1 optimization of vlsi circuit by genetic algorithms

8/10/2019 1 Optimization of VLSI circuit by Genetic Algorithms

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Optimization of VLSI circuit byGenetic Algorithms

Mirza Nazrul Alam

GA Quick Overview

What is genetic Algorithm :Genetic algorithm are computerizedsearch and optimization algorithmsbased on the mechanics of naturalgenetics and natural selection.genetic Algorithms are good at takinglarger, potentially huge, search spaceand navigating them looking for optimalsolutions which we might not find in a lifetime.


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Idea of evolutionary computing was First Introduced byRechenberg in 1960 in his work Evolutionary strategies.

Prof. Holland of University of Michigan, Ann Arborenvisaged the concept in the mid sixties and publishedhis seminal work ( Holland 1975).

There after a number of students and others researchershave contributed to the development of this field.

History:

Three important aspects of using GA

1 Definition of objective function2. Definition and implementationof genetic representation3. Definition and implementationof genetic operators.


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Objective function

The function f(x,y,z...) that has to beoptimized.Each parameter of the function has

its own limit i.e., the lower and upperbound

Genetic Representation


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Search Space

The space for all possible feasiblesolutions.Each solution is marked by its valueof fitness.

Looking for solution means lookingfor extrema (either maximum orminimum ) in search space.

Set of solutions in the search space. The initial populations are random

numbers in the search space The populations are represented as

chromosomes Binary ,octal or hexadecimal encoding

are used to represent the chromosomes.

Population


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Basic Operators

Reproduction or selectionCrossover

mutation

Reproduction

Chromosomes are selected from thepopulation to crossover and produce

offspring Obey the law of Darwin They best one should survive and

create offspring.


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Types of Reproduction

Roulette-wheel selection Tournament Selection Rank selection

Steady state selection

Roulette-wheel Selection


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Main idea: better individuals get higher chance Chances proportional to fitness Implementation: roulette wheel technique

Assign to each individual a part of theroulette wheelSpin the wheel n times to select n

individuals

Roulette wheel

fitness(A) = 3

fitness(B) = 1

fitness(C) = 2

A C

1/6 = 17%

3/6 = 50%

B2/6 = 33%

Tournament competition among Nindividuals(N=2) are held atrandom.The highest fitness value is thewinner.Tournament is repeated untill themating pool for generating newoffspring is filled.

Tournament Selection


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Rank selection

Roulette-wheel has problemwhen the fitness value differ verymuch.In rank selection the worst valuehas fitness 1, the next 2,......,and the best will have fitness N.

1 23

4

5

5

1

2

3

4

5%2%

8%

10%

75%

33%

7%

13%

20%

27%

Rank selection

Roulette-wheel Rank selection


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Single-point crossover

Choose a random point on the two parentsSplit parents at this crossover pointCreate children by exchanging tailsP c typically in range (0.6, 0.9)

n-point crossover

Choose n random crossover pointsSplit along those pointsGlue parts, alternating between parents

Generalisation of 1 point (still some positional bias)


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Uniform crossover

Assign 'heads' to one parent, 'tails' to the otherFlip a coin for each gene of the first childMake an inverse copy of the gene for the second childInheritance is independent of position

operators: mutation

Alter each gene independently with a probability p mp m is called the mutation rate Typically between 1/pop_size and 1/ chromosome_length


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SGA technical summary table

Emphasis on crossoverSpeciality

All children replace parentsSurvivor selection

Fitness-ProportionateParent selection

Bitwise bit-flipping with fixedprobability

Mutation

N-point or uniformRecombination

Binary stringsRepresentation

SGA reproduction cycle

1. Select parents for the mating pool(size of mating pool = population size)

2. Shuffle the mating pool3. For each consecutive pair apply crossover with

probability p c , otherwise copy parents4. For each offspring apply mutation (bit-flip with

probability p m independently for each bit)5. Replace the whole population with the resulting

offspring


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X2 example: crossover

X2 example: mutation


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Applications of GA

Design-VLSI circuit, aircraft design, communication network

Robotics-Trajectory plannings Machine learning-designing neural network Control-pole balancing, misile evasion combinatorial optimization-travelling sales man, routing, bin packing , graph colouring.

Optimization in VLSI circuit

Designing VLSI circuits consistof two steps:

1)topological design2) parameter determination .


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Why GA in parameter optimizationof VLSI circuit?

1)After designing a topology suitable for the circuit, thedesigner selects an appropriate value for each circuitelement from a circuit analysis.

2) This step is difficult and time consuming becausedesigner must consider many factors simultaneously.

3) Attempt has been made on how to simplify thisparameter design level using evolutionaryprogramming that is currently gaining significantattention in optimization technique.

Concluding remarks

It doesnt need a complex formulation for circuitanalysis. It is sufficient to select appropriateparts for optimization and to determine a

suitable range of each parameter.It can be applied to the other circuits easily.When the specification of the circuit ischanged, it is only necessary to rewrite thecost function according to specification.


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Reference

[1] Fogel, L.J., Owens, A.J., and Walsh, M.J., ArtificialIntelligence Through Simulated Evolution, John Wiley,Chichester, Uk, 1996.[2] Glover, F., Heuristics for Integer ProgrammingUsing Surrogate Constraints, Decision Sciences, Vol.8,No.1, pp.156-166, 1977.[3] Holland, J.H. Adaptation in Natural and ArtificialSystems, University of Michigan Press, Ann Arbor,1975.[4] Koza, J.R., Genetic Programming. MIT Press,Cambridge, MA, 1992.[5] Douglas A. Pucknell, Kamran Eshraghian, BasicVLSI Design, p-287

1 optimization of vlsi circuit by genetic algorithms

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