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Use of Genetic Programming for Automatic Synthesis of Post-2000 Patented Analog Electrical
Circuits and Patentable Controllers
Matthew J. StreeterGenetic Programming, Inc.Mountain View, California
Martin A. KeaneEconometrics, Inc.
Chicago, [email protected]
John R. KozaStanford UniversityStanford, California [email protected]
OPTI 2003, Detroit, May 19-21
Outline
• Overview of Genetic Programming (GP)
• Circuit Synthesis using GP
• Five post-2000 circuits
• Patentable new controllers
Overview of Genetic Programming (GP)
Main Ideas of GP
• Breed computer programs to solve problems
• Programs represented LISP expressions
• Programs can create anything (e.g., circuit, controller)
Pseudo-code for GP
1) Create initial random population
2) Evaluate fitness
3) Select fitter individuals to reproduce
4) Apply reproduction operations (crossover, mutation) to create new population
5) Return to 2 and repeat until solution found
Random initial population
• Function set: {+, *, /, -}
• Terminal set: {A, B, C}
+ +
*
1
2
+
*
A B
C
(1) Choose “+” (2) Choose “*” (3-5) Choose “A”, “B”, “C”
Fitness Evaluation
• 4 random equations shown
• Fitness is shaded areaTarget curve
(x2+x+1)
Crossover
• Subtrees are swapped to create offspring
0.234Z + X – 0.789
X 0.789
–
0.234 Z
*
+
ZY(Y + 0.314Z)
Z Y
*
0.314 Z
*Y
+
*1 1
2 25 5
8 9
3 34 46 7 76
X 0.789
–
+
0.314 Z
*Y
+
Y + 0.314Z + X – 0.789
Z Y
*
*
0.234 Z
*
0.234Z Y2
Pickedsubtree
Parents
Offspring
Pickedsubtree
Circuit Synthesis using GP
• Computer programs represent circuits via developmental process
• Programs grow a circuit from an initial embryo
• Fitness measured (primarily) by circuit’s frequency or transient response
Initial Circuit
• Consists of test fixture (VSOURCE, RSOURCE, RLOAD) and embryo (Z0, Z1)
C FLIP
LIST1
2 3
-
Developmental Process
• Component-inserting functions
• Topology-modifying functions
• Connection functions
C FLIP
LIST1
2 3
-
Fitness Measure
• Curve-matching (like earlier example) based on circuit’s response in frequency or time domain
• Sometimes have additional constraints (e.g., distortion, low component count)
Common setup
• 1000 node Beowulf cluster with 350 MHz Pentium II processors
• Island model with asynchronous subpopulations
• Population size: 100,000
• 70% crossover, 20% constant mutation, 9% cloning, 1% subtree mutation
Five Post-2000 Patented Circuits
Patent Inventor InstitutionLow-voltage balun circuit
Sang Gug Lee Information and Communications University
Mixed analog-digital variable capacitor
Turgut Sefket Aytur
Lucent Technologies Inc.
Voltage-current converter
Akira Ikeuchi and Naoshi Tokuda
Mitsumi Electric Co., Ltd.
High-current load circuit
Timothy Daun-Lindberg and Michael Miller
IBM Corporation
Low-Voltage cubic function generator
Stefano Cipriani and Anthony A. Takeshian
Conexant Systems, Inc.
Setup: Low-voltage Balun Circuit
• Produces two half-amplitude signals with 180 degree phase difference
• Patented circuit operates with 1 V power supply
Patented circuit
Setup: Low-voltage Balun Circuit
• Frequency sweep fitness cases for magnitude & phase angle
• Penalty for total harmonic distortion (THD)
Embryo & Test fixture
Setup: Low-voltage Cubic Function Generator
• Cubing computational circuit using 2 V supply
• Four time-domain fitness cases
Patented circuit
Results: Low-voltage Balun Circuit
• Evolved solution is better in terms of frequency response & THD
• C302 is in the patent claims
• Evolved circuit reads on some, but not all, claims of patent Evolved circuit
Results: Low-voltage Cubic Function Generator
• Evolved solution has 59% of absolute error of patent circuit on our fitness cases
Evolved circuit
Four Patentable Controllers
Basis for Comparison: the Åström-Hägglund controller
• Applied dominant pole design to 16 plants from 4 representative families of plants
• Used curve-fitting to obtain generalized solution
• Equations are expressed in terms of ultimate gain (Ku) and ultimate period (Tu)
The Åström-Hägglund controller
0.56 0.12+ 2
0.25*Ku KueEquation 1 (b):
Equation 2 (Kp) :
1.6 1.2+
20.72* *
Ku KuuK e
Equation 3 (Ki):
Equation 4 (Kd):
1.6 1.2+ 2
1.3 0.38+ 2
0.72* *
0.59* *
Ku Kuu
Ku Kuu
K e
T e
1.6 1.2 1.4 0.56+ +
2 20.108* * * *
K Ku uK Ku uu uK T e e
One evolved controller: topology
Equation 31: Equation 32:
Equation 33:
Equation 34:
( )loglog - + log
+1
L
r uu
LT T
T
( ) ( )( )2 3NLM log - abs( ) +1 - 2L L Lu u r uL L T T T e T e
( )( )( )NLM log - 2 2 log - log +L L Lu u u u uL T e K K e L T K e
log +1rT
NLM(x) = 100 if x < -100 or x > 10010(-100/19-x/19) if -100 x < -510(100/19-x/19) if 5 < x 10010x if -5 x 5
One evolved controller: tuning
Results
• 66.4% of setpoint ITAE of Åström-Hägglund (64.1% out-of-sample)
• 85.7% of disturbance rejection ITAE of A-H (84.9% OOS)
• 94.6% of 1/(minimum attenuation) of A-H (95.8% OOS)
• 92.9% of maximum sensitivity of A-H (93.5% OOS)
Conclusions
• GP can be used to invent circuits, controllers, and other structures (e.g., antennas)
• GP takes a lot of computer time, but:
• Moore’s Law is on our side