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Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 1
Designing Like Mother NatureAn Introduction to Genetic Algorithms
Dr. Derek S. Linden(703) 561-3400 [email protected]
2
About the Speaker, Derek Linden
• B.S., USAF Academy, 1991, Applied Physics (Elec. Systems)
• M.S., MIT, 1993, EE (Solid State Devices/Superconductivity)
• Rome Lab, 1993 - 1996, basic research on superconductors atmicrowave frequencies, antennas, GAs
• Ph.D., MIT, 1997, Thesis: “Automated Design andOptimization of Wire Antennas Using Genetic Algorithms”
• Current research: Increasing GA efficiency, applying GAs tonew problems
• Linden Innovation Research LLC
– Automated Design and Optimization Consulting, Trainingand Software
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 2
3
Introduction to GAs: Overview
• Goal: to introduce the fundamental concepts of a GA– What is a GA?
– GA basics
– Examples
4
What is a GA?
• A probabilistic, iterative search and optimizationstrategy
• Mimics biological intra-species adaptation andevolution through mating and survival-of-the-fittest
• Finds optima for many types of numerical problems
• Requires:– A coding strategy
– An objective function
– A mating and mutation scheme
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 3
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The GA Iterative Process
Choose mates andcreate children
Mutate children
Initialize newpopulation
Simulate and evaluatenew members
Rank-order allmembers
Is convergencecriteria met?
Output results
YES
NO
6
GA Terms
0 0 1 1 1 0 1 0 1 0 0.546 0.010 0.530 0.223 0.750 0.456
0 0 1 1 0 0 1 1 0 0 0.754 0.122 0.822 0.564 0.438 0.990
0 1 1 1 0 1 1 0 0 1 0.945 0.678 0.800 0.442 0.901 0.198
1 0 1 0 1 1 0 0 1 0 0.248 0.548 0.401 0.881 0.058 0.451
1 1 1 0 0 1 1 1 0 0 0.700 0.890 0.540 0.111 0.878 0.002
Alleles
Genes
Population
Chromosomes
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 4
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An Example Design Problem
h
d
Mt
4 Variables, with Constraints:Material: ceramic, glass, plasticDiameter: 2”-5”Height: 3”-6”Thickness: 0.1”-0.5”
Dependent constraint:Weight < 1.5 lbs.
Optimize for:Heat Retention = f(M,d,h,t)Cost = f(M,d,h,t)Volume = f(d,h)
8
Setup for GA Optimization
h
d
Mt
Objective Function = Heat Retention + Volume - Cost - Penalty * Weight
(Penalty is non-zero only if Weight above 1.5 lbs.)
HeightDiameter ThicknessMaterial
01 1010 0100 1101
Glass 4.0” 2.8” 0.447”
Chromosome:
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 5
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Snapshot During the GA Process
P
G
C P
G
C
10
Brief History
• Before the GA, algorithms based on mutation weretried
• John Holland (University of Michigan)– Holland had the basic GA by the mid-1960s
– Monograph in 1975—“Adaptation in Natural andArtificial Systems”
– Purpose: to understand adaptive processes in naturalsystems and design artificial systems that mimicnatural system behavior
• David Goldberg—textbook in 1989
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 6
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Current Areas of Application
• Mechanical Engineering
• Software Design
• Electromagnetics
• Electrostatics
• Artificial Intelligence/Artificial Life
• Robotics
• Aeronautical Engineering
• Financial
12
The GA Process
• Set up simulator/equations to evaluate members of population
• Define problem—constraints, unknowns, variables
• Determine objective function
• Determine chromosome mapping
• Determine genetic algorithm characteristics– mating selection, crossover, mutation, population size, etc.
• Run the GA optimization process
• Output the optimal design characteristics
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 7
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Objective Function
• Gives a single score based on simulation results
• Used to rank-order the members of the population
• Single criteria or multi-criteria
• Include any penalty terms for violating constraints
Fitness = -c1 * gain + c2 * mismatch + c3 * distortion+ c4 * (amount of power violation)
14
1-D Binary and Real Chromosomes
• Binary: 0 0 1 1 1 0 1 0 1 0
– Usually each variable consists of several bits
– Most commonly used by far, good for most problems
• Real: 0.546 0.010 0.530 0.223 0.750 0.456 0.555
– Usually each variable consists of only one number
– Use for problems involving mostly real, continuousvariables
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 8
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Chromosome Mapping: Example
GroundPlane
(0.05 - 0.50)λ
(0.01 - 0.10)λ
(0.05 - 0.50)λ
(0.05 - 0.50)λ
(0.01 - 0.10)λ
Z4
Z1
Z2Z3 X1
X2
(0.03 - 0.35)λ
00000 11111 00000 11111 00000 11111 Z1 Z2 Z3 Z4 X1 X2
0.452 0.335 0.102 0.873 0.525 0.651
Binary 1-D
Real 1-D
16
Mating Process
• The basic mating process:– Eliminate poor performers (total population remains
constant)
– Choose chromosomes to mate
– Create offspring
• Simple GA: replaces whole population with newchildren, though some are copies of parents
• Steady-State GA: saves a portion of the populationeach generation
• Elitist: saves top chromosome
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 9
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• In biology, mates are chosen through natural selection– Brightest flower, strongest male, most attractive call
• Most common GA method: weighted roulette wheel
• Usually weighted by fitness, or qualities like similarity
Mating Selection
Spin 1: First Parent
Spin 2: Second Parent
1 = Most fit member
10 = Least fit member1
23
4
56 7 8 9 10
18
Concept: Crossover
A ba B
c
C
A bA
Baa
c
C
Ab
A B
a b
a B
cc
C
C
A b c
a b c
A B C
a B C
Chiasma
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 10
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1-D Binary Mating—Single-Point Crossover
• Parent chromosomes:
[00011110]
{11001100}
• Let the crossover point be between the 5th and 6th bit(but could be between any two bits)
• Children: [00011]{100}
{11001}[110]
• Works the same way for real chromosomes, exceptno functional genes are able to be split
20
1-D Real Chromosome Mating
• Heuristic crossover
• Quadratic crossover
• Many other methods existAdewuya, 1996
gene value
;;
12
3fitnesschild
;;
1
2fitness child
gene value
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 11
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1-D Binary and RealChromosome Mutation
• Binary: Bit flip– Flip a randomly selected 1 0 or 0 1
• Real: Uniform mutation
• Real: Gaussian mutation
lower limit upper limit
lower limit upper limit
22
The GA Parameters
• Population Size: 30 - 10,000(most I’ve heard of: 1,000,000)
• Parent pool size (overlap): 10%-50%
• Probability of mutation: < 2%
• Convergence criteria:– # generations
– # simulations
– non-improvement
– loss of diversity
– when I choose to stop it
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 12
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Putting the Process Together
Choose mates andcreate children
Mutate children
Initialize newpopulation
Simulate and evaluatenew members
Rank-order allmembers
Is convergencecriteria met?
Output results
YES
NO
24
Typical GA Behavior: Fitness
• Best fitness, Average fitness vs. Generation
0
2000
4000
6000
8000
10000
12000
14000
1 11 21 31 41 51 61 71 81 91
Fitn
ess
Generation
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 13
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GA Advantages
• Properly implemented, it can lead to optimal solutionsrelatively rapidly and efficiently
• Prevents the solution from getting trapped in local minimathrough parallelism
• Is zeroth-order/blind—requires no information other than theobjective function value for each chromosome
• Can optimize very complicated systems with no humanintervention (not even an initial guess!)
• Very robust to parameters, coding, etc.
• Able to be implemented in a parallel manner GA
Sim 3Sim 2
Sim 1
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GA Examples
• Discrete problems– Truss topology design
– VLSI connection design
– Job Shop Process Planning
• Continuous problems
– Turbine engine design
– Pattern nesting (Parts layout)
– Simple wire antenna
– Folded monopole & Crooked-wire antennas
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 14
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Truss Topology Design
• Use a GA to determine an optimal truss structure withthe least amount of material given a load
Chapman et al.,1994
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Truss Topology Design
• Example optimized designs at differing resolutions
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 15
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Job Shop Process Planning
• Minimize the cost and hassle in machining custom parts
• Many different combinations of machine, tool, and setup arepossible to create the same part
Zhang, et al.,1997
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Job Shop Process Planning
Minimize Machine Setup Tool Cost
Machine 0 11 13 2664
Setup 8 0 10 3799
Tool 12 5 0 5014
Cost 1 3 8 1739
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 16
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VLSI Connection Design
• Rather complex GA technique compared with 2-4 other standardVLSI techniques in each of 10 classic benchmarks
• GA was best method for each benchmark in numbers of vias
• Best for overall wire length in 7 of 10 benchmarks
• 2nd best in the other 3 benchmarks, and usually a close second
• Crosstalk requirements can be added, which none of the othertechniques can handle
Leinig, 1997
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Turbine Engine Design
At least 100 variables, eachwith a continuous range
Search space of 10387 points
Fitness: compliance withabout 50 constraints +performance measures
Engineer: 8 weeks for a satisfactory designEngineer + Expert system: less than 1 day w/ 2x improvementGA + Expert system: 2 days w/ 3x improvement over engineer alone
Holland, 1992
Pratt&Whitney Engine
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 17
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Dighe & Jakiela, 1996
Pattern Nesting
• Applications in many industries– Clothing
– Shipbuilding
– Automobile part manufacturing
34
Pattern Nesting
• Minimizing rectangular enclosure
68.4% 69.0%
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 18
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Pattern Nesting
• Minimizing height
70.4% 72.4%
36
Simple Wire Antenna
• The design
Drive point(in center of element)
Reflector element 0 - 4 λ
Driven element 0.5 λ
Separation distance 0.04 - 2 λ
Linden, 1997
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 19
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0.02
0.22
0.42
0.62
0.82
1.02
1.22
1.42
1.62
1.82
2.02
2.22
2.42
2.62
2.82
3.02
3.22
3.42
3.62
3.82
0.08
0.28
0.48
0.68
0.88
1.08
1.28
1.48
1.68
1.88
-2
0
2
4
6
8
10
Gain
Length
Separation
Simple Wire Antenna
• The search space
38
Simple Wire Antenna
• The objective function– Maximize gain in forward direction (already a single
number)
• The chromosome– Two real values for length and separation
• GA parameters– 20 chromosomes, 50% overlap, 0.6% mutation
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 20
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Simple Wire Antenna
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
1 2 5
8 11 14
17 20 23
40
Folded Monopole, Crooked-WireAntennas
• The problem: Our goal in each case was to achieve asingle objective: the broadest beam possible over theupper hemisphere
– Folded monopole — power gain only
– Crooked wire antennas — RH circular polarizationgain
Score = Σover all θ,φ(Gain(θ,φ) - Avg. Gain)2
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 21
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The Folded Monopole Chromosome
GroundPlane
(0.05 - 0.50)λ
(0.01 - 0.10)λ
(0.05 - 0.50)λ
(0.05 - 0.50)λ
(0.01 - 0.10)λ
Z4
Z1
Z2Z3 X1
X2
(0.03 - 0.35)λ
00000 11111 00000 11111 00000 11111 Z1 Z2 Z3 Z4 X1 X2
Goal: Hemispherical coverage, regardless of polarization
42
Folded Monopole Results
5
0
-10
-5
10
Gain
-70 -50 -30 -10 10 30 50 70θ
f = 1600MHz
-90 90
(dB)
(deg.)
45°(dash)
90°(solid)
φ=0°(dot)
θ
φ
Altshuler & Linden, 1997
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 22
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Crooked-Wire Genetic AntennaSpace
Goal: Coverage over hemisphere 10 above the horizonwith right-hand circular polarization
0.5λ
0.5λ
0.5λ
Ground
Ground
(X1,Y1,Z1)(X2,Y2,Z2)(X3,Y3,Z3)...(X7,Y7,Z7) 105 bits
44
Crooked-Wire Genetic AntennaResults
-5
-1070
5
0
10
Gain
-70 -50 -30 -10 10 30 50
θ
f = 1600MHz
-90 90
(dB
(deg.)
φ=0°
45°
135° 90°
Linden & Altshuler, 1996
Designing Like Mother Nature: An Introduction to Genetic Algorithms IEEE CS Meeting, April 15, 1999
(c) Linden Innovation Research LLC 23
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References
• A. Adewuya, “ New Methods in Genetic Search with Real-valued Chromosomes,” Master'sThesis, Mech. Engr. Dept., MIT, 1996
• C.D. Chapman, K. Saitou, M.J. Jakiela. “Genetic Algorithms as an Approach to Configurationand Topology Design.” Journal of Mechanical Design,Vol. 116, December 1994.
• F. Zhang, Y.F. Zhang, A.Y.C Nee. “Using Genetic Algorithms in Process Planning for JobShop Machining.” IEEE Trans. on Evolutionary Computation, Vol. 1, No. 4, November 1997.
• J. Lienig. “A Parallel Genetic Algorithm for Performance-Driven VLSI Routing.” IEEETrans. on Evolutionary Computation, Vol. 1, No. 1, April 1997.
• J.H. Holland. “Genetic Algorithms.” Scientific American, July 1992.
• R. Dighe and M.J. Jakiela. “Solving Pattern Nesting Problems with Genetic AlgorithmsEmploying Task Decomposition and Contact Detection.” Evolutionary Computation, Vol. 3,No. 3, 1996.
• D.S. Linden. “Automated Design and Optimization of Wire Antennas using GeneticAlgorithms.” Ph.D. Thesis, MIT, September 1997.
• E.E. Altshuler and D.S. Linden. “Design of a Loaded Monopole Having HemisphericalCoverage Using a Genetic Algorithm.” IEEE Trans. on Antennas and Propagation., Vol. 45,No. 1, January 1997.
• D.S. Linden and E.E. Altshuler. “Automating Wire Antenna Design using GeneticAlgorithms.” Microwave Journal, Vol. 39, No. 3, March 1996.