Genetic Algorithms in Materials Processing N. Chakraborti Department of Metallurgical & Materials Engineering Indian Institute of Technology Kharagpur (W.B) INDIA

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 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 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 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 Algorithms The problem of Hamming Cliff   128 XOR operation  Gray coded as   Gray coded as 

Island Model A number of island A number of tribes in each Inter-tribe migration Inter-island migration Occasional immigration and replacement Most suitable for parallel processing

Micro Genetic Algorithms Small population size, usually 5 Tournament selection Uniform crossover No mutation Elitism Periodic replenishing of population Good for non-stationary objective functions

Multi-modality and Pareto- optimality The genetic drift Sharing and Niching in multi-dimensional hyperspace Euclidean vs. Hamming distance Dominated vs. non-dominated solutions

Pareto Converging Genetic Algorithms Island and tribes Provisions for Elitism Rank based Tournament Selection Intra-tribe and Inter-tribe Ranking Rank histogram and Rank ratio Immense scope for Parallel Processing

Strength Pareto Evolutionary Algorithm 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- Objective 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 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 problems that turn me on! To begin with, they all deal with materials of one kind or the other…..

Geometry Optimization of Clusters Material design and geometry optimization Electronic and particle interactions Tight-binding formulation Studies on Si-H, Cu and Ag clusters How do the evolutionary algorithms perform?

Some Copper Clusters

That’s how they evolved! SGA Gray DE Optimum

Some Si-H Clusters

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

Tales of Continuous Casting

Why it’s a difficult problem? Need to maximize casting speed Need an optimum shell thickness Plenty of variables Several constraints Requires solution of non-linear heat transfer equations Single and multi-objective formulations

Optimization works better!

Some more results!

Metal Rolling

A typical optimized schedule

Studies on ALON

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- Rehological Fluids

One can consider four multi- objective 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 Problem

The are many more problems that I have attempted to solve, and there are lot more that I simply couldn’t do! However, I realize all the time that………

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