GECCO 2012 tutorial

Abstract

Cartesian Genetic Programming (CGP) is an increasingly popular and efficient form of Genetic Programming that was developed by Julian Miller in 1999 and 2000. In its classic form, it uses a very simple integer based genetic representation of a program in the form of a directed graph. Graphs are very useful program representations and can be applied to many domains (e.g. electronic circuits, neural networks). In a number of studies, CGP has been shown to be comparatively efficient to other GP techniques. It is also very simple to program.
Since then, the classical form of CGP has been developed made more efficient in various ways. Notably, by including automatically defined functions (modular CGP) and self-modification operators (self-modifying CGP). SMCGP was developed by Julian Miller, Simon Harding and Wolfgang Banzhaf. It uses functions that cause the evolved programs to change themselves as a function of time. Using this technique it is possible to find general solutions to classes of problems and mathematical algorithms (e.g. arbitrary parity, n-bit binary addition, sequences that provably compute pi and e to arbitrary precision, and so on).
The tutorial will cover the basic technique, advanced developments and applications to a variety of problem domains.

Full text

1
GECCO 2012 Tutorial:
Cartesian Genetic Programming
Julian F. Miller
Dept of Electronics
University of York, UK
julian.miller@york.ac.uk
Simon L. Harding
IDSIA, Galleria 2
6928 Manno-Lugano, Switzerland
Machine Intelligence Ltd, UK
slh@evolutioninmaterio.com
Copyright is held by the author/owner(s).
GECCO’12 Companion, July 7–11, 2012, Philadelphia, PA, USA.
ACM 978-1-4503-1178-6/12/07
2
Abstract
Cartesian Genetic Programming (CGP) is an increasingly popular and efficient form of
Genetic Programming that was developed by Julian Miller in 1999 and 2000.
In its classic form, it uses a very simple integer based genetic representation of a program in the form
of a directed graph. Graphs are very useful program representations and can be applied to many
domains (e.g. electronic circuits, neural networks). In a number of studies, CGP has been shown to
be comparatively efficient to other GP techniques. It is also very simple to program.
Since then, the classical form of CGP has been developed made more efficient in various ways.
Notably, by including automatically defined functions (modular CGP) and self-modification operators
(self-modifying CGP). SMCGP was developed by Julian Miller, Simon Harding and Wolfgang Banzhaf.
It uses functions that cause the evolved programs to change themselves as a function of time.
Using this technique it is possible to find general solutions to classes of problems and
mathematical algorithms (e.g. arbitrary parity, n-bit binary addition, sequences that provably compute pi
and e to arbitrary precision, and so on).
The tutorial will cover the basic technique, advanced developments and applications to a variety
of problem domains.
3
Classic CGP
Modular CGP
Self-modifying CGP
Developmental CGP
Cyclic CGP
Applications
Resources
Bibliography
Contents
4
Genetic Programming
The automatic evolution of computer programs
• Tree-based, Koza 1992
• Stack-based, Perkis 1994, Spector 1996 onwards
(push-pop GP)
• Linear GP, Nordin and Banzhaf 1996
•Cartesian GP, Miller 1997
• Parallel Distributed GP, Poli 1996
• Grammatical Evolution, Ryan 1998
• Lots of others…
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Origins of Cartesian Genetic
Programming (CGP)
Grew out of work in the evolution of digital
circuits, Miller and Thomson 1997. First
actual mention of the term Cartesian Genetic
Programming appeared at GECCO in 1999.
Originally, represents programs or circuits as
a two dimensional grid of program
primitives.
This is loosely inspired by the architecture of
digital circuits called FPGAs (field
programmable gate arrays)
6
What defines CGP?
The genotype is a list of integers (and possibly
parameters) that represent the program primitives and
how they are connected together
• CGP represents programs as graphs in which there
are non-coding genes
The genes are
• Addresses in data (connection genes)
• Addresses in a look up table of functions
• Additional parameters
This representation is very simple, flexible and
convenient for many problems
7
CGP General form
m outputs
node
Note: Nodes in the same column are not allowed to be connected to each other
n inputs Levels-back
r rows
c columns
8
Allelic constraints for directed acyclic
graphs
All function genes fimust takes allowed function
alleles: 0 ≤fi≤nf
Nodes connections Cij of a node in column j, and
levels-back l, must obey (to retain directed acyclicity)
j≥l n + (j-l)r≤Cij ≤n+ jr
j< l0 ≤Cij ≤n+ jr
Output genes (can connect to any previous node or
input)
0 ≤0i≤n+ cr -1
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Types of graphs easily controlled
Depending on rows, columns and levels-back a wide
range of graphs can be generated
When rows =1 and levels-back = columns arbitrary
directed graphs can be created with a maximum
depth
• In general choosing these parameters imposes the least
constraints. So without specialist knowledge this is the best
and most general choice
10
CGP genotype
f0C0 0 … C0 a …f(c+1)r C(c+1)r 0 … C(c+1)r a O1,…Om
Usually, all functions have as many inputs as the maximum
function arity
Unused connections are ignored
Output genes
function genes
Connection genes
11
Example
0 0 1 1 0 0 1 3 1 2 0 1 0 4 4 2 5 4 2 5 7 3
Encoding of graph as a list of integers (i.e. the
genotype)
12
Example: Function look up table
The function genes are the addresses in a user-defined
lookup table of functions
0+ Add the data presented to inputs
1- Subtract the data presented to inputs
2* Multiply data presented to inputs
3/ Divide data presented to inputs (protected)
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Obtaining the graph
00 1 1 0 0 1 3 1 2 0 1 0 4 4 2 5 4 2 5 7 3
Encoding of graph as a list of integers (i.e. the
genotype)
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So what does the graph
represent?
15
What happened to the node whose
output label is 6?
00 1 1 0 0 1 3 1 2 0 1 0 4 4 2 5 4 2 5 7 3
The node was not used so the genes are silent or non-coding
16
The CGP genotype-phenotype map
When you decode a CGP genotype many
nodes and their genes can be ignored because
they are not referenced in the path from
inputs to outputs
These genes can be altered and make no
difference to the phenotype, they are non-
coding
Clearly there is a many-to-one genotype to
phenotype map
How redundant is the mapping?
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A mathematical aside: CGP and
Stirling numbers
Assume that a CGP graph has the following parameters
Number of rows_= 1
Levels-back = num_cols = n
Arity of functions = 1
There is one input
Assume that the output is taken from the last node
The number of genotypes, G, that have a phenotype of size k(nodes)
can be shown to obey a recurrence relation obeyed by unsigned
Stirling numbers of the first kind.
G(n+1, k) = nG(n,k) + G(n, k-1)
18
How many genotypes of length nmap
to a phenotypes of length k?
k
n
13654645362244967284118124109584403209
12832219606759131321306850408
121175735162417647207
115852252741206
1103550245
161164
1323
112
11
987654321
Average number of active nodes in a genotype of length 9 is 2.83
Clearly, with say a genotype of 100 nodes, the number of genotypes that map
to a phenotype with say about 10 nodes is an astronomical number
19
// L = MaxGraph.Length
// I = Number of program inputs
// N = Number of program outputs
bool ToEvaluate[L]
double NodeOutput[L+I]
int NodesUsed[M]
1
// identify initial nodes that need to be evaluated
p = 0
do
ToEvaluate[OutputGene[p]] = true
p = p + 1
while (p < N)
// determine nodes used
p = L-1
q=0
do
if(ToEvaluate[p])
x = Node[p].Connection1
y = Node[p].Connection2
ToEvaluate[x] = true
ToEvaluate[y] = true
q=q+1
NodesUsed[q]=p;
endif
p = p - 1
while ( p >= 0)
2
// load input data values
p = 0
do
NodeOutput[p] = InputData[p]
p = p + 1
while (p < I)
3
//Execute graph
for p = I to p < q+I
x = Node[NodesUsed[p]].Connection1
y = Node[NodesUsed[p]].Connection2
z = Node[NodesUsed[p]].Function
NodeOutput[p] = ComputeNode(NodeOutput[x], NodeOutput[y],z)
endfor
4
Decoding CGP chromosomes is easy
20
Point mutation
Most CGP implementations only use mutation.
Carrying out mutation is very simple. It consists of the
following steps. The genes must be chosen to be valid alleles
//Decide how many genes to change:num_mutations
while (mutation_counter < num_mutations)
{
get gene to change
if (gene is a function gene)
change gene to randomly chosen new valid function
else if (gene is a connection gene)
change gene to a randomly chosen new valid connection
else
change gene to a new valid output connection
}
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Evolutionary Strategy
CGP often uses a variant of a simple
algorithm called (1 + 4) Evolutionary
Strategy
• However, an offspring is always chosen if it is
equally as fit or has better fitness than the parent
22
Crossover or not?
Recombination doesn’t seem to add
anything (Miller 1999, “An empirical
study…”)
However if there are multiple chromosomes
with independent fitness assessment then it
helps a LOT (Walker, Miller, Cavill 2006,
Walker, Völk, Smith, Miller, 2009)
Some work using a floating point
representation of CGP has suggested that
crossover might be useful (Clegg, Walker,
Miller 2007)
23
Silent mutations and their effects
Original
24
Silent mutations and their effects
No change in phenotype but it changes the
programs accessible through subsequent
mutational change
After silent
mutation
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Non-silent mutations and their
effects
Massive change in phenotype is
possible through simple mutation
Original
26
Non-silent mutations and their
effects
Massive change in
phenotype is possible
through simple mutation
After active
mutation
27
Neutral search is fundamental to
success of CGP
A number of studies have been carried
out to indicate the importance to
neutral search
•Miller and Thomson 2000, Vassilev and
Miller 2000, Yu and Miller 2001, Miller
and Smith 2006)
28
Neutral search and the three bit multiplier problem
(Vassilev and Miller 2000)
Importance of neutral search
can be demonstrated by
looking at the success rate in
evolving a correct three-bit
digital parallel multiplier
circuit.
Graph shows final fitness
obtained in each of 100 runs of
10 million generations with
neutral mutations enabled
compared with disabled neutral
mutations.
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In CGP, large genotypes and small mutation evolve
solutions to problems more quickly [Miller and Smith
2006]
Two-bit multiplier with gate set
{AND, OR, NAND, NOR}.
Even 3 parity with gate set
{AND, OR, NAND, NOR}.
•However big genotypes does NOT mean big phenotypes
(programs)….
30
Phenotype length versus genotype length
(two-bit multiplier)
SEARCH MOST EFFECTIVE
WHEN 95% OF ALL GENES ARE
INACTIVE!!
NO BLOAT
Average proportion of active nodes in
genotype at the conclusion of
evolutionary run for all mutation rates
versus genotype length
Average phenotype length for the
initial population contrasted with
the average phenotype length at
conclusion of evolutionary run
versus genotype length with 1%
mutation
31
Modular/Embedded CGP (Walker, Miller 2004)
So far have described a form of CGP (classic) that
does not have an equivalent of Automatically
Defined Functions (ADFs)
Modular CGP allows the use of modules (ADFs)
• Modules are dynamically created and destroyed
• Modules can be evolved
• Modules can be re-used
34
Representation Modification 1
Each gene encoded by two integers in M-
CGP
• Function/module number and node type
• Node index and node output
– nodes can have multiple outputs
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Representation Modification 2
M-CGP has a bounded variable length genotype
• Compression and expansion of modules
– Increases/decreases the number of nodes
• Varying number of module inputs
– Increases/decreases the number of genes in a node
36
Modules
Same characteristics as M-
CGP
• Bounded variable length
genotype
• Bounded variable length
phenotype
Modules also contain
inactive genes as in CGP
Modules can not contain
other modules!
37
Node Types
Three node types:
• Type 0
– Primitive function
• Type I
– Module created by compress operator
• Type II
– Module replicated by genotype point-mutation
Control excessive code growth
• Genotype can return to original length at any
time
38
Creating and Destroying a Module
Created by the compress operator
• Randomly acquires sections of the genotype into a module
– Sections must ONLY contain type 0 nodes
Destroyed by the expand operator
• Converts a random type I module back into a section of the
genotype
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Module Survival
Twice the probability of a module being
destroyed than created
Modules have to replicate to improve their
chance of survival
• Lower probability of being removed
Modules must also be associated with a high
fitness genotype in order to survive
• Offspring inherit the modules of the fittest parent
40
Evolving a Module I
Structural mutation
• Add input
• Remove input
• Add output
• Remove output
41
Evolving a Module II
Module point-
mutation operator
• Restricted version of
genotype point-
mutation operator
– Uses only primitive
functions
42
Re-using a Module
Genotype point-mutation operator
• Modified CGP point-mutation operator
Allows modules to replicate in the genotype
• Primitive (type 0) module (type II)
• Module (type II) module (type II)
• Module (type II) primitive (type 0)
Does NOT allow type I modules to be mutated into
primitives (type 0) or other modules (type II)
• Type I modules can only be destroyed by
Expand (and are only created by Compress)
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Experimental parameters
NOTES: ◊these parameters only apply to Modular
(Embedded) CGP
Results heavily dependent on the maximum number of
nodes allowed. Much better results are obtained when
larger genotype lengths are used.
44
Even Parity Results
0
10,000,000
20,000,000
30,000,000
40,000,000
50,000,000
60,000,000
70,000,000
80,000,000
3-bit 4-bit 5-bit 6-bit 7-bit 8 -bit
Parity
CE
CGP M-CGP(5) GP GP ADF EP EP ADF
0
5,000,000
10,000,000
15,000,000
20,000,000
25,000,000
30,000,000
35,000,000
3-bit 4-bit 5-bit 6-bit 7-bit 8-bit
Parity
CE
CGP M-CGP(5) GP ADF EP ADF
45
Digital Multiplier
Two digital multiplier problems:
• 2-bit and 3-bit
Function set:
• AND, AND (one input inverted),
XOR, OR
Fitness Function:
• Number of phenotype output bits that
differ from the perfect n-bit digital
multiplier solution
• Perfect solution has a fitness of zero
Results are averaged over fifty
independent runs
ha
a b
z
2x1
ha
c
y
d
2x1
x
w
46
Multiplier Results
0
5,000,000
10,000 ,000
15,000 ,000
20,000 ,000
25,000 ,000
30,000 ,000
2-bit 3-b it
Multiplier
CE
CGP M-C GP(5)
0
10,000
20,000
30,000
40,000
50,000
60,000
2-bit
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Symbolic Regression
Two problems:
x6 - 2x4 + x2
x5 - 2x3 + x
Function set:
+, -, *, / (protected)
Fitness Function:
Absolute error over all fifty points in the input set
Solution found when absolute error is within 0.01 of each
point
Results averaged over fifty independent runs
*
-
x
1
*
*
Out
48
Symbolic Regression Results
0
200,000
400,000
600,000
800,000
1,000,000
1,200,000
1,400,000
1,600,000
x6-2x4+x2 x5-2x3+x
CE
CGP M-CGP(3) M-CGP(5) M-CGP(8) GP GP ADFs
x6– 2x4 + x2x5– 2x3 + x
49
Self-modifying Cartesian
Genetic programming
A developmental form of Cartesian
Genetic Programming (CGP)
• Includes self modification functions.
• ‘General purpose’ GP system
• Phenotype can vary over time (with
iteration)
• Can switch off its own self-modification
50
Changes to CGP: relative addressing
Replaced direct node addressing
with relative addressing
• Always use 1 row (not rectangular)
•Connection genes say how many
nodes back
0
1
2
3
1
5
2
4
3
6
0
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Changes to CGP: Inputs
Replace input calls with a function.
• We call these functions INP, INPP, SKIPINP
Pointer keeps track of ‘current input’.
• Call to INP returns the current input, and moves
the pointer to the next input.
Connections beyond graph are assigned
value 0.
52
Removed output nodes.
Genotype specifies which nodes are
outputs.
If no OUTPUT function then last active
node is used
• Other defaults are used in situations where the
number of outputs does not match the number
required
Changes to CGP: Outputs
53
Nodes also contain a number of
‘arguments’.
• 3 floating point numbers
• Used in various self-modification
instructions
• Cast to integers when required
Changes to CGP: Arguments
54
SMCGP Nodes: summary
Each node contains:
• Function type
• Connections as relative addresses
• 3 floating point numbers
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SMCGP: Functions
Two types of functions:
• Computational
– Usual GP computational functions
• Self-modifying
– Passive computational role (see later)
56
Some Self-Modification Functions
Operator Parameters:
use node address and the
three node arguments
Function
MOVE Start, End, Insert Moves each of the nodes between
Start and End into the position
specified by Insert
DUP Start, End, Insert Inserts copies of the nodes
between Start and End into the
position specified by Insert
DELETE Start, End Deletes the nodes between Start
and End indexes
CHF Node, New Function Changes the function of a
specified node to the specified
function
CHC Node, Connection1,
Connection2
Changes the connections in the
specified node
57
SMCGP Execution
Important first step:
• Genotype is duplicated to phenotype.
• Phenotypes are executed:
Self modifications are only made to the
phenotype.
58
Self Modification Process: The To
Do list
Programs are iterated.
If triggered, self modification instruction
is added to a To Do list.
At the end of each iteration, the
instructions on this list are processed.
The maximum size of the To Do list can
be predetermined
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Computation of a SM node
Functions are appended to the To Do list
if:
• The first input > the second input.
And:
• The To Do list isn’t too big.
60
Publications using SMCGP
General Parity Problem (CEC 2009)
Mathematical Problems (EuroGP 2009, GECCO 2007)
Learning to Learn (GECCO 2009)
Generating Arbitrary Sequences (GECCO 2007)
Computing the mathematical constants
pi and e (GECCO 2010 in GDS track)
General adder and many other problems
(GPEM Tenth Anniversary Special Issue, 2010)
Authors: Harding, Miller, Banzhaf
61
Evolving Parity
Each iteration of program should produce the
next parity circuit.
• On the first iteration the program has to solve 2 bit
parity. On the next iteration, 3 bit ... up to 22 parity
• Fitness is the cumulative sum of incorrect bits
Aim to find general solution
• Solutions can be proved to general
– See GPEM 2010 paper
CGP or GP cannot solve this problem as they
have a finite set of inputs (terminals)
62
Parity results: SMCGP versus CGP and
ECGP
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Scaling behaviour of SMCGP
64
Evolving pi
Iterate a maximum of 10 times
If program output does not get closer to pi at the
next iteration, the program is stopped and large
fitness penalty applied
Fitness at iteration, i, is absolute difference of
output at iteration iand pi
One input: the numeric constant 1.
65
Evolving pi: an evolved solution
An evolved solution
f(10) is correct to the first 2048 digits of pi
It can be proved that f(i) rapidly converges to
pi in the limit as itends to infinity
66
Further results
Other mathematically provable results found
so far:
• Evolved a program that can carry out the bitwise
addition of an arbitrary number of inputs
• Evolved a sequence that converges to e
Other results
• Evolved a sequence function that generates the
first 10 Fibonacci numbers
• Evolved a power function x n
• Bioinformatics classification problem (finite
inputs)
– SMCGP performed no worse than CGP
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Two dimensional SMCGP (SMCGP2)
Active nodes
output node
SMCGP2: genes
• Function
• Connections
• Numeric Constant
Arguments are now
2 D vectors
• SM size (SMS)
• SM location (SML)
68
SMCGP2: Vector relative addressing and
Empty nodes
There are empty nodes are
represented by X
The relative address from C to B
is (2, 1)
• meaning 2 nodes to the left, and one
node up.
The relative address of C to A is
(4,1).
Note how the empty nodes are
not counted when computing
how many nodes back to
connect.
69
SMCGP2: Self Modifying Functions
Simplified SM function set
• Duplicate section, insert elsewhere.
• Duplicate section, overwrite elsewhere.
• Crop to a section.
• Delete a section.
• Add a row or column.
• Delete a row or column.
• NULL
70
SMCGP2: Solving even-n parity
Time
n = 2 n = 3 n = 4 n = 5
n = 12
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SMCGP:Some observations
In SMCGP there are implicit
• Loops
• Recursion
• Modules/functions
• Halting (telomeres)
Also have “partial” loops/recursion
73
Multi-type CGP (MT-CGP)
Genotype pretty much classic CGP
• Genotype is a (partly connected, feed-forward) graph
• Graph is a list of nodes
– Each node contains:
-Function (from a function set)
-Two connections (to other nodes)
-real number (to use for parameters)
Handles multiple data types
• So far: reals and vectors
Adds lots of functionality
• Domain knowledge
See GECCO2012 paper for more details
74
MT-CGP: Example
75
MT-CGP
Has a big function set
Trying to incorporate domain knowledge
• Easy to add new functions to help with a
particular problem
Functions deal with multiple data types
• Functions are overloaded
• Attempts are made at human readable consistency
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Evolving Image Filters with CGP
Detecting/locating objects with the iCub
cameras
We do this by evolving image filters that take
a camera image, and return only the objects
we are looking for.
Input Target
Evolved
filter
77
Grey
Red
Green
Blue
Hue
Saturation
Luminosity
Image from camera
Split colour image is used as inputs
Evolved
filter
Input data
78
1 23 OUT
INP INP INP
3
-1
-2
4.3
Function
Connection 1
Connection 2
A real number
Genotype representation (like SMCGP
but no SM functions)
79
NOP LOG TRIANGLES
INP MAX LINES
INPP MIN SHIFTDOWN
SKIP EQ SHIFTUP
ADD GAMMA SHIFTLEFT
SUB GAUSS SHIFTRIGHT
CONST SOBELX SIFTa
MUL SOBELY GABOR
ADDC AVG NORMALIZE
SUBC UNSHARPEN RESCALE
MULC THRESHOLD GRABCUT
ABSDIFF THRESHOLDBW MINVALUE
CANNY SMOOTHMEDIAN MAXVALUE
DILATE GOODFEATURESTOTRACK AVGVALUE
ERODE SQUARES RESCALE
LAPLACE CIRCLES RESIZETHENGABOR
Large Function Set
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•Fitness = sum of mean square error of pixel values
between each input/target
Fitness
81
Evolved Filter code
82
Output
Inputs
Evolved Filter
Dataflow
83
Things we can do already:
Generate different filters for other
objects.
Find fast running filters.
Find them quickly.
Show that filters are robust.
Transfer code from offline learning
to yarp module.
• Software emits C# and C++ code
• Running on Windows/Linux/Mac.
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84
Tea-box filter: demonstration
85
CGP encoded Artificial Neural
Networks (CGPANN)
CGP has been used to encode both feed-forward ANNs and
recursive ANNs. The nodes genes consist of:
• Connection genes (as usual)
• Function genes (two)
– Sigmoid, hyperbolic tangent
• Weights
– Each connection gene carries a real-numbered weight
• Switch genes
– Binary genes that switch off or on the connection
Applied to Markovian and non-Markovian single and double
pole-balancing problems
• Shown to outperform all previously published topology and weights
altering evolutionary ANNS (TWEANNs) (Khan, Khan and Miller
2010)
Breast cancer detection (see GECCO 2012 proceedings)
86
Cyclic CGP
When outputs are allowed to connect to
inputs through a clocked delay (flip-flop) it is
possible to allow CGP to include feedback.
By feeding back outputs generated by CGP to
an input, it is possible to get CGP to generate
sequences
• In this way iteration is possible
There are a couple of recent publications
using recursion or iteration in CGP (Khan,
Khan and Miller 2010, Walker, Liu,
Tempesti,Tyrrell 2010)
87
Applications of CGP
Digital Circuit Design
• ALU, parallel multipliers, digital filters, analogue circuits
Mathematical functions
• Prime generating polynomials
Control systems
• Maintaining control with faulty sensors, helicopter control, general
control, simulated robot controller
Image processing
• Image filters
• Mammary Tumour classification
Bio-informatics
• Molecular Post-docking filters
Artificial Neural Networks
Developmental Neural Architectures
• Wumpus world, checkers, maze solving
Evolutionary Art
Artificial Life
• Regenerating ‘organisms’
Optimization problems
• Applying CGP to solve GA problems
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CGP Resources
Home site:
http://www.cartesiangp.co.uk
Julian Miller: C implementations of CGP and
SMCGP available at
http://www.cartesiangp.co.uk
Simon Harding
http://www.evolutioninmaterio.com
David Oranchak has implemented CGP in Java.
Documentation is available at
http://oranchak.com/cgp/doc/
Cartesian Genetic Programming book
• Published in 2011 by Springer
89
Conclusions
Cartesian Genetic Programming is a graph based GP
method capable of representing many computational
structures
• programs, circuits, neural networks, systems of
equations…
Genetic encoding is compact, simple and easy to
implement and can handle multiple outputs easily.
The unique form of genetic redundancy in CGP
makes mutational search highly effective
The effectiveness of CGP has been compared with
many other GP methods and it is very competitive
90
CGP Bibliography
Ashmore L. An investigation into cartesian genetic programming within the field of evolutionary art.
http://www.emoware.org/evolutionary_art.asp, Department of Computer Science, University of
Birmingham (2000)
Clegg J., Walker J. A., Miller J. F. A New Crossover Technique for Cartesian Genetic Programming. Proceedings
of Genetic and Evolutionary Computation Conference, ACM Press (2007) 1580-1587.
DiPaola S., Gabora L. Incorporating characteristics of human creativity into an evolutionary art algorithm, Genetic
Programming and Evolvable Machines (2009) Vol. 10. For further info see: http://dipaola.org/evolve/
DiPaolo S. Evolving Creative Portrait Painter Programs using Darwinian Techniques with an Automatic Fitness
Function. Electronic Visualizationa and the Arts Conference (2005)
Gajda, Z., Sekanina, L.. Gate-Level Optimization of Polymorphic Circuits Using Cartesian Genetic Programming,
Proceedings of Congress on Evolutionary Computation. IEEE Press (2009)
Gajda Z., Sekanina, L.. Reducing the Number of Transistors in Digital Circuits Using Gate-Level Evolutionary
Design, Proceedings of Genetic and Evolutionary Computation Conference. ACM, (2007) 245-252.
Garmendia-Doval B., Miller J.F., Morley S.D. Post Docking Filtering using Cartesian Genetic Programming.
Genetic Programming Theory and Practice II. O'Reilly U-M., Yu T., Riolo R., Worzel B. (Eds.).
University of Michigan Illinois USA. Springer (2004).
Glette K., Torresen J., Paul Kaufmann P., Platzner., M. A Comparison of Evolvable Hardware Architectures for
Classification Tasks. In Proceedings of the 8th International Conference on Evolvable Systems: From
Biology to Hardware,Springer LNCS 5216 (2008) 22-33.
Harding S. L., Leitner, J., Schmidhuber, J.. Cartesian Genetic Programming for Image Processing, Genetic
Programming Theory and Practice, University of Michigan Illinois USA. Springer. 2012
Harding S. L., Miller J. F. Banzhaf W. Developments in Cartesian Genetic Programming: Self-modifying CGP.
Genetic Programming and Evolvable Machines, Vol. 11 (2010)
Harding S. L., Miller J. F. Banzhaf W. Self Modifying Cartesian Genetic Programming: Finding algorithms that
calculate pi and e to arbitrary precision, Proceedings of the Genetic and Evolutionary Computation
Conference, 2010.
Harding S. L., Miller J. F., Banzhaf W. A Survey of Self-Modifying CGP. Genetic Programming Theory and
Practice, Riolo R., (Eds.). University of Michigan Illinois USA. Springer. 2010
91
Harding S. L., Miller J. F. Banzhaf W. Self Modifying Cartesian Genetic Programming: Parity. Proceedings of
Congress on Evolutionary Computation, IEEE Press (2009) 285-292
Harding S. L., Miller J. F. Banzhaf W. Self Modifying Cartesian Genetic Programming: Fibonacci, Squares,
Regression and Summing, Proceedings of the 10th European Conference on Genetic Programming,
Springer LNCS (2009) 133-144
Harding S. L., Miller J. F., Banzhaf W. Self-Modifying Cartesian Genetic Programming, Proceedings of Genetic
and Evolutionary Computation Conference, ACM Press, (2007) 1021-1028.
Harding S., Banzhaf W. Fast Genetic Programming on GPUs. Proceedings of 10th European Conference on
Genetic Programming, Springer LNCS 4445 (2007) 90-101
Harding S. L., Miller J. F. Evolution of Robot Controller Using Cartesian Proceedings of the 6th European
Conference on Genetic Programming, Springer LNCS 3447 (2005) 62-72.
Hirayama Y., Clarke T, Miller J. F. Fault Tolerant Control Using Cartesian Genetic Programming, Proceedings
of Genetic and Evolutionary Computation Conference, ACM Press, (2008) 1523-1530 .
Kalganova T., Miller J. F., Evolving More Efficient Digital Circuits by Allowing Circuit Layout Evolution and
Multi-Objective Fitness. Proceedings of the First NASA/DOD Workshop on Evolvable Hardware,
IEEE Computer Society (1999) 54-63.
Kalganova T., Miller J. F., Fogarty T. C. Some Aspects of an Evolvable Hardware Approach for Multiple-
Valued Combinational Circuit Design Proceedings of the 2nd International Conference on Evolvable
Systems: From Biology to Hardware. Springer LNCS 1478 (1998) 78-89.
Kaufmann P., Platzner M. Advanced Techniques for the Creation and Propagation of Modules in Cartesian
Genetic Programming. Proceedings of the Genetic and Evolutionary Computation Conference, ACM
Press, (2008) 1219-1226.
Kaufmann P., Platzner M. MOVES: A Modular Framework for Hardware Evolution. In Proceedings of the
NASA/ESA Conference on Adaptive Hardware and Systems, IEEE Computer Society Press (2007)
447-454
Kaufmann P., Platzner M. Toward Self-adaptive Embedded Systems: Multiobjective Hardware Evolution.
In Proceedings of the 20th International Conference on Architecture of Computing Systems,
Springer, LNCS 4415 (2007) 119-208.
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92
M. M. Khan, G. M. Khan, and J. F. Miller, “Efficient representation of recurrent neural networks for
markovian/non-markovian non-linear control problems,” in Proceedings of the 10th International
Conference on Intelligent Systems Design and Applications (ISDA2010) (2010) 615–620
Khan, G. M., Miller J. F., Khan, M. M. Evolution of Optimal ANNs for Non-Linear Control Problems Using
Cartesian Genetic Programming. Proceedings of International Conference on Artificial Intelligence
(ICAI 2010)
Khan, G. M., Halliday, D. M., Miller, J. F.,Intelligent agents capable of developing memory of their
environment, Angelo Loula A., Queiroz, J. (Eds.) Advances in Modelling Adaptive and Cognitive
Systems, Editora UEFS (2010)
Khan G. M., Halliday D. M., Miller J. F. In Search of Intelligent Genes: The Cartesian Genetic Programming
Neuron. Proceedings of Congress on Evolutionary Computation, IEEE Press (2009)
Khan G. M., Halliday D. M., Miller J. F. Breaking the synaptic dogma: evolving a neuro-inspired developmental
network. Proceedings of 7th International Conference on Simulated Evolution and Learning, LNCS,
5361 (2008) 11-20
Khan G. M., Halliday D. M., Miller J. F. Coevolution of neuro-developmental programs that play checkers.
Evolvable Systems: From Biology to Hardware. Springer LNCS 5216 (2008) 352 - 361.
Khan G. M., Halliday D. M., Miller J. F. Coevolution of Intelligent Agents using Cartesian Genetic
Programming. Proceedings of Genetic and Evolutionary Computation Conference, ACM Press, (2007)
269-276.
Kuyucu T., Trefzer M. A., Miller J. F., Tyrrell. A. M. On the Properties of Artificial Development and Its Use in
Evolvable Hardware. Proceedings of Symposium on Artificial Life , Part of IEEE Symposium on
Computational Intelligence, IEEE Press (2009).
Liu H., Miller J. F., Tyrrell A. M. , Intrinsic evolvable hardware implementation of a robust biological
development model for digital systems, Proceedings of the NASA/DOD Evolvable Hardware
Conference, IEEE Computer Society (2005) 87-92.
Liu H., Miller J. F., Tyrrell A. M. A Biological Development Model for the Design of Robust Multiplier.
Applications of Evolutionary Computing: EvoHot 2005, Springer LNCS 3449 (2005) 195-204
Liu H., Miller J. F., Tyrrell A. M. An Intrinsic Robust Transient Fault-Tolerant Developmental Model for
Digital Systems. Workshop on Regeneration and Learning in Developmental Systems, Genetic and
Evolutionary Computation Conference (2004).
93
Sekanina, L. Evolvable Components - From Theory to Hardware Implementations, Springer (2003)
Sekanina, L. Image Filter Design with Evolvable Hardware, Proceedings of Evolutionary Image Analysis and
Signal Processing, Springer LNCS 2279 (2002) 255-266.
Sekanina, L, Vašíček Z. On the Practical Limits of the Evolutionary Digital Filter Design at the Gate Level,
Proceedings of EvoHOT, Springer, LNCS 3907 (2006) 344-355.
Miller J. F. Cartesian Genetic Programming, Springer 2011.
Miller J.F., Smith S.L. Redundancy and Computational Efficiency in Cartesian Genetic Programming. IEEE
Transactions on Evolutionary Computation, 10 (2006) 167-174.
Miller J. F. Evolving a self-repairing, self-regulating, French flag organism. Proceedings of Genetic and
Evolutionary Computation Conference, Springer LNCS 3102 (2004) 129-139.
Miller J. F., Thomson P. Beyond the Complexity Ceiling: Evolution, Emergence and Regeneration. Workshop
on Regeneration and Learning in Developmental Systems, Genetic and Evolutionary Computation
Conference (2004).
Miller J.F., Banzhaf W., Evolving the Program for a Cell From French Flags to Boolean Circuits. Kumar S.,
Bentley P. On Growth, Form and Computers. Elsevier Academic Press (2003).
Miller J. F., Thomson P. A Developmental Method for Growing Graphs and Circuits. Proceedings of the 5th
International Conference on Evolvable Systems: From Biology to Hardware, Springer LNCS 2606
(2003) 93-104.
Miller J. F. Evolving developmental programs for adaptation, morphogenesis, and self-repair. Proceedings of the
7th European Conference on Artificial Life, Springer LNAI 2801 (2003) 256-265.
Miller J. F. What bloat? Cartesian Genetic Programming on Boolean problems. Genetic and Evolutionary
Computation Conference, Late breaking paper (2001) 295 - 302.
Miller J. F., Hartmann M. Evolving messy gates for fault tolerance: some preliminary findings. Proceedings of
the 3rd NASA/DOD Workshop on Evolvable Hardware. IEEE Computer Society (2001) 116-123.
Miller J. F., Hartmann M. Untidy evolution: Evolving messy gates for fault tolerance. Proceedings of the 4th
International Conference on Evolvable Systems: From Biology to Hardware. Springer LNCS 2210
(2001) 14-25.
Miller J.F., Kalganova T., Lipnitskaya N., Job D. The Genetic Algorithm as a Discovery Engine: Strange
Circuits and New Principles. Creative Evolutionary Systems. Morgan Kaufmann (2001).
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Miller J.F., Job D., Vassilev V.K. Principles in the Evolutionary Design of Digital Circuits - Part I. Journal of
Genetic Programming and Evolvable Machines, 1 (2000) 8-35.
Miller J.F., Job D., Vassilev V.K. Principles in the Evolutionary Design of Digital Circuits - Part II. Journal of
Genetic Programming and Evolvable Machines, 3 (2000) 259-288.
Miller J. F., Thomson P. Cartesian Genetic Programming. Proceedings of the 3rd European Conference on
Genetic Programming. Springer LNCS 1802 (2000) 121-132.
Miller J. F. On the filtering properties of evolved gate arrays. Proceedings of the First NASA/DOD Workshop
on Evolvable Hardware. IEEE Computer Society (1999) 2-11.
Miller J. F. Digital Filter Design at Gate-level using Evolutionary Algorithms. Proceedings of the 1st Genetic
and Evolutionary Computation Conference. Morgan Kaufmann (1999) 1127-1134.
Miller J. F. An empirical study of the efficiency of learning boolean functions using a Cartesian Genetic
Programming Approach. Proceedings of the 1st Genetic and Evolutionary Computation Conference.
Morgan Kaufmann (1999) 1135-1142.
Miller J. F. Evolution of Digital Filters using a Gate Array Model. Proceedings of the First Workshop on Image
Analysis and Signal Processing. Springer LNCS 1596 (1999) 17-30.
Miller J. F., Kalganova T., Lipnitskaya N., Job D. The Genetic Algorithm as a Discovery Engine: Strange
Circuits and New Principles. Proceedings of the workshop on the AISB Symposium on Creative
Evolutionary Systems. AISB (1999) 65-74.
Miller J. F., Thomson P. Aspects of Digital Evolution: Evolvability and Architecture. Proceedings of The Fifth
International Conference on Parallel Problem Solving from Nature. Springer LNCS 1498 (1998) 927-
936.
Miller J. F., Thomson P. Aspects of Digital Evolution: Geometry and Learning. Proceedings of the 2nd
International Conference on Evolvable Systems: From Biology to Hardware. Springer LNCS 1478
(1998) 25-25.
Miller J. F., Thomson P. Evolving Digital Electronic Circuits for Real-Valued Function Generation using a
Genetic Algorithm . Proceedings of the 3rd Conference on Genetic Programming. Morgan Kaufmann
(1998) 863-868.
95
Miller J.F., Thomson P., Fogarty T.C. Designing Electronic Circuits Using Evolutionary Algorithms:
Arithmetic Circuits: A Case Study. Genetic Algorithms and Evolution Strategies in Engineering and
Computer Science: Recent Advancements and Industrial Applications. Quagliarella, D., Periaux J.,
Poloni C., Winter G. (Eds.). Wiley (1997)
Payne, A. J., Stepney, S.. Representation and Structural biases in CGP, Proceedings of Congress on
Evolutionary Computation, IEEE Press (2009)
Rothermich J., Wang F., Miller J. F. Adaptivity in Cell Based Optimization for Information Ecosystems.
Proceedings of the Congress on Evolutionary Computation. IEEE Press (2003) 490-497.
Rothermich J., Miller J. F. Studying the Emergence of Multicellularity with Cartesian Genetic Programming in
Artificial Life. Proceedings of the 2002 U.K. Workshop on Computational Intelligence (2002).
Seaton, T., Brown G., Miller J. F.., Analytic Solutions to Differential Equations under Graph-based Genetic
Programming. Proceedings of the 13th European Conference on Genetic Programming. Springer LNCS
6021 (2010) 232-243
Vašíček Z, Sekanina L. Hardware Accelerators for Cartesian Genetic Programming, In: Eleventh European
Conference on Genetic Programming, Springer (2008) 230-241
Vašíček, Z. Sekanina, L.. Formal verification of candidate solutions for post-synthesis evolutionary
optimization in evolvable hardware. Genetic Programming and Evolvable Machines, 12(3) (2011) 305-
327, 2011.
Vassilev V. K., Miller J. F. Scalability Problems of Digital Circuit Evolution. Proceedings of the 2nd
NASA/DOD Workshop on Evolvable Hardware. IEEE Computer Society (2000) 55-64.
Vassilev V. K., Miller J. F. The Advantages of Landscape Neutrality in Digital Circuit Evolution. Proceedings
of the 3rd International Conference on Evolvable Systems: From Biology to Hardware. Springer LNCS
1801 (2000) 252-263.
Vassilev V. K., Miller J. F. Towards the Automatic Design of More Efficient Digital Circuits. Proceedings of
the 2nd NASA/DOD Workshop on Evolvable Hardware. IEEE Computer Society (2000) 151-160.
Vassilev V. K., Miller J. F., Fogarty T. C. Digital Circuit Evolution and Fitness Landscapes. Proceedings of the
Congress on Evolutionary Computation. IEEE Press (1999) 1299-1306.
Vassilev V. K., Miller J. F., Fogarty T. C. On the Nature of Two-Bit Multiplier Landscapes. Proceedings of the
First NASA/DOD Workshop on Evolvable Hardware. IEEE Computer Society (1999) 36-45.
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96
Voss M. S. Social programming using functional swarm optimization. In Proceedings of IEEE Swarm
Intelligence Symposium (2003)
Voss M. S., Howland, J. C. III.Financial modelling using social programming. Financial Engineering and
Applications (2003)
Völk K., Miller J. F., Smith, S. L. Multiple Networks CGP for the Classification of Mammograms. Proceedings
of the 11th European Workshop on Image Analysis and Signal Processing (EvoIASP), Springer
LNCS (2009).
Walker J. A., Liu Y., Tempesti G., Tyrrell A. M., “Automatic Code Generation on a MOVE Processor Using
Cartesian Genetic Programming,” in Proceedings of the International Conference on Evolvable
Systems: From Biology to Hardware, Springer LNCS vol. 6274 (2010) 238–249
Walker J.A., Völk, K. , Smith, S. L., Miller, J. F. Parallel evolution using multi-chromosome cartesian genetic
programming, Genetic Programming and Evolvable Machines, 10 (4), (2009) pp 417-445
Walker J. A., Hilder, J. A., Tyrrell. A. M. Towards Evolving Industry-feasible Intrinsic Variability Tolerant
CMOS Designs, Proceedings of Congress on Evolutionary Computation, IEEE Press (2009)
Walker J.A., Miller J.F. The Automatic Acquisition, Evolution and Re-use of Modules in Cartesian Genetic
Programming. IEEE Transactions on Evolutionary Computation, 12 (2008) 397-417.
Walker J. A. Modular Cartesian Genetic Programming. PhD thesis, University of York, 2008.
Walker J. A., Miller J. F. Solving Real-valued Optimisation Problems using Cartesian Genetic Programming.
Proceedings of Genetic and Evolutionary Computation Conference, ACM Press (2007) 1724-1730.
Walker J. A., Miller J. F. Changing the Genospace: Solving GA Problems using Cartesian Genetic
Programming, Proceedings of 10th European Conference on Genetic Programming, Springer LNCS
4445 (2007) 261-270.
Walker J. A., Miller J. F. Predicting Prime Numbers using Cartesian Genetic Programming, Proceedings of 10th
European Conference on Genetic Programming. Springer LNCS 4445, (2007) 205-216
Walker J. A., Miller J. F., Cavill R. A Multi-chromosome Approach to Standard and Embedded Cartesian
Genetic Programming, Proceedings of the 2006 Genetic and Evolutionary Computation Conference.
ACM Press, (2006) 903-910.
97
Walker J. A., Miller J. F. Embedded Cartesian Genetic Programming and the Lawnmower and Hierarchical-if-
and-only-if Problems, Proceedings of the 2006 Genetic and Evolutionary Computation Conference.
ACM Press, (2006) 911-918.
Walker J. A., Miller J. F. Improving the Evolvability of Digital Multipliers Using Embedded Cartesian Genetic
Programming and Product Reduction. Proceedings of 6th International Conference in Evolvable
Systems. Springer, LNCS 3637 (2005) 131-142.
Walker J. A., Miller J. F. Investigating the performance of module acquisition in Cartesian Genetic
Programming, Proceedings of the 2005 conference on Genetic and Evolutionary Computation. ACM
Press (2005) 1649-1656.
Walker J. A., Miller J. F. Evolution and Acquisition of Modules in Cartesian Genetic Programming. Proceedings
of the 7th European Conference on Genetic Programming. Springer LNCS 3003 (2004) 187-197.
Yu T., Miller J.F., Through the Interaction of Neutral and Adaptive Mutations Evolutionary Search Finds a Way.
Artificial Life, 12 (2006) 525-551.
Yu T., Miller J. F. Finding Needles in Haystacks Is Not Hard with Neutrality. Proceedings of the 5th European
Conference on Genetic Programming. Springer LNCS 2278 (2002) 13-25.
Yu T., Miller J. F. Neutrality and Evolvability of a Boolean Function Landscape, Proceedings of the 4th
European Conference on Genetic Programming. Springer LNCS, 2038, (2001) 204-217.
Zhan S., J.F. Miller, A. M., Tyrrell. An evolutionary system using development and artificial Genetic Regulatory
Networks for electronic circuit design, Biosystems, 96 (3) (2009) pp 176-192
Zhan S., Miller J. F., Tyrrell A. M. Obtaining System Robustness by Mimicking Natural Mechanisms .
Proceedings of Congress on Evolutionary Computation. IEEE Press (2009)
Zhan S., Miller J. F., Tyrrell A. M. A Development Gene Regulation Network For Constructing Electronic
Circuits . Evolvable Systems: From Biology to Hardware. LNCS 5216 (2008) 177 – 188
Zhan S., Miller J. F., Tyrrell A. M. An Evolutionary System using Development and Artificial Genetic
Regulatory Networks Proceedings of 9th IEEE World Congress on Computational Intelligence.
Congress on Evolutionary Computation. IEEE Press (2008) 815-822.
Zhang Y., Smith S. L., Tyrrell A. M. Digital circuit design using intrinsic evolvable hardware,Proceedings of the
NASA/DOD Evolvable Hardware Conference, IEEE Computer Society (2004) 55-62.
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