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Genetic Algorithms

Genetic Algorithms. Genetic Algorithms : mimicking the process of natural evolution. Nature as an optimizer (adapting to the environment): Structural Engineer : Bee-hive, Bamboo CFD solver: Birds , fishes Drag reducer : Penguin body Optimization procedure :

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Genetic Algorithms

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  1. Genetic Algorithms

  2. Genetic Algorithms : mimicking the process of natural evolution • Nature as an optimizer (adapting to the environment): • Structural Engineer : Bee-hive, Bamboo • CFD solver: Birds , fishes • Drag reducer : Penguin body • Optimization procedure : • Inheritance :Useful information is passed on from one generation to another • Crossover and mutation: Offspring having characteristics of both parents are created • Natural selection : “Better” individuals are retained while the “weaker” ones die out.

  3. Working principle of GA

  4. Problem • Design a can with a volume of at least 300ml and least cost.

  5. Representation(Coding of decision variables) • All the decision variables are represented as binary strings. • Depending on variable bounds and required precision the length of string is decided as follows: • In current example let: 0< d,h <31 and we represent both with strings of length 5 each : • So a can with height 10 cm and diameter 8 cm is represented as (d,h)=(8,10)cm Chromosome: 01000 01010 d h

  6. Fitness Assignment • Based on value of decision variables the objective function value is calculated and accordingly a fitness value is assigned, if the solution is infeasible, it is penalized by adding an extra artificial cost. • Can1: 01000 01010  (d,h)=(8,10) f= 0.065[π(8)2 /2 + π(10)(8) ] = 23 g= π(8)2 (10) /4 =502 >300 Fitness of Can1 is 23 • Can2: 00100 00101  (d,h)=(4,5) f= 0.065[π(4)2 /2 + π(4)(5) ] = 5.72 g= π(4)2 (5) /4 =63 < 300 Penalty = (300-g)/7.5 = 32 Fitness of Can2 is 37.72 23 38

  7. Population initialization • To start a GA run, randomly the decision variables are initialized : Can1 : 01000 01010 ------ Can2 : 00100 00101 -------------------------- Can3 : 01110 00110 ------ Can4 : 01010 00111 -------------------------- Can5 : 01100 01010----- Can6: 00100 01000 ----------------------------

  8. Survival of fittest : Selection operator • Tasks of selection operator : • Identify good solutions • Make multiple copies of good solutions • Eliminate bad solutions from the population so that the population size remains constant. • Various selection operators • Tournament selection • Proportionate selection • Ranking selection

  9. Tournament selection MATING POOL 30 23 23 30 8 +14 30 + 32 25 23 25 23 + 32 6 37 25 25 37 37 8 +14

  10. Creation by Crossover • New solutions having characteristics of both “parents” are created, i.e crossover is responsible for search aspect of GA • Single point crossover : • Two point crossover : • In order to preserve some good individuals selected during reproduction operator ,not all individuals are crossed over. (10 6) 0 1 0 0 0 0 1 0 1 0 0 1 0 1 0 0 0 1 1 0 22 (8 10) 23 0 1 1 1 0 0 0 1 1 0 (14 6) (12 10) 0 1 1 0 0 0 1 0 1 0 39 37 (14 10) 0 1 0 0 0 0 1 0 1 0 0 1 1 1 0 0 1 0 1 0 (8 10) 23 49 0 1 1 1 0 0 0 1 1 0 (14 6) (8 6) 0 1 0 0 0 0 0 1 1 0 16 37

  11. Creation by mutation • Changes a 1 to 0 and vice versa with a certain mutation probability. • Keeps diversity in population. • Very helpful in taking out population from a local optima (8 6) 0 1 0 1 0 0 0 1 1 0 (10 6) 0 1 0 0 0 0 0 1 1 0 22 16

  12. Simulation • Rastrigin function: • Local optima at each integer • Global Optima at xi = 0 • In present simulation, • n = 2 • Population = 20 initialized in range [20 60]

  13. Rastrigin : Two variable version

  14. Rastrigin : Two variable version

  15. Simulation:

  16. Rastrigin : 100 variable version

  17. Advantages Of GA and Comparison with Classical Methods • Work with a discrete search space hence discontinuous functions can be handled. • Exploits similarities in the string structures to make an effective search. • Unlike classical methods which use single solution ,GA ’s work with population of solutions that are processed simultaneously ,hence chances of obtaining global optimum are more. • No auxiliary problem information like gradient is required. • Classical methods work on fixed transition rules to move from one solution to another i.e the destiny of these methods is predetermined, so these methods can only be applied to a certain class of problems. GA’s on the other hand use probabilistic rules to guide their search, this allows GA’s to recover quickly from early mistakes , if any , and also enables them to handle wide class of problems

  18. Refernces • Kalyanmoy Deb , Multi-objective using Evolutionary Algorithms

  19. Questions • What can be the possible drawbacks of GA • In process of finding global optimum can we also report the local optimum solutions. • Is it guaranteed that GA will always find the global optimum or even a local optimum • What can be the possible termination criteria's of a GA run • In case of problems having multiple optima’s will GA always give the same solution.

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