01 dr. g.l samuel - iitm

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Genetic Algorithms- An introduction and applications and Optimization

through Intelligent Techniques

Dr. G.L. SamuelManufacturing Engineering Section

Department of Mechanical EngineeringINDIAN INSTITUTE OF TECHNOLOGY, MADRAS

Chennai – 600 036

1.0 Introduction

In today’s rapidly changing manufacturing scenario, manufacturers must adapt to respond

effectively to severe competitiveness and increasing demand of products with improved quality,

functionality, and performance. To remain competitive and promote growth, such rapidly

changing market demands necessitate advanced manufacturing systems with improved

performance. The decisive point is that most of the production processes are underutilized; and

the use of mature, accessible mathematical technology unlocks that latent capacity of the

manufacturing system, which is of considerable value. A significant improvement in process

efficiency may be obtained by process parameter optimization that identifies and determines the

regions of critical process control factors leading to desired outputs or responses with acceptable

variations ensuring a lower cost of manufacturing. Optimization methods in manufacturing

systems, considered to be a vital tool for continual improvement in product conformance and

process characterization. Performance of a manufacturing system is managed by modifying the

inputs (decisions made) as shown in Fig.1. Improved performance with existing assets is

achieved by the best possible modifications: altogether, the optimum, which depends on the

values of the uncontrolled inputs.

Fig.1. Improving performance of a manufacturing system

Performance metric

Input

Advanced

Manufacturing

System

Cycle time

Process parameters

Output

Layout Production rate

Product tolerance

Ambient conditions

Raw material condition

Un controlled inputs



Efficient computing techniques are essential for modeling the input–output and in-process

characteristics of the manufacturing system and determination of optimal conditions for

improving its performance.

2.0 Soft computing techniques

Soft computing, a term coined by Zadeh is basically a synergistic integration of three computing

paradigms: neural networks, fuzzy logic and genetic algorithm to provide a frame work for

flexible information processing applications designed operate in the real world. All these

techniques differ from one another in their time scales of operation as highlighted in Fig. 2.

Fig.2 Soft computing techniques for optimization of manufacturing systems

These soft computing techniques exploit the tolerance for imprecision, uncertainty and partial

truth to achieve tractability, robustness, low solution cost and better rapport with reality. Genetic

Algorithms (GA) are one the popular techniques in optimization of manufacturing systems.

3.0 Genetic algorithm

The working of GA (Goldberg, 2006) generally preferred for large and complex optimization

problems, is based on three basic operators, viz., reproduction, crossover, and mutation, in order

to offer a population of solutions. The algorithm creates new population from an initial random

Fuzzy logic

(Linguistic

information

Genetic Algorithms

(Evolutionary

algorithms)

Neural networks

(Learning

generalization)

Soft computing

techniques



population (obtained from different feasible combination of process decision variables) by

reproduction, crossover, and mutation in an iterative process. The selection, crossover and

mutation on initial population create a new generation, which is evaluated with pre-defined

termination criteria. The procedure for one generation of genetic algorithm is shown in Fig.3.

Fig.3 Basic genetic algorithm

3.1 Population

A population is generated by choosing random input values. There are no fixed rules for size of

the population and it is dependent upon the type of problem.

3.2 Representation of chromosome

A suitable coding scheme is defined to describe the population composed of number of

individuals. Each individual is represented by a finite array of symbols, known as a string

(chromosome). Each individual string encodes a possible solution in the given problem space.

1. Initial population

4. Children

Cross over

Mutation

One generation of

basic genetic algorithm

Ideal case

?

2. Fitness test

=

5. New population

3. Selection



3.3 Fitness evaluation

The fitness of individual strings is a relative matter. Population is evaluated based on

corresponding values of the formulated objective function. An individual which dominates other

members of a population by taking all criteria into consideration is considered fitter. The most

dominant, i.e. those who dominate all others are referred to as Pareto solutions.

3.4 Selection

It is a process of generating a mating pool by selecting good fitness strings from the population.

GAs operates over a number of generations. Selection methods can be employed by many

approaches like roulette wheel, tournament. Fitter solutions (i.e. those most dominant) have a

better chance of surviving than the other weaker individuals.

3.5 Cross over

Two strings are picked from the selected mating pool at random and chromosome patterns

between individuals are exchanged to create offspring for the next generation. In a single point

cross over operation, a cross over site is chosen at random and all bits to the right of the cross

over site are exchanged between the two strings as shown in Fig.4.

Fig.4 Single point cross over

Single point cross over preserves the maximum amount of information between generations, but

it is restricted in search capability. Normally cross over is not performed on entire population. A

cross over probability of pc dictates that pc x 100 percent strings in the population are used in the

cross over operation and that best(1-pc)X100 per cent of current population can be copied

deterministically to the new population, this performed at random.

3.6 Mutation

Mutation operation is used to enhance the search in a GA. The mutation operator flips a bit string

with a very small mutation probability. Mutation is necessary to maintain diversity in the

population which would otherwise converge very quickly to very similar strings.

1 1 1 | 0 1 0 1 1 1 |1 1 0

1 0 0 |1 1 0 1 1 1 | 0 1 0

⇒



3.7 Termination

There are no definitive methods of establishing how many generations a GA should run for.

Simple problems may converge on good solutions after only 20 or 30 generations. More complex

problems may need more. It is not unusual to run a GA for 400 generations for more complex

problems such as jobshops.

3.8 Advantages of GA

(i) It has the global view of search space and internal parallel processing capability to obtain

better solutions to the problems

(ii) Search direction or transition rule is probabilistic, not deterministic, in nature, and hence,

the chance of avoiding local optimality is more

(iii) it works with a population of solution points rather than a single solution point as in

conventional techniques, and provides multiple near-optimal solutions

(iv) It has the ability to solve convex, and multi-modal function, multiple objectives and non-

linear response function problems,

(v) It can be applied to both discrete and continuous objective functions.

3.9 Limitations of GA

(i) Convergence of the GA is not always assured

(ii) No universal rule exists for appropriate choice of algorithm parameters, such as

population size, number of generations to be evaluated, crossover probability, mutation

probability, and string length;

(iii) GA may require a significant execution time to attain near-optimal solutions, and

convergence speed of the algorithm may be slow.

(iv) Moreover the repeatability of results obtained by GA with same initial decision variable

setting conditions is not guaranteed.

4.0 References

1. David Goldberg, (2006),Genetic algorithms in search, Optimization & Machine

learning, Pearson education.

2. Nikos Drakos, (1997), Genetic Algorithms as a Computational Tool For Design ,

Computer Based Learning Unit, University of Leeds.

01 dr. g.l samuel - iitm

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