1. GENETIC ALGORITHMS AND GENETIC PROGRAMMING

2. John R. Koza Consulting Professor (Medical Informatics)
Department of Medicine
School of Medicine
Consulting Professor
Department of Electrical Engineering
School of Engineering
Stanford University
Stanford, California 94305

3. DEFINITION OF THE GENETIC ALGORITHM (GA)
The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation.

4. GENETIC ALGORITHM (GA)
Generation 0
Generation 1
Individuals
Fitness
Offspring
011 $3
111
001 $1
010
110 $6 $2

5. HAMBURGER RESTAURANT PROBLEM
Price
1 = $ 0.50 price
0 = $10.00 price
Drink
1 = Coca Cola
0 = Wine
Ambiance
1 = Fast snappy service
0 = Leisurely service with tuxedoed waiter

6. CHROMOSOME (GENOME) OF THE GLOBAL OPTIMUM
McDONALD's 1

7. THE SEARCH SPACE Alphabet size K=2, Length L=31
000 2
001 3
010 4
011 5
100 6
101 7
110 8
111
Alphabet size K=2, Length L=3
Size of search space: KL=2L=23=8

8. IMPRACTICALITY OF RANDOM OR ENUMERATIVE SEARCH
81-bit problems are very small for GA
However, even if L is as small as 81, 281 ~ 1027 = number of nanoseconds since the beginning of the universe 15 billion years ago

9. GA FLOWCHART

10. GENERATION 0 Generation 0 1 011 3 2 001 110 6 4 010 Total Worst
Average
Best

11. DEFINITION OF THE GENETIC ALGORITHM (GA)
The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation.

12. PROBABILISTIC SELECTION BASED ON FITNESS
Better individuals are preferred
Best is not always picked
Worst is not necessarily excluded
Nothing is guaranteed
Mixture of greedy exploitation and adventurous exploration
Similarities to simulated annealing (SA)

13. DARWINIAN FITNESS PROPORTIONATE SELECTION
Generation 0
Mating pool 1
011 3
.25 2
001
.08
110 6
.50 4
010
.17
Total 12 17
Worst
Average
3.00
4.5
Best

14. DEFINITION OF THE GENETIC ALGORITHM (GA)
The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation.

15. MUTATION OPERATION Parent chosen probabilistically based on fitness
Mutation point chosen at random
One offspring
Parent
010
Parent
--0
Offspring
011

16. AFTER MUTATION OPERATION
Generation 0
Mating pool
Generation 1 1
011 3
.25 2
001
.08
110 6
.50 4
010
.17
---
Total 12 17
Worst
Average
3.00
4.5
Best

17. CROSSOVER OPERATION
2 parents chosen probabilistically based on fitness
Parent 1
Parent 2
011
110

18. CROSSOVER (CONTINUED)
Interstitial point picked at random
2 remainders
2 offspring produced by crossover
Fragment 1
Fragment 2
01-
11-
Remainder 1
Remainder 2
- - 1
- - 0
Offspring 1
Offspring 2
111
010

19. AFTER CROSSOVER OPERATION
Generation 0
Mating pool
Generation 1 1
011 3
.25 2
111 7
001
.08
110 6
010
.50 4
.17
Total 12 17
Worst
Average
3.00
4.5
Best

20. AFTER REPRODUCTION OPERATION
Generation 0
Mating pool
Generation 1 1
011 3
.25 2
001
.08
110 6
.50
--- 4
010
.17
Total 12 17
Worst
Average
3.00
4.5
Best

21. DEFINITION OF THE GENETIC ALGORITHM (GA)
The genetic algorithm is a probabalistic search algorithm that iteratively transforms a set (called a population) of mathematical objects (typically fixed-length binary character strings), each with an associated fitness value, into a new population of offspring objects using the Darwinian principle of natural selection and using operations that are patterned after naturally occurring genetic operations, such as crossover (sexual recombination) and mutation.

22. GENERATION 1 Generation 0 Mating pool Generation 1 1 011 3 .25 2 111 7
001
.08
110 6
010
.50
--- 4
.17
Total 12 17 18
Worst
Average
3.00
4.5
Best

23. PROBABILISTIC STEPS The initial population is typically random
Probabilistic selection based on fitness
- Best is not always picked
- Worst is not necessarily excluded
Random picking of mutation and crossover points
Often, there is probabilistic scenario as part of the fitness measure

24. GENETIC PROGRAMMING
BBB4003

25. THE CHALLENGE
"How can computers learn to solve problems without being explicitly programmed? In other words, how can computers be made to do what is needed to be done, without being told exactly how to do it?"
 Attributed to Arthur Samuel (1959)

26. CRITERION FOR SUCCESS
"The aim [is] ... to get machines to exhibit behavior, which if done by humans, would be assumed to involve the use of intelligence.“
 Arthur Samuel (1983)

27. REPRESENTATIONS Binary decision diagrams Decision trees
Formal grammars
Coefficients for polynomials
Reinforcement learning tables
Conceptual clusters
Classifier systems
Decision trees
If-then production rules
Horn clauses
Neural nets
Bayesian networks
Frames
Propositional logic

28. A COMPUTER PROGRAM
BBB121

29. GENETIC PROGRAMMING (GP)
GP applies the approach of the genetic algorithm to the space of possible computer programs
Computer programs are the lingua franca for expressing the solutions to a wide variety of problems
A wide variety of seemingly different problems from many different fields can be reformulated as a search for a computer program to solve the problem.

30. GP  MAIN POINTS
Genetic programming now routinely delivers high-return human-competitive machine intelligence.
Genetic programming is an automated invention machine.
Genetic programming has delivered a progression of qualitatively more substantial results in synchrony with five approximately order-of-magnitude increases in the expenditure of computer time.

31. GP FLOWCHART
BBB2028 (converted to BMP)

32. A COMPUTER PROGRAM IN C int foo (int time) { int temp1, temp2;
if (time > 10)
temp1 = 3;
else
temp1 = 4;
temp2 = temp ;
return (temp2); }

33. OUTPUT OF C PROGRAM
Time
Output 6 1 2 3 4 5 7 8 9 10 11 12

34. PROGRAM TREE
(+ 1 2 (IF (> TIME 10) 3 4))

35. CREATING RANDOM PROGRAMS
Creation.avi (creation.gif converted to AVI movie file)

36. CREATING RANDOM PROGRAMS
Available functions F = {+, -, *, %, IFLTE}
Available terminals T = {X, Y, Random-Constants}
The random programs are:
Of different sizes and shapes
Syntactically valid
Executable

37. GP GENETIC OPERATIONS Reproduction Mutation
Crossover (sexual recombination)
Architecture-altering operations

38. MUTATION OPERATION
Mutation.avi

39. MUTATION OPERATION
Select 1 parent probabilistically based on fitness
Pick point from 1 to NUMBER-OF-POINTS
Delete subtree at the picked point
Grow new subtree at the mutation point in same way as generated trees for initial random population (generation 0)
The result is a syntactically valid executable program
Put the offspring into the next generation of the population

40. CROSSOVER OPERATION
Crossover.avi

41. CROSSOVER OPERATION
Select 2 parents probabilistically based on fitness
Randomly pick a number from 1 to NUMBER-OF-POINTS for 1st parent
Independently randomly pick a number for 2nd parent
The result is a syntactically valid executable program
Put the offspring into the next generation of the population
Identify the subtrees rooted at the two picked points

42. REPRODUCTION OPERATION
Select parent probabilistically based on fitness
Copy it (unchanged) into the next generation of the population

43. FIVE MAJOR PREPARATORY STEPS FOR GP
Determining the set of terminals
Determining the set of functions
Determining the fitness measure
Determining the parameters for the run
Determining the method for designating a result and the criterion for terminating a run
BBB3666 (converted to BMP from eps)
The following were cut as parameter subpoints so that the text fit on a slide
population size
number of generations
minor parameters

44. PREPARATORY STEPS Objective:
Find a computer program with one input (independent variable X) whose output equals the given data 1
Terminal set:
T = {X, Random-Constants} 2
Function set:
F = {+, -, *, %} 3
Fitness:
The sum of the absolute value of the differences between the candidate program’s output and the given data (computed over numerous values of the independent variable x from –1.0 to +1.0) 4
Parameters:
Population size M = 4 5
Termination:
An individual emerges whose sum of absolute errors is less than 0.1

45. POPULATION OF 4 RANDOMLY CREATED INDIVIDUALS FOR GENERATION 0
SYMBOLIC REGRESSION
POPULATION OF 4 RANDOMLY CREATED INDIVIDUALS FOR GENERATION 0
BBB3663 was broken into 4 components and converted to BMP files for the incremental unveiling

46. SYMBOLIC REGRESSION x2 + x + 1
FITNESS OF THE 4 INDIVIDUALS IN GEN 0
BBB3662 was broken up into 4 indidual BMP files from the original eps file to satisfy display constraings
x + 1
x2 + 1 2 x
0.67
1.00
1.70
2.67

47. SYMBOLIC REGRESSION x2 + x + 1
GENERATION 1
Second offspring of crossover of (a) and (b)
 picking “+” of parent (a) and left-most “x” of parent (b) as crossover points
Copy of (a)
Mutant of (c)
picking “2” as mutation point
First offspring of crossover of (a) and (b) 
picking “+” of parent (a) and left-most “x” of parent (b) as crossover points
BBB3664 was broken up into 4 indidual BMP files from the original eps file to satisfy display constraings

48. WALL-FOLLOWER
BBB??? No number, only existed as embedded word file

49. FITNESS
BBB??? No number, only existed as embedded word file

50. BEST OF GENERATION 57
BBB??? No number, only existed as embedded word file

51. SUBROUTINE DUPLICATION
Branch-duplication.avi

52. SUBROUTINE CREATION
Branch-creation.avi

53. SUBROUTINE DELETION
Branch-deletion.avi

54. ARGUMENT DUPLICATION
Arg-duplication.avi

55. ARGUMENT DELETION
Arg-deletion.avi

56. 16 ATTRIBUTES OF A SYSTEM FOR AUTOMATICALLY CREATING COMPUTER PROGRAMS
Starts with "What needs to be done"
Tells us "How to do it"
Produces a computer program
Automatic determination of program size
Code reuse
Parameterized reuse
Internal storage
Iterations, loops, and recursions
Self-organization of hierarchies
Automatic determination of program architecture
Wide range of programming constructs
Well-defined
Problem-independent
Wide applicability
Scalable
Competitive with human-produced results

57. PROGRESSION OF QUALITATIVELY MORE SUBSTANTIAL RESULTS PRODUCED BY GP
Toy problems
Human-competitive non-patent results
20th-century patented inventions
21st-century patented inventions
Patentable new inventions

58. GP AS AN INVENTION MACHINE

59. To be on satellite to be launched in 2004
NASA EVOLVED ANTENNA
lohn-st5-evolved-antenna.gif (bmp version for power point)
To be on satellite to be launched in 2004

60. CHARACTERISTICS SUGGESTING USE OF GP
(1) discovering the size and shape of the solution,
(2) reusing substructures,
(3) discovering the number of substructures,
(4) discovering the nature of the hierarchical references among substructures,
(5) passing parameters to a substructure,
(6) discovering the type of substructures (e.g., subroutines, iterations, loops, recursions, or storage),
(7) discovering the number of arguments possessed by a substructure,
(8) maintaining syntactic validity and locality by means of a developmental process, or
(9) discovering a general solution in the form of a parameterized topology containing free variables

61. DESIGNING A GIRAFFE Long neck Long tongue
Vegetable-digesting enzymes in stomach
4 legs
Long legs
Brown coloration

62. THE DESIGN OF A GOOD GIRAFE
Neck length
Tongue length
Carnivorous?
Number of legs
Leg length
Coloration
15.11 feet
14 inches No 4
9.96 feet
Brown
Floating point
Boolean
Integer
Categorical

63. NON-LINEARITY — GIRAFE
Taken one-by-one, some gene values found in a giraffe, such as the long neck contribute (alone) negatively to fitness
requires considerable material to construct
requires considerable energy to maintain
prone to injury (thereby hurting rate of survival and reproduction)
Thus, maximizing any one variable will not lead to the global optimum solution

64. NON-LINEARITY (CONTINUED)
When the variables are taken in pairs (there are 15 possible pairs), many combinations of pairs (e.g., Long neck and long tongue) are doubly detrimental

65. NON-LINEARITY (CONTINUED)
But, certain combinations of traits, when taken together, are "co-adapted sets of alleles" that yield a very fit animal for eating high acacia leaves in the jungle environment, having good camouflage, having high escape velocity when faced with predators, and exploiting a niche (and avoiding competition) with other animals feeding on low-hanging vegetation

66. SEARCH METHODS IN GENERAL
Initial structure(s)
Fitness measure
Operations for creating new structures
Parameters
Termination criterion and method of designating the result

67. SPACE WITH MANY LOCAL OPTIMA

68. SEARCH METHODS
Blind random search does not use acquired information in deciding on the future direction of the search
Hill combing and gradient descent use acquired information; however, they are prone to becoming trapped on local optima
The previous point is especially true for non-trivial search spaces

69. 7 DIFFERENCES BETWEEN GP AND ARTIFICIAL INTELLIGENCE AND MACHINE LEARNING APPROACHES

70. REPRESENTATION Genetic programming overtly conducts it
search for a solution to the given problem
in program space

71. ROLE OF POINT-TO-POINT TRANSFORMATIONS IN THE SEARCH
Genetic programming does not conduct its
search by transforming a single point in the
search space into another single point, but
instead transforms a set of points into
another set of points

72. ROLE OF HILL CLIMBING IN THE SEARCH
Genetic programming does not rely
exclusively on greedy hill climbing to
conduct its search, but instead allocates a
certain number of trials, in a principled
way, to choices that are known to be
inferior

73. DETERMINISM IN THE SEARCH
Genetic programming conducts its search
probabilistically

74. ROLE OF AN EXPLICIT KNOWLEDGE BASE
Genetic programming does NOT make use
of a knowledge base

75. ROLE OF FORMAL LOGIC IN THE SEARCH
Genetic programming does not utilize
formal logic in it’s search strategy. Contradictory alternatives are created and actively maintained.

76. UNDERPINNINGS OF THE TECHNIQUE
Biologically inspired

77. TURING (1948) Turing made the connection between
searches and the challenge of getting a
computer to solve a problem without
explicitly programming it in his 1948 essay
“Intelligent Machines”
"Further research into intelligence of machinery will probably be very greatly concerned with 'searches' ... “

78. TURING’S 3 APPROACHES TO MACHINE INTELLIGENCE (1948)
LOGIC-BASED SEARCH
One approach that Turing identified is a
search through the space of integers
representing candidate computer
programs.

79. TURING’S 3 APPROACHES (CONTINUED)
CULTURAL SEARCH
A second approach is the "cultural search“
which relies on knowledge and expertise
acquired over a period of years from
others (akin to present-day knowledge-
based systems).

80. TURING’S 3 APPROACHES (CONTINUED)
GENETICAL OR EVOLUTIONARY SEARCH
"There is the genetical or evolutionary
search by which a combination of genes is
looked for, the criterion being the survival
value.“

81. TURING (1950) From Turing’s 1950 paper "Computing
Machinery and Intelligence" …
“We cannot expect to find a good child-machine at the first attempt. One must experiment with teaching one such machine and see how well it learns. One can then try another and see if it is better or worse. There is an obvious connection between this process and evolution, by the identifications”

82. TURING (1950) (CONTINUED) “Structure of the child machine =
Hereditary material
“Changes of the child machine =
Mutations
“Natural selection = Judgment of the experimenter”