Genetic Algorithm and Other Experimental Design Methods

8/6/2019 Genetic Algorithm and Other Experimental Design Methods

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06/27/2011


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Search Techniqes

Calculus Base

TechniqesGuided random search

techniques

Enumerative

Techniqes

BFSDFS Dynamic

Programming

Tabu Search Hill

Climbing

Simulated

Anealing

Evolutionary

Algorithms

Genetic

Programming

Genetic

Algorithms

Fibonacci Sort


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The Genetic Algorithm

y Originally developed by John Holland (1975)

y Aclass of probabilistic optimization and search

algorithms based on the mechanics of naturalselection and genetic inheritance.


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Quick Overviewy Inspired bynatural evolution

y Population of individuals

y Individual is feasible solution to problem

y

Each individual is characterized by a Fitness functiony Higher fitness is better solution

y Based on their fitness, parents are selected to reproduceoffspring for a new generation

y Fitter individuals have more chance to reproduce

y New generation has same size as old generation; old generationdies

y Offspring has combination of properties of two parents

y If well designed, population will converge to optimal solution


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Components of a GAAproblem to solve, and ...

y Encoding technique (gene, chromosome)

y Initialization procedure (creation)y Evaluation function (environment)

y Selection of parents (reproduction)

y Genetic operators (mutation, Crossover)

y Termination Criteria (End GA)


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Encoding in GAy Binary Encoding

In binary encoding every chromosome is a string ofbits, 0 or 1

y Value Encoding In value encoding, every chromosome is a string of some values.

Values can be anything connected to problem, real numbers or

chars to some complicated objects.

y Tree Encoding In tree encoding every chromosome is a tree of some objects, such

as functions or commands in programming language.


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Selection in GA

y Roulette wheel selection

y Rank Selection

y Tournament Selection

y Stochastic universal sampling

y SteadyState Selection

y Elitism


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Mutation Generating new offspring from single parent

y Maintaining the diversity of the individualsy

Crossover can only explore the combinations of the currentgene pool

y Mutation can generate new genes


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A Simple Example[1]y Simple problem: max x2 over {0,1,,31}

y GAapproach:

y Representation: binary code, e.g. 01101m 13y Population size: 4

y 1-point xover, bitwise mutation

y Roulette wheel selection

y Random initialization


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x2

example: selection


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X2 example: crossover


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X2 example: mutation


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Genetic Programming

Objective: Find a computer program with inputvariables (X1,X2,,Xn) whose output

equals the given data

1 Terminalset: T = {X1,X2,..,Xn, Random-

Constants}

2 Function set: F = {+, -, *, %...etc.}

3 Fitness: The sum of the absolute value of the

difference between the candidate

programs output and the given data

(computed over numerous values of the

variables)

4 Parameters: Population sizeM

5 Termination: An individualemerges whosesum of

absoluteerrors isless than 0.1


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Using Trees To Represent Computer

Programs(+ 2 3 (* X7) (/ Y5))

+

2 3 * /

X 7 5Y

Functions

Terminals


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Multi-Objective Optimization

y Uses concept of pareto-optimality.

y Investigate a set of solutions, each of which satisfies

the objectives at an acceptable level without beingdominated by any other solution.

y Diversity of solutions are maintained by fitnesssharing and niching.

y Elitism is used.


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NSGA II[2]

y Aset of N population is chosen. Set t=0, P0y Q0 is generated by first selecting solutions from P0 and then

doing Crossover and Mutationy Rt = Pt UQty Identification of non dominated fronts F1,.Fk in Rt.y

For i=1,kCalculate crowding distance of the solution in Fi.

Pt+1 is created as follows : -Case I If [Pt+1] + [Fi] N , then add least crowded

N-[Pt+1] solutions from Fi to Pt+1 Use binary tournament selection based on crowding distance to

select parents from Pt+1


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When to Use a GAy Alternate solutions are too slow or overly complicated

y Need an exploratory tool to examine new approaches

y Problem is similar to one that has already beensuccessfully solved by using a GA

y Want to hybridize with an existing solution

y Benefits of the GAtechnology meet key problem

requirements


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Some GA Application Types

Domain Application Types

Control gas pipeline, pole balancing, missile evasion, pursuit

Design semiconductor layout, aircraft design, keyboardconfiguration, communication networks

Schedulingmanufacturing, facility scheduling, resource allocation

Robotics trajectory planning

Machine Learning designing neural networks, improving classificationalgorithms, classifier systems

Signal Processing filter design

Game Playing poker, checkers, prisoners dilemma

CombinatorialOptimization

set covering, travelling salesman, routing, bin packing,graph colouring and partitioning


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Benefits of Genetic Algorithms

y Concept is easy to understand

y Modular, separate from application

y Supports multi-objective optimizationy Good for noisy environments

y Always an answer; answer gets better with time

y Inherently parallel; easily distributed


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TaguchiMethod Developed byDr. Genichi Taguchi.

Investigates how different parameters affect the meanand variance of a process performance characteristics.

Involves use oforthogonal arrays. Analysis of variance on the collected data from theTaguchi design of experiments can be used to selectnew parameter values to optimize the performance

characteristics.


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Taguchis Orthogonal Array Selector


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Analysis of Experimental Data


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Analysis of Experimental Data


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Limitationsy Interactions are part of the real world. In Taguchi's

arrays, interactions are confounded and difficult to

resolve.y Relative method, do not exactly indicate the true

effects of parameters on performance characteristicsvalue.

y

Offline method, so inappropriate for a dynamicallychanging process, such as simulation study.


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Response Surface Methodology

y Developed by Box andWilson in 1950.

y RSM usually involves three stages:

(1) Design of experiments

(2)Response surface modeling through regression

(3) Optimization


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Steps ofRSMThe steps by which the response surface method should beundertaken can be summarized as follows:

y Conduct the experiment with the independent variables varyingaround the present operating point.

y Obtain a fitted equation with data obtained in the experiment.

Normally, regression methods are used in this step. Frequently, alinear model represents the model sufficiently well.

y Move the experimental point in the direction of steepest ascent(or descent if a minimum is sought) and repeat the previoussteps.

y When little improvement is obtained, the optimum is near.y Conduct a 3-level factorial experiment around this point.

y Obtain a fitted quadratic equation by regression methods.

y Based on this quadratic equation, determine the optimum


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Referencesy [1] GeneticAlgorithms by David E. Goldberg, 1989.y [2] Multi-Objective optimization using genetic

algorithm byA. Konak, D. Coit,A. Smith,2006.

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Genetic Algorithm and Other Experimental Design Methods