1. Genetic Algorithms in Materials Processing N. Chakraborti Department of Metallurgical & Materials Engineering Indian Institute of Technology Kharagpur (W.B) 721 302 INDIA

2. 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

3. 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

4. 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; }

5. 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; }

6. Gray Coded Genetic Algorithms The problem of Hamming Cliff 01111111  127 10000000  128 XOR operation 01111111  Gray coded as  01000000 10000000  Gray coded as  11000000

7. 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

8. 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

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

10. 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

11. 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

12. 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

13. 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.

14. 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…..

15. 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?

16. Some Copper Clusters

17. That’s how they evolved! SGA Gray DE Optimum

18. Some Si-H Clusters

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

20. Tales of Continuous Casting

21. 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

22. Optimization works better!

23. Some more results!

24. Metal Rolling

25. A typical optimized schedule

26. Studies on ALON

27. 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

28. Studies on Magneto- Rehological Fluids

29. 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

30. A Welding Problem

31. 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………

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