Fast, Effective Genetic Algorithms for Large, Hard Problems
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Fast, Effective Genetic Algorithms for Large, Hard Problems

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Tutorial by David E. Goldberg at 2009 ACM Genetic and Evolutionary Computation Summit in Shanghai, China.

Tutorial by David E. Goldberg at 2009 ACM Genetic and Evolutionary Computation Summit in Shanghai, China.

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  • Honor Escaping Hierarchical Traps with Competent GAs

Fast, Effective Genetic Algorithms for Large, Hard Problems Fast, Effective Genetic Algorithms for Large, Hard Problems Presentation Transcript

  • Fast, Effective GAs for Large, Hard Problems 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 GAs had legs.
    • In 90s, logical continuation of GA thinking has led to
      • Completion of theory in certain sense,
      • & GAs that solve large, hard problems quickly, reliably, and accurately.
    • Consider design theory and designs that have led to reliable solution of difficult problems.
    Andy Warhol (1928-1987)
  • Roadmap
    • One-minute genetic algorithmist.
    • The unreasonableness of GAs.
    • Airplane & toaster design: A lesson from the Wright Brothers.
    • Goals of GA design.
    • Design decomposition step by step.
    • Competent GA design from the fast messy GA to hBOA.
    • From competence to efficiency: When merely fast is not enough.
    • A billion bits or bust.
  • 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.
  • Selection
    • Darwinian survival of the fittest.
    • Give more copies to better guys.
    • Ways to do:
      • roulette wheel
      • tournament
      • truncation
    • Gedanken experiment: Run repeatedly without crossover or mutation.
    • By itself, pick best.
  • Crossover
    • Combine bits and pieces of good parents.
    • Speculate on, new, possibly better children.
    • Gedanken experiment: 50, 11111 & 50, 00000.
    • By itself, a random shuffle
    • Example
    Before X After X 11111 11000 00000 00111
  • Mutation
    • Mutation is a random alteration of a string.
    • Change a gene, small movement in the neighborhood.
    • Gedanken experiment: 100, 11111.
    • By itself, a random walk.
    • Example
    Before M After M 11111 11011
  • The Unreasonableness of GAs
    • How do individually uninteresting operators yield interesting behavior?
    • Others 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)
  • Airplane & Toaster Design
    • Airport story.
    • Why do the rules change?
    • Legacy of Descartes: Separation of mind and body.
    • Material machines (airplanes, toasters, autos, etc.) vs. conceptual machines (GAs, neural nets, computer programs, algorithms).
    • Design is design is design.
  • Two Bicycle Mechanics from Ohio
    • Four years, 1899-1903.
    • Three gliders.
    • Orville and Wilbur Wright created powered flight from scratch.
    • Query: Why were the Wright brothers the first to fly?
  • Hypotheses
    • Wrights flew because they were bicycle mechanics.
    • Wrights flew because it was part of the zeitgeist.
    • Wrights flew because they were bachelors!
    • Maybe the Wrights flew because they were better inventors.
  • December 17, 1903: The Most Famous Moment in Aviation History
  • The Wright Brothers’ Secret
    • Functional decomposition.
    • Three subproblems:
      • Stability : wing-warping plus elevator in 1899 glider model. 1902 glider had three-axis active control.
      • Lift and Drag : wing shape improved on Lilenthal’s through air tunnel experiments.
      • Propulsion : rotary wing with forward lift is a propeller.
  • But Decomposition is Old Hat to Moderns
    • Computer science is about one thing: busting big problems up into lots of little problems.
    • Descartes’s theory of decomposition (1637). Discourse on Method of Rightly Conducting the Reason and Seeking Truth in the Sciences.
    • What else distinguishes Wrights’ method of invention? Method of modeling and integration was different.
  • Lessons of the Wright Brothers
    • Effective design decomposition of your problem.
    • Facetwise, economic models of subproblem facets.
    • Bounding empirical study and calibration.
    • Scaling laws (dimensional analysis) particularly important.
  • Goals of GA Design
    • Solve
      • hard problems,
      • quickly,
      • accurately,
      • and reliably.
    • Call a GA that achieves these goals competent.
    • Can we design competent GAs?
  • Effective Theory in GA 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.
  • Play the GA Game
    • Give you a population of strings S i .
    • Give a list of associate f i values (bigger is better).
    • Ask you to create a better string.
    • Blind: no equation relating f i and S i .
  • What Are We Processing?
    • Similarities among strings.
    • Schemata are similarity subsets.
    • Schemata described by similarity templates.
    • Example: *1*** = {strings with 1 second position}.
    • Population contains 2 l - n 2 l schemata .
  • Schema Theorem (Holland 1975)
    • where
      • f - fitness
      • H - schema
      • M - number of schema representatives
      •  - defining length
      • o - schema order
      • P c - probability of crossover
      • P m - probability of mutation
      • l - string length
    • Little schemata grow logistically.
    • A necessary condition for BB growth.
  • Practical Schema Theorem for Design
    • Fitness multiplier = s.
    • Overall disruption =  .
    • Goldberg & Sastry, 2001
  • Problem Difficulty
    • There are hard problems & easy problems.
    • 3 way decomposition.
    • The core:
      • deception - intra
      • scaling - inter
      • noise - extra
  • Easy Problems & Hard Problems
    • The OneMax problem:
    • Linear, uniformly scaled
    • Define u, unitation variable
      • # or ones in binary string
    • Needle-in-a-haystack (NIAH) problem:
    • No regularity to infer where good solutions might lie.
    • Nothing does better than enumeration or random search.
  • Designing a Harder Problem
    • Low-order estimates mislead GA
    • x * = 111 : f 111 > f i , i  111 .
    • Require complementary schemata better than competitors.
    • Squashed Hamming cube representation:
  • 4-bit Deceptive Trap
  • Good Decisions: 2- & k -Armed Bandit
    • Competing order-one schemata form a two- armed bandit. Example: 0**** versus 1****.
    • Exponentially increasing trials to the observed best.
    • fff**, a 2 3 = 8-armed bandit.
    • Many bandit problems played in parallel.
  • Gambler’s Ruin Population Size
    • Make P bb = Q and solve for n :
    •  = 1 - Q
    • In terms of signal and noise:
    • Compare with populationwise pop-sizing equation:
  • 100-bit Onemax
  • The Complexity Temptation
    • First complexity results for GAs.
    • Calculate the W=nt
    • Function evaluations as product of population size and run duration (single epoch.
  • 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
  • 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, 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).
  • 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]
  • Dr. Jekyll & Mr. Hyde in Practice
    • GA literature full of evidence for this problem.
    • Evolution of the “typical practitioner.”
      • First application goes swimmingly.
      • More complex application needs TLC.
      • Big Kahuna needs compute time = length of universe.
    • Why are we fiddling with codings and operators?
    • Aren’t GAs robust?
    • No. First-generation GAs are not.
  • Simple GAs Are Mixing Limited
    • With growing difficulty, “sweet spot” vanishes.
    • Or populations must grow exponentially.
  • The Key: Not the Schema Theorem
    • Much theory focuses on Holland’s schema theorem.
    • Schema theorem a piece of cake.
    • Make sure GA fires on all seven cylinders of the design decomposition.
    • Surprise: Mixing is the key.
    • To mix well, must get building blocks right.
    • Effective GAs identify structure of problem.
    Data mine early samples for structure of the landscape.
  • GA Kitty Hawk: 1993
    • 1993 & the fast messy GA.
    • Moveable bits, cutting and splicing, building-block filtering mechanism.
    • Original mGA complexity estimated: O( l 5 )
    • Compares favorably to hillclimbing, too (Muhlenbein 1992).
    [Goldberg, Deb, Kargupta, & Harik, 1993]
  • Look Ma, No Genetics: hBOA
    • Replace genetics with probabilistic model building  PMBGA or estimation of distribution algorithm: EDA
    • 3 main elements:
      • Decomposition (structural learning): Learn what to mix and what to keep intact.
      • Representation of BBs (chunking): Means of representing alternative solutions.
      • Diversification of BBs (niching): Preserve alternative chunks of solutions.
    • Test on adversarially designed functions so works on yours.
  • Schematic of BOA Structure Current population Selection New population Bayesian network
  • Results on Spin Glasses Pelikan et al. (2002) 64 100 144 196 256 324 400 10 3 Problem Size Number of Evaluations hBOA O(n 3.51 )
  • From Competence to Efficiency
    • Motivation: Even competent GAs require O ( I 2 ) time.
    • 1000*1000 = a million function evaluations.
    • In real problems, this can be a problem.
    • How can we systematically achieve speedups.
  • IlliGAL Decomposition of Efficiency
    • 1. Space: parallelization
    • 2. Time: continuation
    • 3. Fitness: Evaluation relaxation
    • 4. Specialization: Hybridization
    • Computation time:
    • Communications time:
    • Less computations, more communications
    Master-Slave Parallel GAs
  • Account for Time (and Quality)
    • Use perspective of the master
    • Minimize time:
  • Master-Slave Example
    • Dummy function T f = 4 ms
    • Communications time T c = 19ms
    • Pop size: 120, length = 80
    Cantu-Paz, E. and Goldberg, D. E.(1999). On the scalability of parallel genetic algorithms, Evolutionary Computation, 7 (4), 429-449.)
  • Speedups and Efficiency
  • 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 !
  • 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.
  • 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.
  • Design Fast, Effective GAs
    • GA design advanced by taking GA ideas and running with them.
    • Large, difficult problems in grasp.
    • Theory and practice in sync.
    • These direct lessons are crucial.
    • Meta-lessons of this style of thinking as important for complex systems & interdisciplinary work, generally.
    • This style of theory works for all GEC.
  • More Information
    • Goldberg, D. E. (2002). The design of innovation: Lessons from and for competent genetic algorithms. Boston, MA: Kluwer Academic Publishers.
    • Lab: www.illigal.org
    • iFoundry: www.ifoundry.illinois.edu
    • Email: [email_address]