1 / 112

Introductory Workshop on Evolutionary Computing

Introductory Workshop on Evolutionary Computing. Part I: Introduction to Evolutionary Algorithms. Dr. Daniel Tauritz Director, Natural Computation Laboratory Associate Professor, Department of Computer Science Research Investigator, Intelligent Systems Center

cedric
Download Presentation

Introductory Workshop on Evolutionary Computing

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Introductory Workshop on Evolutionary Computing Part I: Introduction to Evolutionary Algorithms Dr. Daniel Tauritz Director, Natural Computation Laboratory Associate Professor, Department of Computer Science Research Investigator, Intelligent Systems Center Collaborator, Energy Research & Development Center

  2. Motivation • Real-world optimization problems are typically characterized by huge, ill-behaved solution spaces • Infeasible to exhaustively search • Defy traditional (gradient-based) optimization algorithms because they are non-linear, non-differentiable, non-continuous, or non-convex

  3. Real-World Example • Electric Power Transmission Systems • Supply is not keeping up with demand • Expansion hampered by: • Social, environmental, and economic constraints • Transmission system is “stressed” • Already carrying more than intended • Dramatic increase in incidence reports

  4. The Grid

  5. The Grid: Failure

  6. The Grid: Redistribution

  7. The Grid: A Cascade

  8. The Grid: Redistribution

  9. The Grid: Unsatisfiable

  10. The Grid: Unsatisfiable

  11. Failure Analysis • Failure spreads relatively quickly • Too quickly for conventional control • Cascade may be avoidable • Utilize unused capacities (flow compensation) • Unsatisfiable condition may be avoidable • Better power flow control to reduce severity

  12. Possible Solution • Strategically place a number of power flow control devices • Flexible A/C Transmission System (FACTS) devices are a promising type of high-speed power-electronics power flow control devices • Unified Power Flow Controller (UPFC)

  13. FACTS Interaction Laboratory UPFC Simulation Engine HIL Line

  14. The placement optimization problem • UPFCs are extremely expensive, so only a limited number can be placed • Placement is a combinatorial problem • Given 1000 high-voltage lines and 10 UPFCs, there are 1000C10 total possible placements (about 2.6 x 1023) • If each placement is evaluated in 1 minute, then it will take about 5 x 1015 centuries to solve using exhaustive search

  15. The placement solution space • Placing individual UPFC devices are not independent tasks • There are complex non-linear interactions between UPFC devices • The placement solution space is ill-behaved, so traditional optimization algorithms are not usable

  16. Evolutionary Computing • The field of Evolutionary Computing (EC) studies the theory and application of Evolutionary Algorithms (EAs) • EAs can be described as a class of stochastic, population-based optimization algorithms inspired by natural evolution, genetics, and population dynamics

  17. Very high-level EA schematic problem instance EA representation fitness function EA operators EA parameters solution

  18. Intuitive view of why EAs work • Trial-and-error (aka generate-and-test) • Graduated solution quality creates virtual gradient • Stochastic local search of solution landscape

  19. (Darwinian) Evolution • The environment contains populations of individuals of the same species which are reproductively compatible • Natural selection • Random variation • Survival of the fittest • Inheritance of traits

  20. (Mendelian) Genetics • Genotypes vs. phenotypes • Pleitropy: one gene affects multiple phenotypic traits • Polygeny: one phenotypic trait is affected by multiple genes • Chromosomes (haploid vs. diploid) • Loci and alleles

  21. Nature versus the digital realm

  22. Scope • Genotype – functional unit of inheritance • Individual – functional unit of selection • Population – functional unit of evolution

  23. Solution Representation • Structural types: linear, tree, FSM, etc. • Data types: bit strings, integers, permutations, reals, etc. • EA genotype encodes solution representation and attributes • EA phenotype expresses the EA genotype in the current environment • Encoding & Decoding

  24. Fitness Function • Determines individuals’ fitness based selection chances • Transforms objective function to linearly ordered set with higher fitness values corresponding to higher quality solutions (i.e., solutions which better satisfy the objective function) • Knapsack Problem Example

  25. Initialization • (Initial) population size • Uniform random • Heuristic based • Knowledge based • Genotypes from previous runs • Seeding

  26. Parent selection • Fitness Proportional Selection (FPS) • Roulette wheel sampling • High risk of premature convergence • Uneven selective pressure • Fitness function not transposition invariant • Fitness Rank Selection • Mapping function (like a cooling schedule) • Tournament selection

  27. Variation operators • Mutation = Stochastic unary variation operator • Recombination = Stochastic multi-ary variation operator

  28. Mutation • Bit-String Representation: • Bit-Flip • E[#flips] = L * pm • Integer Representation: • Random Reset (cardinal attributes) • Creep Mutation (ordinal attributes)

  29. Mutation cont. • Floating-Point • Uniform • Non-uniform from fixed distribution • Gaussian, Cauche, Levy, etc. • Permutation • Swap • Insert • Scramble • Inversion

  30. Recombination • Recombination rate: asexual vs. sexual • N-Point Crossover (positional bias) • Uniform Crossover (distributional bias) • Discrete recombination (no new alleles) • (Uniform) arithmetic recombination • Simple recombination • Single arithmetic recombination • Whole arithmetic recombination

  31. Survivor selection • (µ+λ) – plus strategy • (µ,λ) – comma strategy (aka generational) • Typically fitness-based • Deterministic vs. stochastic • Truncation • Elitism • Alternatives include completely stochastic and age-based

  32. Termination • CPU time / wall time • Number of fitness evaluations • Lack of fitness improvement • Lack of genetic diversity • Solution quality / solution found • Combination of the above

  33. Simple Genetic Algorithm (SGA) • Representation: Bit-strings • Recombination: 1-Point Crossover • Mutation: Bit Flip • Parent Selection: Fitness Proportional • Survival Selection: Generational

  34. Problem solving steps • Collect problem knowledge (at minimum solution representation and objective function) • Define gene representation and fitness function • Creation of initial population • Parent selection, mate pairing • Define variation operators • Survival selection • Define termination condition • Parameter tuning

  35. Typical EA Strategy Parameters • Population size • Initialization related parameters • Selection related parameters • Number of offspring • Recombination chance • Mutation chance • Mutation rate • Termination related parameters

  36. EA Pros • More general purpose than traditional optimization algorithms; i.e., less problem specific knowledge required • Ability to solve “difficult” problems • Solution availability • Robustness • Inherent parallelism

  37. EA Cons • Fitness function and genetic operators often not obvious • Premature convergence • Computationally intensive • Difficult parameter optimization

  38. Behavioral aspects • Exploration versus exploitation • Selective pressure • Population diversity • Fitness values • Phenotypes • Genotypes • Alleles • Premature convergence

  39. Genetic Programming (GP) • Characteristic property: variable-size hierarchical representation vs. fixed-size linear in traditional EAs • Application domain: model optimization vs. input values in traditional EAs • Unifying Paradigm: Program Induction

  40. Program induction examples • Optimal control • Planning • Symbolic regression • Automatic programming • Discovering game playing strategies • Forecasting • Inverse problem solving • Decision Tree induction • Evolution of emergent behavior • Evolution of cellular automata

  41. GP specification • S-expressions • Function set • Terminal set • Arity • Correct expressions • Closure property • Strongly typed GP

  42. GP notes • Mutation or recombination (not both) • Bloat (survival of the fattest) • Parsimony pressure

  43. Case Study employing GPDeriving Gas-Phase Exposure History through Computationally Evolved Inverse Diffusion Analysis

  44. Find Contaminants and Fix Issues Examine Indoor Exposure History Unexplained Sickness Introduction

  45. Background • Indoor air pollution top five environmental health risks • $160 billion could be saved every year by improving indoor air quality • Current exposure history is inadequate • A reliable method is needed to determine past contamination levels and times

  46. Problem Statement • A forward diffusion differential equation predicts concentration in materials after exposure • An inverse diffusion equation finds the timing and intensity of previous gas contamination • Knowledge of early exposures would greatly strengthen epidemiological conclusions

  47. Proposed Solution • Use Genetic Programming (GP) as a directed search for inverse equation • Fitness based on forward equation x^5 + x^4 - tan(y) / pi x^2 + sin(x) sin(cos(x+y)^2) sin(x+y) + e^(x^2) 5x^2 + 12x - 4 x^2 - sin(x) X + Sin / ?

  48. Related Research • It has been proven that the inverse equation exists • Symbolic regression with GP has successfully found both differential equations and inverse functions • Similar inverse problems in thermodynamics and geothermal research have been solved

More Related