Selection of the optimal parameters for machine learning tasks is challenging. Some results may be bad not because the data is noisy or the used learning algorithm is weak, but due to the bad selection of the parameters values. This presentation gives a brief introduction about evolutionary algorithms (EAs) and describes genetic algorithm (GA) which is one of the simplest random-based EAs. A step-by-step example is given in addition to its implementation in Python 3.5. --------------------------------- Read more about GA: Yu, Xinjie, and Mitsuo Gen. Introduction to evolutionary algorithms. Springer Science & Business Media, 2010. https://www.kdnuggets.com/2018/03/introduction-optimization-with-genetic-algorithm.html https://www.linkedin.com/pulse/introduction-optimization-genetic-algorithm-ahmed-gad

1. Genetic Algorithm (GA) Optimization –
Step-by-Step Example with Python
Implementation
Ahmed Fawzy Gad
ahmed.fawzy@ci.menofia.edu.eg
MENOUFIA UNIVERSITY
FACULTY OF COMPUTERS AND INFORMATION
ARTIFICIAL INTELLIGENCE
ALL DEPARTMENTS
‫المنوفية‬ ‫جامعة‬
‫الحاسبات‬ ‫كلية‬‫والمعلومات‬
‫اإلصطناعي‬ ‫الذكاء‬
‫األقسام‬ ‫جميع‬‫المنوفية‬ ‫جامعة‬

2. Training a Machine Learning Model
• Goal is to find the set of parameters (𝒘 𝟏:𝒘 𝟔) that maps the following
input to its output.
𝒚 = 𝒘 𝟏 𝒙 𝟏+𝒘 𝟐 𝒙 𝟐+𝒘 𝟑 𝒙 𝟑+𝒘 𝟒 𝒙 𝟒+𝒘 𝟓 𝒙 𝟓+𝒘 𝟔 𝒙 𝟔
𝒙 𝟏 𝒙 𝟐 𝒙 𝟑 𝒙 𝟒 𝒙 𝟓 𝒙 𝟔 𝒚
4 -2 7 5 11 1 44.1
𝒚′
= 𝟒𝒘 𝟏 − 𝟐𝒘 𝟐 + 𝟕𝒘 𝟑 + 𝟓𝒘 𝟒 + 𝟏𝟏𝒘 𝟓 + 𝒘 𝟔
Data

3. 𝒘 𝟏 𝒘 𝟐 𝒘 𝟑 𝒘 𝟒 𝒘 𝟓 𝒘 𝟔
2.4 0.7 8 -2 5 1.1
Solution 1
𝒚′
= 𝟒𝒘 𝟏 − 𝟐𝒘 𝟐 + 𝟕𝒘 𝟑 + 𝟓𝒘 𝟒 + 𝟏𝟏𝒘 𝟓 + 𝒘 𝟔
𝒚′
= 𝟏𝟏𝟎. 𝟑
Absolute Error 𝒆𝒓𝒓𝒐𝒓 = |𝒚 − 𝒚′
|
𝒆𝒓𝒓𝒐𝒓 = 𝟔𝟔. 𝟐
𝒆𝒓𝒓𝒐𝒓 = 𝟒𝟒. 𝟏 − 𝟏𝟏𝟎. 𝟑

4. 𝒘 𝟏 𝒘 𝟐 𝒘 𝟑 𝒘 𝟒 𝒘 𝟓 𝒘 𝟔
-0.4 2.7 5 -1 7 0.1
Solution 2
𝒚′
= 𝟏𝟎𝟎. 𝟏
Absolute Error 𝒆𝒓𝒓𝒐𝒓 = |𝒚 − 𝒚′
|
𝒆𝒓𝒓𝒐𝒓 = 𝟓𝟔
𝒆𝒓𝒓𝒐𝒓 = 𝟒𝟒. 𝟏 − 𝟏𝟎𝟎. 𝟏

5. 𝒘 𝟏 𝒘 𝟐 𝒘 𝟑 𝒘 𝟒 𝒘 𝟓 𝒘 𝟔
-1 2 2 -3 2 0.9
Solution 3
𝒚′
= 𝟏𝟑. 𝟗
Absolute Error 𝒆𝒓𝒓𝒐𝒓 = |𝒚 − 𝒚′
|
𝒆𝒓𝒓𝒐𝒓 = 𝟑𝟎. 𝟐
𝒆𝒓𝒓𝒐𝒓 = 𝟒𝟒. 𝟏 − 𝟏𝟑. 𝟗

6. 𝒘 𝟏 𝒘 𝟐 𝒘 𝟑 𝒘 𝟒 𝒘 𝟓 𝒘 𝟔
-1 2 2 -3 2 0.9
Solution 3
𝒚′
= 𝟏𝟑. 𝟗
Absolute Error 𝒆𝒓𝒓𝒐𝒓 = |𝒚 − 𝒚′
|
𝒆𝒓𝒓𝒐𝒓 = 𝟑𝟎. 𝟐
𝒆𝒓𝒓𝒐𝒓 = 𝟒𝟒. 𝟏 − 𝟏𝟑. 𝟗
Difficult to find the best solution manually.
Use optimization technique such as Genetic Algorithm (GA).

7. • Genetic algorithm is based on natural evolution of organisms.
• A brief biological background will be helpful in understanding GA.
Genetic Algorithm (GA)

8. • Genetic algorithm is based on natural evolution of organisms.
• A brief biological background will be helpful in understanding GA.
Chromosomes
Genes
Eye
Color
Dimples Freckles
Organism
Cells
Genetic Algorithm (GA)

9. • Genetic algorithm is based on natural evolution of organisms.
• A brief biological background will be helpful in understanding GA.
Chromosomes
Genes
Eye
Color
Dimples Freckles
Organism
Cells
Genetic Algorithm (GA)
https://www.icr.org/article/myth-human-evolution

10. • Genetic algorithm is based on natural evolution of organisms.
• A brief biological background will be helpful in understanding GA.
Chromosome
Genes
GA
Individuals/Solutions
Genetic Algorithm (GA)
Chromosomes
Genes
Eye
Color
Dimples Freckles
Organism
Cells

11. What are the Genes?
• Gene is anything that is able to enhance the results when changed.
• By exploring the following model, the 6 weights are able to enhance
the results. Thus each weight will represent a gene in GA.
𝒚 = 𝒘 𝟏 𝒙 𝟏+𝒘 𝟐 𝒙 𝟐+𝒘 𝟑 𝒙 𝟑+𝒘 𝟒 𝒙 𝟒+𝒘 𝟓 𝒙 𝟓+𝒘 𝟔 𝒙 𝟔
Gene 0 Gene 1 Gene 2 Gene 3 Gene 4 Gene 5
𝒘 𝟏 𝒘 𝟐 𝒘 𝟑 𝒘 𝟒 𝒘 𝟓 𝒘 𝟔

12. 2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
Initial Population of Solutions (Generation 0)
Population Size = 6

13. 2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
Initial Population of Solutions (Generation 0)
Chromosome
Gene

14. Survival of the Fittest
Fitness Function
Fitness Value
The Higher the Value,
the Better the Solution
Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

15. Survival of the Fittest
Fitness Function
Fitness Value
The Higher the Value,
the Better the Solution
𝑭 𝒄 =
𝟏
𝒆𝒓𝒓𝒐𝒓
=
𝟏
|𝒚 − 𝒚′|
Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

16. Initial Population of Solutions (Generation 0)
𝒚′ 𝑭(𝑪)
2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

17. Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
𝒚′ 𝑭(𝑪)
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

18. Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
𝒚′ 𝑭(𝑪)
𝒚′
= 𝟒𝒘 𝟏 − 𝟐𝒘 𝟐 + 𝟕𝒘 𝟑 + 𝟓𝒘 𝟒 + 𝟏𝟏𝒘 𝟓 + 𝒘 𝟔
𝒚′
= 𝟒 ∗ 𝟐. 𝟒 −2 ∗ 0.7 + 7 ∗ 8 + 5 ∗ -2 + 11 ∗ 5 + 𝟏. 𝟏
𝒚′
= 𝟏𝟏𝟎. 𝟑
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

19. Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
𝒚′ 𝑭(𝑪)
110.3
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

20. Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
𝒚′ 𝑭(𝑪)
110.3
𝑭 𝒄 =
𝟏
𝒆𝒓𝒓𝒐𝒓
=
𝟏
|𝟒𝟒. 𝟏 − 𝟏𝟏𝟎. 𝟑|
=
𝟏
𝟔𝟔. 𝟐
= 0.015
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

21. Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
𝒚′ 𝑭(𝑪)
110.3 0.015
𝑭 𝒄 =
𝟏
𝒆𝒓𝒓𝒐𝒓
=
𝟏
|𝟒𝟒. 𝟏 − 𝟏𝟏𝟎. 𝟑|
=
𝟏
𝟔𝟔. 𝟐
= 0.015
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

22. Initial Population of Solutions (Generation 0)
2.4 0.7 8 -2 5 1.1
𝒚′ 𝑭(𝑪)
110.3 0.015
100.1 0.018
13.9 0.033
127.9 0.012
69.2 0.0398
3 0.024
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

23. Mating Pool
Select best individuals as parents for mating to
generate new individuals.
𝒚′ 𝑭(𝑪)
110.3 0.015
100.1 0.018
13.9 0.033
127.9 0.012
69.2 0.0398
3 0.024
2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

24. Mating Pool
Add best 3 individuals to the mating pool for producing
the next generation of solutions.
𝒚′ 𝑭(𝑪)
110.3 0.015
100.1 0.018
13.9 0.033
127.9 0.012
69.2 0.04
3 0.024
2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

25. Mating Pool
2.4 0.7 8 -2 5 1.1
-0.4 2.7 5 -1 7 0.1
-1 2 2 -3 2 0.9
4 7 12 6.1 1.4 -4
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
Add best 3 individuals to the mating pool for producing
the next generation of solutions.
𝒚′ 𝑭(𝑪)
110.3 0.015
100.1 0.018
13.9 0.033
127.9 0.012
69.2 0.04
3 0.024

26. Mating Pool
-1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3

27. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
Mating Pool

28. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
Mating Pool Crossover

29. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
Mating Pool Crossover

30. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
Mating Pool Crossover
-1 2 2 2.4 4.8 0Offspring

31. Mating Pool Mutation
-1 2 2 2.4 4.8 0Offspring

32. Mating Pool Mutation
-1 2 2 2.4 4.8 0Offspring

33. Mating Pool Mutation
-1 2 2 2.4 4.8 0Offspring
= 𝟒. 𝟖/𝟐
= 𝟐. 𝟒

34. Mating Pool Mutation
-1 2 2 2.4 4.8 0Offspring
= 𝟒. 𝟖/𝟐
= 𝟐. 𝟒
-1 2 2 2.4 2.4 0Mutant

35. Mating Pool
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
Crossover
3.1 4 0 6 3 3Offspring

36. Mating Pool
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
Crossover
3.1 4 0 6 3 3Offspring
Mutation
3.1 4 0 6 1.5 3Mutant

37. Mating Pool
-2 3 -7 6 3 3
Crossover
-2 3 -7 -3 2 0.9Offspring
-1 2 2 -3 2 0.9

38. Mating Pool
-2 3 -7 6 3 3
Crossover
-2 3 -7 -3 2 0.9Offspring
Mutation
-2 3 -7 -3 1 0.9Mutant
-1 2 2 -3 2 0.9

39. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0
Old
Individuals
New
Individuals
New Population (Generation 1)

40. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0
Old
Individuals
New
Individuals
New Population (Generation 1)
Why Reusing Old Individuals?

41. -1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0
Old
Individuals
New
Individuals
New Population (Generation 1)
Why Reusing Old Individuals?
GA is a random-based optimization technique. There is no guarantee that the new individuals will be better
than the previous individuals. Keeping the old individuals at least saves the results from getting worse.

42. New Population (Generation 1)
Old
Individuals
New
Individuals
Population Mating Pool Crossover MutationFitness Value
-1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0

43. New Population (Generation 1)
𝒚′ 𝑭(𝑪)
13.9 0.033
69.2 0.04
3 0.024
44.4 3.333
53.9 0.102
-66.1 0.009
-1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0

44. New Population (Generation 1)
𝒚′ 𝑭(𝑪)
13.9 0.033
69.2 0.04
3 0.024
44.4 3.333
53.9 0.102
-66.1 0.009
Some new individuals make the results worse.
This is why it is preferred to keep the best old individuals.
-1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0

45. New Population (Generation 1)
𝒚′ 𝑭(𝑪)
13.9 0.033
69.2 0.04
3 0.024
44.4 3.333
53.9 0.102
-66.1 0.009
-1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0

46. New Population (Generation 1)
𝒚′ 𝑭(𝑪)
13.9 0.033
69.2 0.04
3 0.024
44.4 3.333
53.9 0.102
-66.1 0.009
-1 2 2 -3 2 0.9
3.1 4 0 2.4 4.8 0
-2 3 -7 6 3 3
-2 3 -7 -3 1 0.9
3.1 4 0 6 1.5 3
-1 2 2 2.4 2.4 0

47. Mating Pool
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3

48. Mating Pool Crossover
3.1 4 0 2.4 2.4 0Offspring
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0

49. Mating Pool Crossover
3.1 4 0 2.4 2.4 0Offspring
Mutation
3.1 4 0 2.4 1.2 0Mutant
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0

50. Mating Pool
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
-1 2 2 6 1.5 3Offspring
Crossover

51. Mating Pool
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
-1 2 2 6 1.5 3Offspring
Mutation
-1 2 2 6 0.75 3Mutant
Crossover

52. Mating Pool
3.1 4 0 6 1.5 3
3.1 4 0 2.4 4.8 0Offspring
Crossover
3.1 4 0 2.4 4.8 0

53. Mating Pool
3.1 4 0 6 1.5 3
3.1 4 0 2.4 4.8 0Offspring
Mutation
3.1 4 0 2.4 2.4 0Mutant
Crossover
3.1 4 0 2.4 4.8 0

54. New Population (Generation 2)
Old
Individuals
New
Individuals
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
3.1 4 0 2.4 2.4 0
-1 2 2 6 0.75 3
3.1 4 0 2.4 1.2 0

55. New Population (Generation 2)
Old
Individuals
New
Individuals
Population Mating Pool Crossover MutationFitness Value
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
3.1 4 0 2.4 2.4 0
-1 2 2 6 0.75 3
3.1 4 0 2.4 1.2 0

56. New Population (Generation 2)
𝒚′ 𝑭(𝑪)
69.2 0.04
44.4 3.333
53.9 0.102
29.6 0.069
47.25 0.318
42.8 0.77
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
3.1 4 0 2.4 2.4 0
-1 2 2 6 0.75 3
3.1 4 0 2.4 1.2 0

57. New Population (Generation 2)
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
3.1 4 0 2.4 2.4 0
-1 2 2 6 0.75 3
3.1 4 0 2.4 1.2 0
𝒚′ 𝑭(𝑪)
69.2 0.04
44.4 3.333
53.9 0.102
29.6 0.069
47.25 0.318
42.8 0.77

58. New Population (Generation 2)
Continue.
3.1 4 0 2.4 4.8 0
-1 2 2 2.4 2.4 0
3.1 4 0 6 1.5 3
3.1 4 0 2.4 2.4 0
-1 2 2 6 0.75 3
3.1 4 0 2.4 1.2 0
𝒚′ 𝑭(𝑪)
69.2 0.04
44.4 3.333
53.9 0.102
29.6 0.069
47.25 0.318
42.8 0.77

59. import numpy
import GARI
# Population size
sol_per_pop = 6
# Mating pool size
num_parents_mating = 3
# Creating an initial population randomly.
new_population = numpy.zeros((6, 6))
new_population[0, :] = [2.4, 0.7, 8, -2, 5, 1.1]
new_population[1, :] = [-0.4, 2.7, 5, -1, 7, 0.1]
new_population[2, :] = [-1, 2, 2, -3, 2, 0.9]
new_population[3, :] = [4, 7, 12, 6.1, 1.4, -4]
new_population[4, :] = [3.1, 4, 0, 2.4, 4.8, 0]
new_population[5, :] = [-2, 3, -7, 6, 3, 3]
for iteration in range(10):
# Measing the fitness of each chromosome in the population.
qualities = GARI.pop_fitness(new_population)
# Selecting the best parents in the population for mating.
parents = GARI.select_mating_pool(new_population, qualities,
num_parents_mating)
# Generating next generation using crossover.
new_population = GARI.crossover(parents,
n_individuals=sol_per_pop)
new_population = GARI.mutation(new_population)
in_sample = [4, -2, 7, 5, 11, 1]
for k in range(6):
print(numpy.sum(new_population[k, :] * in_sample))
Python
Implementation

60. import numpy
import GARI
# Population size
sol_per_pop = 6
# Mating pool size
num_parents_mating = 3
# Creating an initial population randomly.
new_population = numpy.zeros((6, 6))
new_population[0, :] = [2.4, 0.7, 8, -2, 5, 1.1]
new_population[1, :] = [-0.4, 2.7, 5, -1, 7, 0.1]
new_population[2, :] = [-1, 2, 2, -3, 2, 0.9]
new_population[3, :] = [4, 7, 12, 6.1, 1.4, -4]
new_population[4, :] = [3.1, 4, 0, 2.4, 4.8, 0]
new_population[5, :] = [-2, 3, -7, 6, 3, 3]
for iteration in range(10):
# Measing the fitness of each chromosome in the population.
qualities = GARI.pop_fitness(new_population)
# Selecting the best parents in the population for mating.
parents = GARI.select_mating_pool(new_population, qualities,
num_parents_mating)
# Generating next generation using crossover.
new_population = GARI.crossover(parents,
n_individuals=sol_per_pop)
new_population = GARI.mutation(new_population)
in_sample = [4, -2, 7, 5, 11, 1]
for k in range(6):
print(numpy.sum(new_population[k, :] * in_sample))
Python
Implementation

61. import numpy
import GARI
# Population size
sol_per_pop = 6
# Mating pool size
num_parents_mating = 3
# Creating an initial population randomly.
new_population = numpy.zeros((6, 6))
new_population[0, :] = [2.4, 0.7, 8, -2, 5, 1.1]
new_population[1, :] = [-0.4, 2.7, 5, -1, 7, 0.1]
new_population[2, :] = [-1, 2, 2, -3, 2, 0.9]
new_population[3, :] = [4, 7, 12, 6.1, 1.4, -4]
new_population[4, :] = [3.1, 4, 0, 2.4, 4.8, 0]
new_population[5, :] = [-2, 3, -7, 6, 3, 3]
for iteration in range(10):
# Measing the fitness of each chromosome in the population.
qualities = GARI.pop_fitness(new_population)
# Selecting the best parents in the population for mating.
parents = GARI.select_mating_pool(new_population, qualities,
num_parents_mating)
# Generating next generation using crossover.
new_population = GARI.crossover(parents,
n_individuals=sol_per_pop)
new_population = GARI.mutation(new_population)
in_sample = [4, -2, 7, 5, 11, 1]
for k in range(6):
print(numpy.sum(new_population[k, :] * in_sample))
Python
Implementation

62. import numpy
import GARI
# Population size
sol_per_pop = 6
# Mating pool size
num_parents_mating = 3
# Creating an initial population randomly.
new_population = numpy.zeros((6, 6))
new_population[0, :] = [2.4, 0.7, 8, -2, 5, 1.1]
new_population[1, :] = [-0.4, 2.7, 5, -1, 7, 0.1]
new_population[2, :] = [-1, 2, 2, -3, 2, 0.9]
new_population[3, :] = [4, 7, 12, 6.1, 1.4, -4]
new_population[4, :] = [3.1, 4, 0, 2.4, 4.8, 0]
new_population[5, :] = [-2, 3, -7, 6, 3, 3]
for iteration in range(10):
# Measing the fitness of each chromosome in the population.
qualities = GARI.pop_fitness(new_population)
# Selecting the best parents in the population for mating.
parents = GARI.select_mating_pool(new_population, qualities,
num_parents_mating)
# Generating next generation using crossover.
new_population = GARI.crossover(parents,
n_individuals=sol_per_pop)
new_population = GARI.mutation(new_population)
in_sample = [4, -2, 7, 5, 11, 1]
for k in range(6):
print(numpy.sum(new_population[k, :] * in_sample))
Python
Implementation

63. 22.def crossover(parents, n_individuals=6):
23. new_population = numpy.empty((6,6))
24.
25. #Previous parents (best elements).
26. new_population[0:parents.shape[0], :] = parents
27. new_population[3, 0:3] = parents[0, 0:3]
28. new_population[3, 3:] = parents[1, 3:]
29. new_population[4, 0:3] = parents[1, 0:3]
30. new_population[4, 3:] = parents[2, 3:]
31. new_population[5, 0:3] = parents[2, 0:3]
32. new_population[5, 3:] = parents[0, 3:]
33.
34. return new_population
35.
36.def mutation(population):
37. for idx in range(population.shape[0]):
38. population[idx, 4] = population[idx, 4]/3
39. return population
1.import numpy
2.
3.def fitness_fun(indiv_chrom):
4. in_sample = [4,-2,7,5,11,1]
5. quality = 1/numpy.abs(44.1-numpy.sum(indiv_chrom*in_sample))
6. return quality
7.
8.def pop_fitness(pop):
9. qualities = numpy.zeros(pop.shape[0])
10. for indv_num in range(pop.shape[0]):
11. qualities[indv_num] = fitness_fun(pop[indv_num, :])
12. return qualities
13.
14.def select_mating_pool(pop, qualities, num_parents):
15. parents = numpy.empty((num_parents, pop.shape[1]))
16. for parent_num in range(num_parents):
17. max_qual_idx = numpy.where(qualities == numpy.max(qualities))
18. max_qual_idx = max_qual_idx[0][0]
19. parents[parent_num, :] = pop[max_qual_idx, :]
20. qualities[max_qual_idx] = -1
21. return parents
Python Implementation

64. References
• Yu, Xinjie, and Mitsuo Gen. Introduction to
evolutionary algorithms. Springer Science &
Business Media, 2010.
• https://www.kdnuggets.com/2018/03/introduc
tion-optimization-with-genetic-algorithm.html
• https://www.linkedin.com/pulse/introduction-
optimization-genetic-algorithm-ahmed-gad