Not Your Grandmother's Genetic Algorithm


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Talk presented in honor of John Holland at Adapation, Order & Emergence

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  • Honor Escaping Hierarchical Traps with Competent GAs
  • Not Your Grandmother's Genetic Algorithm

    1. 1. 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:
    2. 2. GAs Had Their Warhol 15, Right? <ul><li>Evolution timeless, GAs so 90s. </li></ul><ul><li>First-generation GA results were mixed in practice. </li></ul><ul><li>Sometimes worked, sometimes not & first impressions stuck. </li></ul><ul><li>But John Holland’s ideas had legs. </li></ul><ul><li>In 90s, logical continuation of John’s thinking has led to </li></ul><ul><ul><li>Completion of theory in certain sense, </li></ul></ul><ul><ul><li>& GAs that solve large, hard problems quickly, reliably, and accurately. </li></ul></ul><ul><li>Consider ways today’s procedures are not your grandmother’s GA. </li></ul><ul><li>Along way, reflect on lessons learned from John. </li></ul>Andy Warhol (1928-1987)
    3. 3. Roadmap <ul><li>A technoscientific fairy tale. </li></ul><ul><li>3 things I learned from John. </li></ul><ul><li>The one-minute genetic algorithmist. </li></ul><ul><li>The unreasonableness of GAs. </li></ul><ul><li>Not your grandmother’s GA: </li></ul><ul><ul><li>Holland theory in design. </li></ul></ul><ul><ul><li>A race & GA convergence. </li></ul></ul><ul><ul><li>A billion bits or bust. </li></ul></ul>
    4. 4. A Technoscientific Fairy Tale <ul><li>Once upon a time… </li></ul><ul><ul><li>There was a civil engineer </li></ul></ul><ul><ul><li>working for Stoner Associates </li></ul></ul><ul><ul><li>doing hydraulics software for pipelines. </li></ul></ul><ul><li>Was starting to do real-time control & </li></ul><ul><ul><li>wondered how human operators </li></ul></ul><ul><ul><li>controlled gas pipelines </li></ul></ul><ul><ul><li>like you or I drive a car. </li></ul></ul><ul><li>Was getting restless and just read a book. </li></ul><ul><li>Called Ben Wylie in Civil Engineering at Michigan and got 25% RA and went back to school. </li></ul>
    5. 5. One Fine Day in A 2 in Fall 1980 <ul><li>First day of classes and was signed up for standard AI course. </li></ul><ul><li>Expert systems were the rage, Prolog was hip, LISP was cool. </li></ul><ul><li>Class was cancelled with little sign on the door. </li></ul><ul><li>Hopes and dreams down the drain. </li></ul><ul><li>Searched and searched for a replacement. </li></ul><ul><li>Found CCS 524, Intro to Adaptive Systems , taught by John Holland. </li></ul>
    6. 6. Some Prof Named Holland <ul><li>Youngish looking prof: </li></ul><ul><ul><li>Talking about biology & genetics. </li></ul></ul><ul><ul><li>Samuel’s checker player. </li></ul></ul><ul><ul><li>Schemas and building blocks. </li></ul></ul><ul><ul><li>Classifier systems. </li></ul></ul><ul><li>What’s nice civil engineer doing in class like this? </li></ul><ul><li>When was Prof Holland going to get to real AI I could use for pipelines? </li></ul><ul><li>Or maybe this was the real AI. </li></ul>
    7. 7. 3 Things I Learned From John <ul><li>Learned many things from John. </li></ul><ul><li>Later will reflect on some specifics. </li></ul><ul><li>Now, 3 meta-lessons: </li></ul><ul><ul><li>Start good science with good story. </li></ul></ul><ul><ul><li>Go broad or go home. </li></ul></ul><ul><ul><li>Adopt a Will Rogers theory of modeling. </li></ul></ul>
    8. 8. Good Stories  Good Science <ul><li>Johns method: Conceptual story  some math  computation. </li></ul><ul><li>John the best conceptual story teller I know. </li></ul><ul><li>Spins self-contained Quine-like “webs of knowledge.” </li></ul><ul><li>John’s webs invent things we don’t yet know, but soon will. </li></ul><ul><li>Stories have persuasive coherence that sustains effort when going gets tough. </li></ul>
    9. 9. Go Broad or Go Home <ul><li>Many talk a good interdisciplinary game. </li></ul><ul><li>Don’t know interdisciplinary until you hang out with John. </li></ul><ul><li>Fearless in plucking results from X (X = math, CS, econ, psych, biology, linguistics, poetry, philosophy, etc.) </li></ul><ul><li>John’s students spoiled. </li></ul><ul><li>Hard to work in typical university after working with John. </li></ul>
    10. 10. Will Rogers Theory of Modeling <ul><li>Will Rogers theory of models: “I never met a model I didn’t like.” </li></ul><ul><li>John likes all kinds of models. </li></ul><ul><li>CS notion of theory has become sterile. </li></ul><ul><li>Theory as sometimes instrumental to thought, not always end goal. </li></ul>Will Rogers (1879-1935)
    11. 11. A Model of Models Error, ε Cost of Modeling, C Engineer/Inventor Scientist/Mathematician
    12. 12. Marginal Analysis <ul><li>When should engineer/inventor adopt more expensive model? </li></ul><ul><li>At the margins, when Δ B ≥ Δ C. </li></ul><ul><li>Marginal benefit of model to technology under development must equal or exceed its marginal cost. </li></ul><ul><li>To engineer/inventor, artifact is the object of study  models almost always instrumental. </li></ul><ul><li>To scientist/mathematician building a model </li></ul><ul><ul><li>may be the object </li></ul></ul><ul><ul><li>or instrumental to some other goal (then engineer’s calculus applies). </li></ul></ul>
    13. 13. 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
    14. 14. One-Minute Genetic Algorithmist <ul><li>What is a GA? </li></ul><ul><li>Solutions as chromosomes. </li></ul><ul><li>Means of evaluating fitness to purpose. </li></ul><ul><li>Create initial population. </li></ul><ul><li>Apply selection and genetic operators: </li></ul><ul><ul><li>Survival of the fittest. </li></ul></ul><ul><ul><li>Mutation </li></ul></ul><ul><ul><li>Crossover </li></ul></ul><ul><li>Repeat until good enough. </li></ul><ul><li>Puzzle: operators by themselves uninteresting. </li></ul>
    15. 15. Crossover Alone Uninteresting <ul><li>Combine bits and pieces of good parents. </li></ul><ul><li>Speculate on, new, possibly better children. </li></ul><ul><li>By itself, random shuffle. </li></ul><ul><li>Gedanken experiments for other ops. </li></ul><ul><li>Example, one-point X: </li></ul>Before X After X 11111 11000 00000 00111
    16. 16. The Unreasonableness of GAs <ul><li>How do individually uninteresting operators yield interesting behavior? </li></ul><ul><li>Others will talk about emergence. </li></ul><ul><li>1983 innovation intuition: Genetic algorithm power like that of human innovation. </li></ul><ul><li>Separate </li></ul><ul><ul><li>Selection + mutation as hillclimbing or kaizen. </li></ul></ul><ul><ul><li>Selection + recombination  Let’s examine. </li></ul></ul><ul><li>Different modes or facets of innovation or invention. </li></ul>
    17. 17. Selection + Recombination = Innovation <ul><li>Combine notions to form ideas. </li></ul><ul><li>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 </li></ul>Paul Valéry (1871-1945)
    18. 18. Holland Theory in Design <ul><li>Many GAs don’t scale & much GA theory inapplicable. </li></ul><ul><li>Need design theory that works: </li></ul><ul><ul><li>Understand building blocks (BBs), notions or subideas. </li></ul></ul><ul><ul><li>Ensure BB supply. </li></ul></ul><ul><ul><li>Ensure BB growth. </li></ul></ul><ul><ul><li>Control BB speed. </li></ul></ul><ul><ul><li>Ensure good BB decisions. </li></ul></ul><ul><ul><li>Ensure good BB mixing (exchange). </li></ul></ul><ul><ul><li>Know BB challengers. </li></ul></ul><ul><li>Can use theory to design scalable & efficient GAs. </li></ul>
    19. 19. A Sense of Time <ul><li>Truncation selection: make s copies each of top 1/ s th of the population. </li></ul><ul><li>P(t+1) = s P(t) until P(t) = 1 </li></ul><ul><li>P(t) = s t P(0) </li></ul><ul><li>Solve for takeover time t *: time to go from one good guy to all good guys (or all but one). </li></ul><ul><li>t * = ln n / ln s </li></ul>
    20. 20. So What? <ul><li>Who cares about selection alone? </li></ul><ul><li>I want to analyze a “real GA”. </li></ul><ul><li>How can selection-only analysis help me? </li></ul><ul><li>Answer: Imagine another characteristic time, the innovation or mixing time. </li></ul>
    21. 21. The Innovation Time, t i <ul><li>Innovation time is the average time to create an individual better than one so far. </li></ul><ul><li>Under crossover imagine pi, the probability of recomb event creating better individual. </li></ul><ul><li>Innovation probability in Goldberg, Deb & Thierens (1993) and Thierens & Goldberg (1993). </li></ul>
    22. 22. Schematic of the Race
    23. 23. Golf Clubs Have Sweet Spots <ul><li>So do GAs. </li></ul><ul><li>Easy problems, big sweet spots. </li></ul><ul><li>Monkey can set GA parameters. </li></ul><ul><li>Hard problems, vanishing sweet spots. </li></ul>[Goldberg, Deb, & Theirens, 1993]
    24. 24. My Dr. Evil Moment <ul><li>Lunchtime question: do real large problems draw attention to theoretical & design findings? </li></ul><ul><li>Dr. Evil’s mistake: Wondered if GAs could go to 10 6 vars. </li></ul><ul><li>Decided to go for a billion. </li></ul><ul><li>Use simple underlying problem (OneMax) with Gaussian noise (0.1 variance of deterministic problem) </li></ul><ul><li>Don’t try this at home!!! </li></ul>We get the warhead and then hold the world ransom for... 1 MILLION DOLLARS !
    25. 25. Road to Billion Paved with Speedups <ul><li>Naïve implementation: 100 terabytes & 2 72 random number calls. </li></ul><ul><li>cGA  Memory O(ℓ) v. O(ℓ 1.5 ). </li></ul><ul><li>Parallelization  speedup n p . </li></ul><ul><li>Vectorize four bits at a time  speedup 4. </li></ul><ul><li>Other doodads (bitwise ops, limit flops, inline fcns, precomputed evals)  speedup 15. </li></ul><ul><li>Gens & pop size scale as expected. </li></ul>
    26. 26. A Billion Bits or Bust <ul><li>Simple hillclimber solves 1.6(10 4 ) or (2 14 ). </li></ul><ul><li>Souped-up cGA solves 33 million (2 25 ) to full convergence. </li></ul><ul><li>Solves 1.1 billion (2 30 ) with relaxed convergence. </li></ul><ul><li>Growth rate the same  Solvable to convergence. </li></ul>
    27. 27. Not Your Grandmother’s GA <ul><li>GA design advanced by taking John’s ideas and running with them. </li></ul><ul><li>Large difficult problems in grasp. </li></ul><ul><li>Theory and practice in sync. </li></ul><ul><li>These direct lessons are crucial. </li></ul><ul><li>Meta-lessons of Holland’s thinking as important for future for complex systems & interdisciplinary work, generally. </li></ul>
    28. 28. More Information <ul><li>Goldberg, D. E. (2002). The design of innovation: Lessons from and for competent genetic algorithms. Boston, MA: Kluwer Academic Publishers. </li></ul><ul><li>Lab: </li></ul><ul><li>DISCUS: / </li></ul><ul><li>iFoundry: / </li></ul><ul><li>WPE-2008: </li></ul>