Not Your Not Your Grandmother’s Grandmother’s Genetic AlgorithmGenetic Algorithm

David E. GoldbergIllinois Genetic Algorithms LaboratoryUniversity of Illinois at Urbana-ChampaignUrbana, IL 61801 USAEmail: deg@illinois.edu; Web: http://www.illigal.uiuc.edu

GAs Had Their Warhol 15, GAs Had Their Warhol 15, Right?Right? Evolution timeless, GAs so 90s. First-generation GA results were

mixed in practice. Sometimes worked, sometimes not

& first impressions stuck. But John Holland’s ideas had legs. In 90s, logical continuation of John’s

thinking has led to ◦ Completion of theory in certain sense,◦ & GAs that solve large, hard problems

quickly, reliably, and accurately. Consider ways today’s procedures

are not your grandmother’s GA. Along way, reflect on lessons

learned from John. Andy Warhol (1928-1987)

RoadmapRoadmap A technoscientific fairy

tale. 3 things I learned from

John. The one-minute genetic

algorithmist. The unreasonableness of

GAs. Not your grandmother’s

GA:◦ Holland theory in design.◦ A race & GA convergence.◦ A billion bits or bust.

A Technoscientific Fairy TaleA Technoscientific Fairy Tale Once upon a time…◦ There was a civil engineer◦ working for Stoner Associates ◦ doing hydraulics software for pipelines.

Was starting to do real-time control &◦ wondered how human operators◦ controlled gas pipelines ◦ like you or I drive a car.

Was getting restless and just read a book.

Called Ben Wylie in Civil Engineering at Michigan and got 25% RA and went back to school.

One Fine Day in AOne Fine Day in A22 in Fall 1980 in Fall 1980 First day of classes and was signed up for

standard AI course. Expert systems were the rage, Prolog was hip,

LISP was cool. Class was cancelled with little sign on the

door. Hopes and dreams down the drain. Searched and searched for a replacement. Found CCS 524, Intro to

Adaptive Systems, taught byJohn Holland.

Some Prof Named HollandSome Prof Named Holland Youngish looking prof:◦ Talking about biology &

genetics.◦ Samuel’s checker player.◦ Schemas and building

blocks.◦ Classifier systems.

What’s nice civil engineer doing in class like this?

When was Prof Holland going to get to real AI I could use for pipelines?

Or maybe this was the real AI.

3 Things I Learned From John3 Things I Learned From John

Learned many things from John. Later will reflect on some specifics. Now, 3 meta-lessons:◦ Start good science with good story.◦ Go broad or go home.◦ Adopt a Will Rogers theory of

modeling.

Good Stories Good Stories Good Science Good Science Johns method: Conceptual story some math computation.

John the best conceptual story teller I know. Spins self-contained Quine-like “webs of

knowledge.” John’s webs invent things we don’t yet know,

but soon will. Stories have persuasive coherence that sustains

effort when going gets tough.

Go Broad or Go HomeGo Broad or Go Home Many talk a good interdisciplinary game. Don’t know interdisciplinary until you

hang out with John. Fearless in plucking results from X (X =

math, CS, econ, psych, biology, linguistics, poetry, philosophy, etc.)

John’s students spoiled. Hard to work in typical university after

working with John.

Will Rogers Theory of Will Rogers Theory of ModelingModeling Will Rogers theory of

models: “I never met a model I didn’t like.”

John likes all kinds of models.

CS notion of theory has become sterile.

Theory as sometimes instrumental to thought, not always end goal. Will Rogers (1879-1935)

A Model of ModelsA Model of Models

Error, ε

Cost of Modeling, C

Engineer/Inventor

Scientist/Mathematician

Marginal AnalysisMarginal Analysis When should engineer/inventor adopt more

expensive model? At the margins, when ΔB ≥ ΔC. Marginal benefit of model to technology under

development must equal or exceed its marginal cost.

To engineer/inventor, artifact is the object of study models almost always instrumental.

To scientist/mathematician building a model◦ may be the object ◦ or instrumental to some other goal (then engineer’s

calculus applies).

What is a “Model?”What is a “Model?”

Low Cost/High Error

High Cost/Low Error

Unarticulated Wisdom

Articulated QualitativeModel

DimensionalModels

FacetwiseModels

Equations of Motion

The Modeling Spectrum

One-Minute Genetic AlgorithmistOne-Minute Genetic Algorithmist What is a GA? Solutions as chromosomes. Means of evaluating fitness to purpose. Create initial population. Apply selection and genetic operators:◦ Survival of the fittest.◦ Mutation◦ Crossover

Repeat until good enough. Puzzle: operators by themselves uninteresting.

Crossover Alone UninterestingCrossover Alone Uninteresting

Combine bits and pieces of good parents.

Speculate on, new, possibly better children.

By itself, random shuffle.

Gedanken experiments for other ops.

Example, one-point X:

Before X After X

11111 11000

00000 00111

The Unreasonableness of GAsThe Unreasonableness of GAs How do individually uninteresting operators

yield interesting behavior? Others will talk about emergence. 1983 innovation intuition: Genetic algorithm

power like that of human innovation. Separate ◦ Selection + mutation as hillclimbing or kaizen. ◦ Selection + recombination Let’s examine.

Different modes or facets of innovation or invention.

Selection + Recombination = InnovationSelection + Recombination = Innovation

Combine notions to form ideas.

It takes two to invent anything. The one makes up combinations; the other chooses, recognizes what he wishes and what is important to him in the mass of the things which the former has imparted to him. P. Valéry

Paul Valéry (1871-1945)

Holland Theory in DesignHolland Theory in Design Many GAs don’t scale & much

GA theory inapplicable. Need design theory that works:◦ Understand building blocks (BBs),

notions or subideas.

◦ Ensure BB supply.

◦ Ensure BB growth.

◦ Control BB speed.

◦ Ensure good BB decisions.

◦ Ensure good BB mixing (exchange).

◦ Know BB challengers.

Can use theory to design scalable & efficient GAs.

A Sense of TimeA Sense of Time Truncation selection: make s copies each

of top 1/sth of the population. P(t+1) = sP(t) until P(t) = 1 P(t) = stP(0) Solve for takeover time t*: time to go

from one good guy to all good guys (or all but one).

t* = lnn / lns

So What?So What? Who cares about selection alone? I want to analyze a “real GA”. How can selection-only analysis help me? Answer: Imagine another characteristic

time, the innovation or mixing time.

The Innovation Time, The Innovation Time, ttii

Innovation time is the average time to create an individual better than one so far.

Under crossover imagine pi, the probability of recomb event creating better individual.

Innovation probability in Goldberg, Deb

& Thierens (1993) and Thierens & Goldberg (1993).

1)( −= nppt ici

Schematic of the RaceSchematic of the Race

Golf Clubs Have Sweet SpotsGolf Clubs Have Sweet Spots So do GAs. Easy problems, big sweet spots. Monkey can set GA parameters. Hard problems, vanishing sweet spots.

[Goldberg, Deb, & Theirens, 1993]

My Dr. Evil MomentMy Dr. Evil Moment Lunchtime question: do real

large problems draw attention to theoretical & design findings?

Dr. Evil’s mistake: Wondered if GAs could go to 106 vars.

Decided to go for a billion. Use simple underlying

problem (OneMax) with Gaussian noise (0.1 variance of deterministic problem)

Don’t try this at home!!!We get the warhead and then hold the world ransom for... 1 MILLION DOLLARS!

Road to Billion Paved with SpeedupsRoad to Billion Paved with Speedups

Naïve implementation: 100 terabytes & 272 random number calls.

cGA Memory O( ) v. ℓO(ℓ1.5).

Parallelization speedup np.

Vectorize four bits at a time speedup 4.

Other doodads (bitwise ops, limit flops, inline fcns, precomputed evals) speedup 15.

Gens & pop size scale as expected.

A Billion Bits or BustA Billion Bits or Bust

Simple hillclimber solves 1.6(104) or (214).

Souped-up cGA solves 33 million (225) to full convergence.

Solves 1.1 billion (230) with relaxed convergence.

Growth rate the same Solvable to convergence.

Not Your Grandmother’s GANot Your Grandmother’s GA GA design advanced by taking John’s

ideas and running with them. Large difficult problems in grasp. Theory and practice in sync. These direct lessons are crucial. Meta-lessons of Holland’s thinking as

important for future for complex systems & interdisciplinary work, generally.

More InformationMore Information Goldberg, D. E. (2002). The design

of innovation: Lessons from and for competent genetic algorithms. Boston, MA: Kluwer Academic Publishers.

Lab: http://www-illigal.ge.uiuc.edu/

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