Download Offspring with genetic variation More fit organisms survive and

CS206
Evolutionary Robotics
Offspring with
genetic variation
BIOLOGICAL EVOLUTION
Less fit organisms
die
More fit organisms
survive and reproduce
CS206
Evolutionary Robotics
Offspring with
genetic variation
Less fit organisms
die
More fit organisms
survive and reproduce
BIOLOGICAL EVOLUTION
THE GENETIC ALGORITHM
0.3 0.4
…
0.7
0.3 0.4
…
0.7
0.3 0.4
…
0.7
-0.2 0.0
…
0.1
-0.2 0.0
…
0.1
0.3 0.5
…
-0.9
0.0 0.1
…
-0.9
0.0 0.1
…
-0.9
0.0 0.1
…
Generate
random solutions
Discard
poor solutions
-0.9
Make modified copies
of the better solutions
CS206
Evolutionary Robotics
Genetic algorithm + robot simulator = evolutionary robotics
Generate
robots
Evolved Neural
Network Controller
Throw away
bad robots
Make modified copies
of the good robots
Modified Controller
Frutiger, D. R., J. C. Bongard and F. Iida (2002) “Iterative Product Engineering: Evolutionary Robot
Design”, in Bidaud, P. and F. B. Amar (eds.), Proceedings of the Fifth International Conference on
Climbing and Walking Robots, Professional Engineering Publishing, pp. 619-629.
CS206
Evolutionary Robotics
Fitness
The Fitness Landscape (Sewall Wright, 1932)
Fitness
Value of gene 1
If a genotype has n genes, the fitness landscape
exists in n+1 dimensions:
the fitness of the phenotype produced
by that genotype is the extra dimension.
Genotype:
Phenotype:
Gene 2
Gene 1
CS206
Evolutionary Robotics
Fitness
The Hill Climber
Population size: 1
0.3 0.4 … 0.7
“parent”
Value of gene 1
0.3 0.4 …
“child”
0.8
CS206
Evolutionary Robotics
Fitness
The Parallel Hill Climber
“parents”
Population size: >1
0.3 0.4 … 0.7
5
0.9 0.1 …
0.3 0.4
0.8
5
0.9 0.0 …
“children”
0.5
…
0.5
Value of gene 1
CS206
Evolutionary Robotics
Fitness
The Genetic Algorithm
“parents”
Population size: >1
0.3 0.4 … 0.7
0.9 0.1
0.3 0.4
…
…
0.5
…
0.7
0.5
0.9 0.1
“children”
Value of gene 1
CS206
Evolutionary Robotics
Fitness
The Evolution Strategy
“Genes”
0.3 0.4
0.1 0.2
…
…
0.7
0.05
Value of gene 1
Fitness
Step sizes, or
strategy parameters
Value of gene 1
CS206
Evolutionary Robotics
Genetic Programming
p1
+
0.8
*
p2
Possible
branch
nodes:
/
1.4 0.2
+
x
x
z=
z=
y
sin(a)
cos(a)
plus(a,b)
minus(a,b)
mult(a,b)
div(a,b)
pow(a,b)
Possible
x,y,5
terminal nodes 0.1,-3.0,5
CS206
Evolutionary Robotics
Genetic Programming
p1
*
+
0.8
p2
/
1.4 0.2
+
x
x
z=
z=
y
p1
+
0.8
c1
+
0.8
z=
*
c2
0.2
x
z=
/
x
*
p2
0.2
/
CS206
Evolutionary Robotics
Genetic Programming: Symbolic Regression
y
y=?
0
3
x
x
y
-0.4
1.4
0.0
0.6
5
5
0.5
2.1
CS206
Evolutionary Robotics
Genetic Programming: Symbolic Regression
y
x
n
y
(xi-xi’)2 + (yi-yi’)2
Error =
y=?
0
3
x
y
0
y’ = x
3
high error low fitness
-0.4
1.4
0.0
0.6
5
5
0.5
2.1
i=1
n
CS206
Evolutionary Robotics
Genetic Programming: Symbolic Regression
y
x
n
y
(xi-xi’)2 + (yi-yi’)2
Error =
y=?
0
3
x
y
1.4
0.0
0.6
5
5
0.5
2.1
i=1
n
y
0
y’ = x
-0.4
3
high error low fitness
0
3
2
y’ = (x-3) low error high fitness
CS206
Evolutionary Robotics
Genetic Programming: Symbolic Regression
Question: What causes toxic algal blooms in Lake Champlain?
i.e., T = ?
Nitrogen
(N)
Phosphorus
(P)
Water
temp (W)
Turbidity
(B)
Rainfall
(R)
5
Toxic
algae/ml
(T)
Malletts
Bay
08/01/99
0.4
0.6
0.2
0.1
0.4
5
0.5
Shelburne
08/02/99
0.1
0.3
0.6
0.4
0.1
5
0.05
Malletts
Bay
07/05/00
0.9
0.1
0.9
0.4
0.6
5
0.8
5
5
5
5
5
5
5
5
CS206
Genetic Programming
Q:
What is a good genotype?
What is the phenotype?
How to compute fitness?
Evolutionary Robotics