Genetic Algorithms in Genetic Algorithms in Materials ProcessingMaterials Processing

N. Chakraborti

Department of Metallurgical & Materials Engineering

Indian Institute of Technology

Kharagpur (W.B) 721 302

INDIA

Why Genetic Algorithms?Why Genetic Algorithms?

To negotiate complex fitness landscapes To handle frequent multi-modality To handle non-differentiable objective function

space To efficiently search for a global optimum To accommodate complex Pareto-optimality Plus the general robustness of a population based

approach

The Algorithms that I have The Algorithms that I have tried out!tried out!

Simple genetic algorithms Gray coded genetic algorithms Differential evolution Island model Micro genetic algorithms Pareto-converging genetic algorithms Strength Pareto evolutionary algorithms Distance based algorithm Predator-prey algorithm

Everybody knows Simple Everybody knows Simple Genetic Algorithms!Genetic Algorithms!

/*a pseudo code of simple genetic algorithm*/{generate a random binary population;repeat {

if (termination criterion) break fitness evaluation;

selection;crossover;mutation;} until (generation less than final);binary to real mapping of solution;

}

Differential EvolutionDifferential Evolution/*a pseudo code of differential evolution*/{generate a random real-coded population vector;select mutation constant and crossover probability;}{for all generations do{repeat {if (termination criterion) break creation of a mutated individual using three random members and the mutation constant; crossover between the mutated individual and a fourth member through exchange of variables ; a trial solution results in that must contain at least one variable from the mutated individual; tournament between the trial solution and the fourth individual; select the winner for next generation; } until (the entire next generation is selected);} od; }

Gray Coded Genetic Gray Coded Genetic AlgorithmsAlgorithms

The problem of Hamming Cliff01111111 12710000000 128XOR operation01111111 Gray coded as 0100000010000000 Gray coded as 11000000

Island ModelIsland Model

A number of islandA number of tribes in eachInter-tribe migrationInter-island migrationOccasional immigration and replacementMost suitable for parallel processing

Micro Genetic AlgorithmsMicro Genetic Algorithms

Small population size, usually 5Tournament selectionUniform crossoverNo mutationElitismPeriodic replenishing of populationGood for non-stationary objective functions

Multi-modality and Pareto-Multi-modality and Pareto-optimalityoptimality

The genetic driftSharing and Niching in multi-dimensional

hyperspaceEuclidean vs. Hamming distanceDominated vs. non-dominated solutions

Pareto Converging Genetic Pareto Converging Genetic AlgorithmsAlgorithms

Island and tribesProvisions for ElitismRank based Tournament SelectionIntra-tribe and Inter-tribe RankingRank histogram and Rank ratioImmense scope for Parallel Processing

Strength Pareto Evolutionary Strength Pareto Evolutionary AlgorithmAlgorithm

A main population and an External Population of prescribed maximum size.

‘Strength’ of the External population members relates to ‘Fitness’ of the main

‘Clustering’ for the External Population

Distance Based Multi-Distance Based Multi-Objective AlgorithmsObjective Algorithms

Two different populations, one being the Elite The Elite population is of variable size Arbitrary Fitness Scale based upon Euclidean

Distances in the function space Continuous updating of Fitness based upon

dominance Crossover and mutation in the main population

Predator-Prey AlgorithmsPredator-Prey Algorithms

Predator kills the ‘weakest’ neighbor

Both the predator and the prey are allowed to move around

A desirable predator prey ratio is maintained.

Now, let’s talk about the Now, let’s talk about the problems that turn me on!problems that turn me on!

To begin with, they all deal with materials of one kind or the other…..

Geometry Optimization of Geometry Optimization of ClustersClusters

Material design and geometry optimizationElectronic and particle interactionsTight-binding formulationStudies on Si-H, Cu and Ag clustersHow do the evolutionary algorithms

perform?

Some Copper ClustersSome Copper Clusters

That’s how they evolved!That’s how they evolved!

SGA

Gray

DE

Optimum

Some Si-H ClustersSome Si-H Clusters

Why do we bother Why do we bother about the clusters, about the clusters, by the way……?!by the way……?!

Tales of Continuous CastingTales of Continuous Casting

Why it’s a difficult problem?Why it’s a difficult problem?

Need to maximize casting speedNeed an optimum shell thicknessPlenty of variablesSeveral constraintsRequires solution of non-linear heat transfer

equationsSingle and multi-objective formulations

Optimization works better!Optimization works better!

0.0

0.4

0.8

1.2

1.6

0 1 2 3 4 5 6 7 8 9

Shell thickness (m)

0.009

0.012

0.0140.016

0.0200.0240.026

0.007

0.010

0.0120.015

0.017.0200.022

Length of Mold (vs) Casting Speed

Casting speed x (10-2)m

Len

gth

of

Mo

ld (

m)

Some more results!Some more results!

Metal RollingMetal Rolling

A typical optimized scheduleA typical optimized schedule

Studies on ALONStudies on ALON

-43 -42 -41 -40 -39 -38 -37 -36 -35 -34 -33 -32 -31 -30 -29

-12

-10

-8

-6

Predominance area diagram

_ _ _ _ _ _ _ _ _ _ _ _ 2123 K

____ _ _ ______ _ _ 2098 K

________________ 2073 KALON

AlN

Al2O3

Al

ln(P

N2)

ln(PO2

)

0.40.60.81.0

1.21.4

1.61.8

2.02.2

98.098.2

98.4

98.6

98.8

99.0

99.2

99.4

99.6

99.8

100.0

20702080

20902100

21102120

2130

Why ALON is so important?Why ALON is so important?

An unusual combination of strength and transparency

Plenty of possible civilian and defense application

Highly cumbersome and expensive to make where genetic algorithms can contribute in a very big way

Studies on Magneto-Studies on Magneto-Rehological FluidsRehological Fluids

One can consider four multi-One can consider four multi-objective scenariosobjective scenarios

Maximum yield stress, maximum force of separation

Maximum yield stress , minimum force of separation

Minimum yield stress, maximum force of separation

Minimum yield stress, minimum force of separation

A Welding ProblemA Welding Problem

The are many more problems that The are many more problems that I have attempted to solve, and I have attempted to solve, and there are lot more that I simply there are lot more that I simply

couldn’t do!couldn’t do!

However, I realize all the time However, I realize all the time that………that………

We need better materials, better designs We need better materials, better designs and more vigorous applications of GA!and more vigorous applications of GA!