Not Your Grandmother’s Genetic Algorithm David E. Goldberg Illinois Genetic Algorithms Laboratory University of Illinois at Urbana-Champaign Urbana, IL 61801 USA Email: [email_address] ; Web: http://www.illigal.uiuc.edu

GAs Had Their Warhol 15, 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)

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.

Roadmap 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 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 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.

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 A 2 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 by John Holland.

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 by John Holland.

Some 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.

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 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.

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 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.

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 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.

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 Modeling 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)

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.

A Model of Models Error, ε Cost of Modeling, C Engineer/Inventor Scientist/Mathematician

Marginal Analysis When should engineer/inventor adopt more expensive model? At the margins, when Δ B ≥ Δ C. 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).

When should engineer/inventor adopt more expensive model?

At the margins, when Δ B ≥ Δ C.

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?” The Modeling Spectrum Low Cost/ High Error High Cost/ Low Error Unarticulated Wisdom Articulated Qualitative Model Dimensional Models Facetwise Models Equations of Motion

One-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.

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 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

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:

The 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.

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 = 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)

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

Holland 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.

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 Time Truncation selection: make s copies each of top 1/ s th of the population. P(t+1) = s P(t) until P(t) = 1 P(t) = s t P(0) Solve for takeover time t *: time to go from one good guy to all good guys (or all but one). t * = ln n / ln s

Truncation selection: make s copies each of top 1/ s th of the population.

P(t+1) = s P(t) until P(t) = 1

P(t) = s t P(0)

Solve for takeover time t *: time to go from one good guy to all good guys (or all but one).

t * = ln n / ln s

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.

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, t i 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).

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).

Schematic of the Race

Golf 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]

So do GAs.

Easy problems, big sweet spots.

Monkey can set GA parameters.

Hard problems, vanishing sweet spots.

My 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 10 6 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 !

Lunchtime question: do real large problems draw attention to theoretical & design findings?

Dr. Evil’s mistake: Wondered if GAs could go to 10 6 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!!!

Road to Billion Paved with Speedups Naïve implementation: 100 terabytes & 2 72 random number calls. cGA  Memory O(ℓ) v. O(ℓ 1.5 ). Parallelization  speedup n p . 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.

Naïve implementation: 100 terabytes & 2 72 random number calls.

cGA  Memory O(ℓ) v. O(ℓ 1.5 ).

Parallelization  speedup n p .

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 Bust Simple hillclimber solves 1.6(10 4 ) or (2 14 ). Souped-up cGA solves 33 million (2 25 ) to full convergence. Solves 1.1 billion (2 30 ) with relaxed convergence. Growth rate the same  Solvable to convergence.

Simple hillclimber solves 1.6(10 4 ) or (2 14 ).

Souped-up cGA solves 33 million (2 25 ) to full convergence.

Solves 1.1 billion (2 30 ) with relaxed convergence.

Growth rate the same  Solvable to convergence.

Not 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.

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 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/ DISCUS: http://www-discus.ge.uiuc.edu / iFoundry: http://ifoundry.illigal.uiuc.edu / WPE-2008: http://www-illigal.ge.uiuc.edu/wpe

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/

DISCUS: http://www-discus.ge.uiuc.edu /

iFoundry: http://ifoundry.illigal.uiuc.edu /

WPE-2008: http://www-illigal.ge.uiuc.edu/wpe