
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.
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.
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:
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)
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
Out side diameter D+d <=Do
Inside diameter D-d<=di
Dmin <= d<= dmax
Dmin <= D <= d max
Nmin <= N <= Nmax
Maximum deflection allowable (8* pmax D3N)
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
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
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
3. These algorithm are computationally simple yet powerful in their search for
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.
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.
G.J.DOUKIDIS &R.J.PAUL (Eds) ARTIFICIAL INTELLIGENCE IN