Hybrid Soft Computing:Where Are We Going?

Hybrid Soft Computing:Where Are We Going?

Piero P. BonissonePiero P. Bonissone

GE Corporate Research & DevelopmentGE Corporate Research & DevelopmentBonissone@crd.ge.comBonissone@crd.ge.com

August 24, 2000 2ECAI 2000

• Soft Computing Overview­ SC­Components:­PR,­FL,­NN,­EA

• Modeling with FL and EA

• Hybrid SC Systems- FLC­Parameter­Tuning­by­EA-EA­Parameter­Setting

• Conclusions

Hybrid SC and EA - OutlineHybrid SC and EA - Outline

August 24, 2000 3ECAI 2000

• Soft Computing Overview­ SC­Components:­PR,­FL,­NN,­EA

• Modeling with FL and EA

• Hybrid SC Systems-FLC­Parameter­Tuning­by­EA-EA­Parameter­Setting

• Conclusions

Hybrid SC and EA - OutlineHybrid SC and EA - Outline

August 24, 2000 4ECAI 2000

Soft ComputingSoft Computing• Soft Computing (SC): the symbiotic use of

many emerging problem-solving disciplines.

• According to Prof. Zadeh:"...in contrast to traditional hard computing, soft computing exploits the tolerance for imprecision, uncertainty, and partial truth to achieve tractability, robustness, low solution-cost, and better rapport with reality”

• Soft Computing Main Components:-Approximate Reasoning:

» Probabilistic­Reasoning,­Fuzzy­Logic­-Search & Optimization:

» Neural­Networks,­Evolutionary­Algorithms

August 24, 2000 5ECAI 2000

Problem Solving TechniquesProblem Solving Techniques

Symbolic­Logic

Reasoning­

Traditional­Numerical­

­Modeling­and­Search

Approximate­Reasoning­

Functional­­Approximation

and­Randomized­Search

HARD COMPUTING SOFT COMPUTING

Precise Models Approximate Models

August 24, 2000 6ECAI 2000

Soft Computing: Hybrid Probabilistic SystemsSoft Computing: Hybrid Probabilistic Systems

Functional Approximation/ Randomized Search

NeuralNetworks

BayesianBelief­Nets­

EvolutionaryAlgorithms

Multivalued &Fuzzy Logics

Dempster-Shafer­

Probabilistic Models

Approximate Reasoning

August 24, 2000 7ECAI 2000

Soft Computing: Hybrid Probabilistic SystemsSoft Computing: Hybrid Probabilistic Systems

Functional Approximation/ Randomized Search

NeuralNetworks

BayesianBelief­Nets­

Fuzzy Influence Diagrams

Belief of Fuzzy Events

EvolutionaryAlgorithms

Multivalued &Fuzzy Logics

Probability of Fuzzy Events

HYBRID PROBABILISTIC SYSTEMS

Dempster-Shafer­

Probabilistic Models

Approximate Reasoning

August 24, 2000 8ECAI 2000

Soft Computing: Hybrid Probabilistic SystemsSoft Computing: Hybrid Probabilistic Systems

Functional Approximation/ Randomized Search

NeuralNetworks

BayesianBelief­Nets­

Fuzzy Influence Diagrams

Belief of Fuzzy Events

EvolutionaryAlgorithms

Multivalued &Fuzzy Logics

Probability of Fuzzy Events

HYBRID PROBABILISTIC SYSTEMS

Dempster-Shafer­

Probabilistic Models

Approximate Reasoning

August 24, 2000 9ECAI 2000

Soft Computing: Hybrid Probabilistic SystemsSoft Computing: Hybrid Probabilistic Systems

Functional Approximation/ Randomized Search

NeuralNetworks

BayesianBelief­Nets­

Fuzzy Influence Diagrams

Belief of Fuzzy Events

EvolutionaryAlgorithms

Multivalued &Fuzzy Logics

Probability of Fuzzy Events

HYBRID PROBABILISTIC SYSTEMS

Dempster-Shafer­

Probabilistic Models

Approximate Reasoning

August 24, 2000 10ECAI 2000

Soft Computing: Hybrid FL SystemsSoft Computing: Hybrid FL Systems

Functional Approximation/ Randomized Search

Probabilistic Models

NeuralNetworks

FuzzySystems­

EvolutionaryAlgorithms

Multivalued &

Fuzzy LogicsMultivaluedAlgebras­

Fuzzy­Logic­Controllers­

Approximate Reasoning

August 24, 2000 11ECAI 2000

Soft Computing: Hybrid FL SystemsSoft Computing: Hybrid FL Systems

Functional Approximation/ Randomized Search

Probabilistic Models

NeuralNetworks

FuzzySystems­

FLC Generatedand Tuned by EA

FLC Tuned by NN(Neural Fuzzy

Systems)

EvolutionaryAlgorithms

Multivalued &

Fuzzy Logics

NN modified by FS(Fuzzy Neural

Systems)

MultivaluedAlgebras­

Fuzzy­Logic­Controllers­

HYBRID FL SYSTEMS

Approximate Reasoning

August 24, 2000 12ECAI 2000

Soft Computing: Hybrid FL SystemsSoft Computing: Hybrid FL Systems

Functional Approximation/ Randomized Search

Probabilistic Models

NeuralNetworks

FuzzySystems­

FLC Generatedand Tuned by EA

FLC Tuned by NN(Neural Fuzzy

Systems)

EvolutionaryAlgorithms

Multivalued &

Fuzzy Logics

NN modified by FS(Fuzzy Neural

Systems)

MultivaluedAlgebras­

Fuzzy­Logic­Controllers­

HYBRID FL SYSTEMS

Approximate Reasoning

August 24, 2000 13ECAI 2000

Soft Computing: Hybrid FL SystemsSoft Computing: Hybrid FL Systems

Functional Approximation/ Randomized Search

Probabilistic Models

NeuralNetworks

FuzzySystems­

FLC Generatedand Tuned by EA

FLC Tuned by NN(Neural Fuzzy

Systems)

EvolutionaryAlgorithms

Multivalued &

Fuzzy Logics

NN modified by FS(Fuzzy Neural

Systems)

MultivaluedAlgebras­

Fuzzy­Logic­Controllers­

HYBRID FL SYSTEMS

Approximate Reasoning

August 24, 2000 14ECAI 2000

Soft Computing: Hybrid NN SystemsSoft Computing: Hybrid NN Systems

Probabilistic Models

Multivalued &Fuzzy Logics

FeedforwardNN­

RBF

RecurrentNN

NeuralNetworks

Hopfield SOM ART

Functional Approximation/ Randomized Search

Approximate Reasoning

EvolutionaryAlgorithms

Single/MultipleLayer­Perceptron

August 24, 2000 15ECAI 2000

Soft Computing: Hybrid NN SystemsSoft Computing: Hybrid NN Systems

Probabilistic Models

Multivalued &Fuzzy Logics

FeedforwardNN­

RBF

RecurrentNN

HYBRID NN SYSTEMS

NN topology &/or

weights generated by EAscontrolled by FLC

NN parameters(learning rate momentum )

NeuralNetworks

Hopfield SOM ART

Functional Approximation/ Randomized Search

Approximate Reasoning

EvolutionaryAlgorithms

Single/MultipleLayer­Perceptron

August 24, 2000 16ECAI 2000

Soft Computing: Hybrid NN SystemsSoft Computing: Hybrid NN Systems

Probabilistic Models

Multivalued &Fuzzy Logics

FeedforwardNN­

Single/MultipleLayer­PerceptronRBF

RecurrentNN

HYBRID NN SYSTEMS

NN topology &/or

weights generated by EAscontrolled by FLC

NN parameters(learning rate momentum )

NeuralNetworks

Hopfield SOM ART

Functional Approximation/ Randomized Search

Approximate Reasoning

EvolutionaryAlgorithms

August 24, 2000 17ECAI 2000

Soft Computing: Hybrid EA SystemsSoft Computing: Hybrid EA Systems

Probabilistic Models

Multivalued &Fuzzy Logics

NeuralNetworks

Evolution­Strategies

Evolutionary­Programs

GeneticProgr.

Genetic­Algorithms

EvolutionaryAlgorithms

Approximate Reasoning

Functional Approximation/ Randomized Search

August 24, 2000 18ECAI 2000

Soft Computing: Hybrid EA SystemsSoft Computing: Hybrid EA Systems

Probabilistic Models

Multivalued &Fuzzy Logics

NeuralNetworks

Evolution­Strategies

Evolutionary­Programs

GeneticProgr.

EA parameters (Pop size, select.)

controlled by EA

Genetic­Algorithms

EA parameters

(N, Pcr , Pmu )

controlled by FLC

EA-based search inter-twined with

hill-climbing

HYBRID EA SYSTEMS

EvolutionaryAlgorithms

Approximate Reasoning

Functional Approximation/ Randomized Search

August 24, 2000 19ECAI 2000

Soft Computing: Hybrid EA SystemsSoft Computing: Hybrid EA Systems

Probabilistic Models

Multivalued &Fuzzy Logics

NeuralNetworks

Evolution­Strategies

Evolutionary­Programs

GeneticProgr.

EA parameters (Pop size, select.)

controlled by EA

Genetic­Algorithms

EA parameters

(N, Pcr , Pmu )

controlled by FLC

EA-based search inter-twined with

hill-climbing

HYBRID EA SYSTEMS

EvolutionaryAlgorithms

Approximate Reasoning

Functional Approximation/ Randomized Search

August 24, 2000 20ECAI 2000

Soft Computing: Hybrid EA SystemsSoft Computing: Hybrid EA Systems

Probabilistic Models

Multivalued &Fuzzy Logics

NeuralNetworks

Evolution­Strategies

Evolutionary­Programs

GeneticProgr.

EA parameters (Pop size, select.)

controlled by EA

Genetic­Algorithms

EA parameters

(N, Pcr , Pmu )

controlled by FLC

EA-based search inter-twined with

hill-climbing

HYBRID EA SYSTEMS

EvolutionaryAlgorithms

Approximate Reasoning

Functional Approximation/ Randomized Search

August 24, 2000 21ECAI 2000

• Soft Computing Overview­ SC­Components:­PR,­FL,­NN,­EA

• Modeling with FL and EA

• Hybrid SC Systems-FLC­Parameter­Tuning­by­EA-EA­Parameter­Setting

• Conclusions

Hybrid SC and EA – Outline (2)Hybrid SC and EA – Outline (2)

August 24, 2000 22ECAI 2000

Fuzzy Logic GenealogyFuzzy Logic Genealogy

• Origins: MVL for treatment of imprecision and vagueness

- 1930s: Post, Kleene, and Lukasiewicz attempted to represent undetermined, unknown, and other possible intermediate truth-values.

- 1937: Max Black suggested the use of a consistency profile to represent vague (ambiguous) concepts

- 1965: Zadeh proposed a complete theory of fuzzy sets (and its isomorphic fuzzy logic), to represent and manipulate ill-defined concepts

August 24, 2000 23ECAI 2000

Fuzzy Logic : Linguistic VariablesFuzzy Logic : Linguistic Variables

• Fuzzy logic give us a language (with syntax and local semantics), in which we can translate our qualitative domain knowledge.

• Linguistic variables to model dynamic systems

• These variables take linguistic values that are characterized by:

- a label - a sentence generated from the syntax

- a meaning - a membership function determined by a local semantic procedure

August 24, 2000 24ECAI 2000

Fuzzy Logic : Reasoning MethodsFuzzy Logic : Reasoning Methods

• The meaning of a linguistic variable may be interpreted as a elastic constraint on its value. • These constraints are propagated by fuzzy inference operations, based on the generalized modus-ponens.

• A FL Controller (FLC) applies this reasoning system to a Knowledge Base (KB) containing the problem domain heuristics.• The inference is the result of interpolating among the outputs of all relevant rules. • The outcome is a membership distribution on the output space, which is defuzzified to produce a crisp output.

August 24, 2000 25ECAI 2000

S

S

L

L

S

L

S

L

LN

SN

SP

LP

Inputs

Fuzzy Logic Control : Inference MethodFuzzy Logic Control : Inference MethodState Variables Output Variable

Rules

Defuzzification

Inter-polation

August 24, 2000 26ECAI 2000

FLC Inference Method (cont.)FLC Inference Method (cont.)

• A FLC (KB + Reasoning Mechanism) defines a deterministic response surface in the cross product of state and output spaces, which approximates the original relationship.

• The FLC leverages the interpolation properties of this reasoning mechanism, to exhibit robustness with respect to parameter variations, disturbances, etc.

August 24, 2000 27ECAI 2000

Example (MISO): Max-min Composition with Centroid Defuzzification

Example (MISO): Max-min Composition with Centroid Defuzzification

•If X is SMALL and Y is SMALL then Z is NEG. LARGE

•If X is SMALL and Y is LARGE the Z is NEG. SMALL

•If X is LARGE and Y is SMALL the Z is POS. SMALL

•If X is LARGE and Y is LARGE then Z is POS. LARGE

ResponseSurfaceTerm

set

Rulesset

August 24, 2000 28ECAI 2000

Evolutionary Algorithms (EA)Evolutionary Algorithms (EA)EA are part of the Derivative-Free Optimization and Search Methods: -­Evolutionary­Algorithms

-­Simulated­annealing­(SA)-­Random­search-­Downhill­simplex­search-­Tabu­search

­EA consists of: -­Evolution­Strategies­(ES)-­Evolutionary­Programming­(EP)-­Genetic­Algorithms­(GA)

-­Genetic­Programming­(GP)

August 24, 2000 29ECAI 2000

Evolutionary Algorithms Characteristics

Evolutionary Algorithms Characteristics

• Most Evolutionary Algorithms can be described by

- x[t] : the population at time t under representation x

- v : is the variation operator(s)

- s : is the selection operator

x[t + 1] = s(v(x[t]))x[t + 1] = s(v(x[t]))

August 24, 2000 30ECAI 2000

Evolutionary Algorithms Characteristics

Evolutionary Algorithms Characteristics

• EA­exhibit­an­adaptive­behavior­that­allows­them­to­handle­non-linear,­high­dimensional­problems­without­requiring­differentiability­or­explicit­knowledge­of­the­problem­structure.

• EA­are­very­robust­to­time-varying­behavior,­even­though­they­may­exhibit­low­speed­of­convergence.

August 24, 2000 31ECAI 2000

ModelingModeling

• Model =

Structure + Parameters + Search Method

• Classical control theory:- Structure: order of the differential equations

- Parameters: coefficients of differential equation.

- Search method: LMSE, Pole-placement, etc.

August 24, 2000 32ECAI 2000

Modeling Using FLC (Mamdani type)

Modeling Using FLC (Mamdani type)

• A Mamdani- type FLC approximates a relationship between a state X and an output Y by using a KB and a reasoning mechanism (generalized modus-ponens).

• The Knowledge Base (KB) is defined by:- Scaling factors (SF): ranges of values of state

and output variables- Termset (TS): membership functions of values- Ruleset (RS): a syntactic mapping of symbols

from X to Y

August 24, 2000 33ECAI 2000

Modeling Using FLC (Mamdani type)

Modeling Using FLC (Mamdani type)

• The structure of the model is the ruleset.

• The parameters of the model are the scaling factors and termsets.

• The search method is initialized by knowledge engineering and refined with some other external methods (SOFC, error minimization, etc.)

August 24, 2000 34ECAI 2000

Modeling Using EA Modeling Using EA

• Similarly, for EA:- The structure of the model is the

representation of an individual in the population (e.g., binary string, vector, parse tree, Finite State Machine).

- The parameters of the model are the Population Size, Probability of Mutation, Prob. of Recombination, Generation Gap, etc.

- The search method is a global search based on maximization of population fitness function

August 24, 2000 35ECAI 2000

• Soft Computing Overview­ SC­Components:­PR,­FL,­NN,­EA

• Modeling with FL and EA

• Hybrid SC Systems-FLC­Parameter­Tuning­by­EA-EA­Parameter­Setting

• Conclusions

Hybrid SC and EA – Outline (3a)Hybrid SC and EA – Outline (3a)

August 24, 2000 36ECAI 2000

Hybrid Soft Computing: FLC Tuned by EAsHybrid Soft Computing: FLC Tuned by EAs

Probabilistic Models

NeuralNetworks

FLC Generatedand Tuned by EA

MultivaluedAlgebras­

HYBRID FLC/EA SYSTEMS

Evolution­Strategies

Evolutionary­Programs

GeneticProgr.

Fuzzy­Logic­Controllers­

FuzzySystems­

Approximate Reasoning

Multivalued &Fuzzy Logics

Genetic­Algorithms

EvolutionaryAlgorithms

Functional Approximation/ Randomized Search

August 24, 2000 37ECAI 2000

FLC Tuned by EA - OutlineFLC Tuned by EA - OutlineFLC Tuned by EA - OutlineFLC Tuned by EA - Outline

• Components & Historical Approaches

• Application to Automatic Train Handling (ATH)

• Solution Architecture

• Analysis of Results

• Remarks

August 24, 2000 38ECAI 2000

FL Controllers Tuned by EAs

• FLC- FLC = KB + Inference Engine (with Defuzz.)

- KB parameters: »Scaling­factors­(SF)»Membership­Functions­(MF)»Rule­set­(RS)

• EA- Encoding:­binary­or­real-valued

- Chromosome:­string­or­table

- Fitness­function:­Sum­quadratic­errors,­entropy

- Operators:­one-point­crossover,­max-min­arithmetical­crossover,­point-radius­crossover.

August 24, 2000 39ECAI 2000

FL Controllers tuned by EAs (cont.)• Historical Approaches:

- Karr 91-93: » Chromosome­=­concatenation­of­all­termsets.

» ­Each­value­in­a­termset­was­represented­by­3­binary-encoded­parameters.

- Lee & Takagi 93: » Chromosome­=­1­TSK­rule­(LHS:­memb.­fnct.­RHS­pol.)

» Binary­encoding­of­3-parameter­repr.­of­each­term

- Surman et al: 93:» Fitness­function­with­added­entropy­term­describing­number­of­activated­rules

August 24, 2000 40ECAI 2000

SC in Train Handling: An ExampleSC in Train Handling: An Example

• Problem Description- Develop an automated train handler to control a massive,

distributed system with little sensor information

- Freight trains consist of several hundred heavy railcars connected by couplers (train length up to two miles)

- Each coupler typically has a dead zone and a hydraulically damped spring

- Railcars can move relative to each other while in motion, leading to a train that can change its length by 50 – 100 ft.

- The position of the cars and couplers cannot be electronically sensed

August 24, 2000 41ECAI 2000

SC in Train Handling: An ExampleSC in Train Handling: An Example• Solution Requirements

• An­automated­system­has­to­satisfy­multiple­goals:­

-­Tracking­a­velocity­reference­(defined­over­distance)­to­enforce­speed­limits­and­respect­the­train­schedule

Multi-body regulation problem, subject to proper slack management, without sensors for most of the state

-­Providing­a­degree­of­train-handling­uniformity­across­all­crews­

-­Operating­the­train­in­fuel-efficient­regimes

-­Maintaining­a­smooth­ride­by­avoiding­sudden­accelerations­or­brake­applications­(slack­control)

August 24, 2000 42ECAI 2000

SC in Train Handling: An ExampleSC in Train Handling: An ExampleSC in Train Handling: An ExampleSC in Train Handling: An Example

• Description of Our Approach - Use a Velocity Profile externally generated

(using classical optimization or Evolutionary Algorithms)

- Use a Fuzzy Logic Control (FLC) to track the velocity reference (Fuzzy PI Control)

- Use an Evolutionary Algorithms to tune the FLC parameters to minimize velocity tracking error and number of throttle changes

- Implement control actions with fuzzy rule set to maintain slack control

August 24, 2000 43ECAI 2000

FLC tuned by EAs: Our ApproachFLC tuned by EAs: Our Approach• Chromosome (real-valued encoding)

- Chr.­1­=­Scaling­factors;­

- Chr.­2­=­Termsets;­

- Chr.­3­=­Rules­(not­used)

• Order of tuning (as in Zheng '92): - Initialize­rulebase­with­standard­PI­structure­and­termsets­with­uniformly­distributed­terms

- Apply­EAs­to­find­best­scaling­factors

- Apply­EAs­to­find­best­termsets

- Apply­EAs­to­find­best­rule­set­(not­used)

• Transition from large to small granularity

August 24, 2000 44ECAI 2000

FLC Sensitivity to Parameter ChangesFLC Sensitivity to Parameter ChangesX1 X2

Very Low Low Medium High Very HighVery Low PH PH PM PL ZE

Low PH PM PL ZE NLMedium PM PL ZE NL NM

High PL ZE NL NM NHVery High ZE NL NM NH NH

X1 X2Very Low Low Medium High Very High

Very Low PH PH PM PL ZELow PH PM PL ZE NL

Medium PM PL ZE NL NMHigh PL ZE NL NM NH

Very High ZE NL NM NH NH

Changinga Scaling

Factor

X1 X2Very Low Low Medium High Very High

Very Low PH PH PM PL ZELow PH PM PL ZE NL

Medium PM PL ZE NL NMHigh PL ZE NL NM NH

Very High ZE NL NM NH NH

X1 X2Very Low Low Medium High Very High

Very Low PH PH PM PL ZELow PH PM PL ZE NL

Medium PM PL ZE NL NMHigh PL ZE NL NM NH

Very High ZE NL NM NH NH

Changinga Term in

X1

X1 X2Very Low Low Medium High Very High

Very Low PH PH PM PL ZELow PH PM PL ZE NL

Medium PM PL ZE NL NMHigh PL ZE NL NM NH

Very High ZE NL NM NH NH

X1 X2Very Low Low Medium High Very High

Very Low PH PH PM PL ZELow PH PM PL ZE NL

Medium PM PL ZE NL NMHigh PL ZE NL NM NH

Very High ZE NL NM NH NH

Changinga Rule

August 24, 2000 45ECAI 2000

Architecture: Modules, Fitness Funct.Architecture: Modules, Fitness Funct.• Architecture

- EA:­pop.size=50;­P(cross)=.6;­P(mut)=.001

- Three­Types­of­fitness­functions

- Train­Simulator:­NSTD­(STD+TEM)

- Fuzzy­PI­(Ke,­Kedot,­Ku)

• Fitness functions (f1, f2, f3)

f1 min( |notchi i notch(i 1) ||dynbrakei dynbrake(i 1) |)

f2 min( |vii vi

d |)

f3 min(w1

|notchi i notch(i 1) |

K1w2

( |vii vi

d |)

K2

August 24, 2000 46ECAI 2000

FLC tuned by GAs

Train­Simulator ­FLC­(PI)

FitnessFunction

GA­(GENESIS) ­SF­or­MF

August 24, 2000 47ECAI 2000

Experiment DesignExperiment Design

• 12 test (4 for each fitness function)- Initial SF with initial MF;

- EA tuned SF with Initial MF

- Initial SF with EA tuned MF;

- EA tuned SF with EA tuned MF

• Train Simulation:- 14 miles long flat track

- 1 uniformly heavy train with 100 cars and 4 locomotives

- Analytically computed velocity profile

August 24, 2000 48ECAI 2000

Experiment DesignExperiment DesignExperiment DesignExperiment Design

• Representation: - SF: 3 floating point values for Ke, Kedot, Ku

- MF (21-9) = 12 values» 21­parameters:­[(Lefti­,Centeri­,­Righti­)­for­i=1,­...,­7]

» 9­dependent­values:­[(Lefti­=­Right(i+1))­for­i=1,­...,­6]

­ +­[Center1=­Center7]+[Right1­=­Left7­=­0]

- Constraints to maintain 0.5 terms overlap, for best interpolation

August 24, 2000 49ECAI 2000

Experiments ResultsExperiments Results• Experiment Results with f1

Description Time Journey Fuel Fitness Gen.Initial SF; Initial MF 26.5 14.26 878 73.2

EA tuned SF; Initial MF 27.8 14.21 857 15.15 4Initial SF; EA tuned MF 26.00 14.18 879 70.93 20

EA tuned SF; EA tuned MF 28.3 14.12 829 14.64 10

• Experiment Results with f3

Description Time Journey Fuel Fitness Gen.Initial SF; Initial MF 26.5 14.26 878 1

EA tuned SF; Initial MF 27.2 14.35 871 0.817 4Initial SF; EA tuned MF 26.26 14.18 871 0.942 20

EA tuned SF; EA tuned MF 27.3 14.35 872 0.817 10

August 24, 2000 50ECAI 2000

Tuning of FLC with EA: RemarksTuning of FLC with EA: Remarks• Verified­tuning­order­proposed­by­Zheng­(92)

»SF­tuning:­major­impact»MF­tuning:­minor­impact»RS­tuning:­almost­no­impact

• For­both­f1­and­f3,­fuel­minimization­is­implicitly­derived­from­throttle­jockeying­minimization

• Complex­fitness­function­(requiring­simulation­run­-­23­sec­for­each­chromosome­evaluation)­limited­trials­number­-­with­no­apparent­impact

• Successfully­tested­on­simulated­43­mile­long­track­with­altitude­excursions

» (Selkirk,­NY->Framingham,­MA)

August 24, 2000 51ECAI 2000

MPH

60.00

50.00

40.00

30.00

20.00

10.00

0.00­

NOTCHPOSITION

8

­

­

4

­

­

0

­NOTCH

POSITION

milemile

milemile

Results of EA Tuned PI on 43 mile TrackResults of EA Tuned PI on 43 mile Track

August 24, 2000 52ECAI 2000

MPH

60.00

50.00

40.00

30.00

20.00

10.00

0.00­

NOTCHPOSITION

8

­

­

4

­

­

0

­NOTCH

POSITION

milemile

milemile

Results of EA Tuned PI on 43 mile TrackResults of EA Tuned PI on 43 mile Track

August 24, 2000 53ECAI 2000

MPH

60.00

50.00

40.00

30.00

20.00

10.00

0.00­

NOTCHPOSITION

8

­

­

4

­

­

0

­NOTCH

POSITION

milemile

milemile

Results of EA Tuned PI on 43 mile TrackResults of EA Tuned PI on 43 mile Track

August 24, 2000 54ECAI 2000

MPH

60.00

50.00

40.00

30.00

20.00

10.00

0.00­

NOTCHPOSITION

8

­

­

4

­

­

0

­NOTCH

POSITION

milemile

milemile

Results of EA Tuned PI on 43 mile TrackResults of EA Tuned PI on 43 mile Track

August 24, 2000 55ECAI 2000

• Soft Computing Overview­ SC­Components:­PR,­FL,­NN,­EA

• Modeling with FL and EA

• Hybrid SC Systems-FLC­Parameter­Tuning­by­EA-EA­Parameter­Setting

• Conclusions

Hybrid SC and EA – Outline (3b)Hybrid SC and EA – Outline (3b)

August 24, 2000 56ECAI 2000

• EA Model:­- Structure,­Parameters­

• EA Parameter Setting­- EA­Parameter­Tuning- EA­Parameter­Control

• An Application to Agile Manufacturing- Object-level­Representation­and­Complexity

• Solution- FLC­KB­- Statistical­Experiments- Analysis­and­Summary­of­1200­Experiments

• Remarks

EA Parameter SettingEA Parameter Setting

August 24, 2000 57ECAI 2000

Object-level­Problem

Object-level GA

Structure&

Parameters

EA ModelEA Model

August 24, 2000 58ECAI 2000

•GA Structural Design Selections:- GA­Type:

»{Simple,­Steady-State,­Niche,…}- Chromosome­Encoding:­

»{Binary,­Integer,­Real,...} - Constraints­Representation:­

»{Penalty­function,­data­structure,­filters,­…}- Fitness­Function:

»{Scalar­function,­Weighted­aggregation­of­multiple­functions,­Vector-valued­function,­…}

EA StructureEA Structure

August 24, 2000 59ECAI 2000

•Adjustable parameters for a GA- N =­Population­size­

Large­pop.­prevent­premature­convergence- Pc­=­Crossover­rate:­

Pcr­*­N­=­#­crossovers­per­generation- Pm =­Mutation­rate:­

Pm­*­N­*­L­=­#­mutations­per­generation- G­ =­Generation­Gap

Percentage­of­population­to­be­replaced- W =­Scaling­Window­Size­=[1,­7]- S­ =­Selection­Strategy­=­{Elitist,­Non-Elitist}

• Other­possible­parameters­that­could­be­adjusted:

- T­ =­Number­of­Trials­=­­Ni­-­where­i=­1,­Max_Gen

- Sm­=­Mutation­step­-­(­in­Normally­distrib.­Mutation­value)

- PS­=­Probability­of­Selection­-­(Parametrized­slope­of­prob­distrib.)

- AS­=­Arity­of­Parents­-­number­of­parents­in­recombination

EA ParametersEA Parameters

August 24, 2000 60ECAI 2000

• EA Model:­- Structure,­Parameters­

• EA Parameter Setting­- EA­Parameter­Tuning- EA­Parameter­Control

• An Application to Agile Manufacturing- Object-level­Representation­and­Complexity

• Solution- FLC­KB- Statistical­Experiments- Analysis­and­Summary­of­1200­Experiments

• Remarks

EA Parameter Setting - OutlineEA Parameter Setting - Outline

August 24, 2000 61ECAI 2000

EAs Parameter SettingEAs Parameter Setting

ParameterTuning

Before the run­­­­­­­­

ParameterControl

ParameterSetting

Duringthe run

August 24, 2000 62ECAI 2000

EAs Parameter SettingEAs Parameter Setting

ParameterTuning

AdaptiveDeterministic

Before the run­­­­­­­­

ParameterControl

Self-Adaptive

ParameterSetting

Duringthe run

August 24, 2000 63ECAI 2000

ParameterTuning

EAs Parameter Setting: Parameter Tuning

EAs Parameter Setting: Parameter Tuning

AdaptiveDeterministic

ParameterControl

Self-Adaptive

ParameterSetting

Duringthe­run

- Off-line Tuning

- Determined before running the GAs on the object-level problem by

»Studying­a­subset­of­five­diverse­problems­ (DeJong, 1975)­

»Running­a­Meta-Genetic­Algorithm­(Grefenstette, 1986)­

Beforethe run

August 24, 2000 64ECAI 2000

Object-level Problem

Object-level GA

Population Size: 50Crossover Rate: 0.6Mutation Rate: 0.001Replacement 100%Scaling Window n=infSelection Strategy Elitist

Suite of 5 problems:- Parabola- Rosenbrock’s saddle

- Step function- Quartic Noise- Shekel’s foxholes

Object-level GA

Off Line Tuning of GA Parameters (DeJong, 1975)

Off Line Tuning of GA Parameters (DeJong, 1975)

August 24, 2000 65ECAI 2000

SC Hybrid Systems: EA Tuning EASC Hybrid Systems: EA Tuning EASC Hybrid Systems: EA Tuning EASC Hybrid Systems: EA Tuning EA

Probabilistic Models

Approximate Reasoning Approaches

Multivalued &Fuzzy Logics

NeuralNetworks

EvolutionStrategies

EvolutionaryPrograms

GeneticProgr.

EA parameters (Pop size, select.) controlled by EA

HYBRID EA SYSTEMS

GeneticAlgorithms

EvolutionaryAlgorithms

Search/Optimization Approaches

August 24, 2000 66ECAI 2000

Off-Line PerformancePopulation Size: 80Crossover Rate: 0.45Mutation Rate: 0.01Replacement 90%Scaling Window n = 1Selection Strategy NonElitist

Object-level Problem

Object-level GA

On-Line Performance

Population Size: 30Crossover Rate: 0.96Mutation Rate: 0.01Replacement 100%Scaling Window n = infSelection Strategy Elitist

Object-level GA

Meta- GA

Off Line Tuning of GA Parameters (Grefenstette, 1986)

Off Line Tuning of GA Parameters (Grefenstette, 1986)

Suite of 5 problems:- Parabola- Rosenbrock’s saddle

- Step function- Quartic Noise- Shekel’s foxholes

Object GAParameter

Set

Object GAPerformance

August 24, 2000 67ECAI 2000

GAs Parameter Setting: Deterministic ControlGAs Parameter Setting: Deterministic Control

AdaptiveDeterministic

ParameterTuning

ParameterControl

Self-Adaptive

Duringthe run

- No feedback information is used.

- A time-varying schedule is used to modify a GA parameter p

- p is replaced by p(t)- Correct design of p(t)

is very difficult

Before­­­­­­­­­the­run­­­­­­­­

ParameterSetting

August 24, 2000 68ECAI 2000

Control of Population sizeBy­decreasing­Population­Size­toward­the­last­part­of­the­Evolution­we­are­trying­to­improve­the­solution­refinement­(e.g.,­more­generations­with­same­number­of­trials)

EAs Parameter Setting: Deterministic Control - Example

EAs Parameter Setting: Deterministic Control - Example

300

500

30% 45% 80% CurrGen/Maxgen

150

PopSize

300

500

30% 45% 80% CurrGen/Maxgen

150

PopSize

338

500

30% 45% CurrGen/Maxgen

150

PopSize

80%

338

500

30% 45% CurrGen/Maxgen

150

PopSize

80%

•Constant­Population­size:­N­=­338

•Number­of­trials­=­­338­*­MaxGen

• Variable­Population­size:­N(t)

• Number­of­trials­=­­338­*­MaxGen

August 24, 2000 69ECAI 2000

- Incorporate parameters into chromosome making them subject to evolution

- Typically used to determine Mutation Step S:

[g1 g2 ... gn S] ­­­

­­­­or

[g1 g2 ... gn S1 S2 ... Sn ]

EAs Parameter Setting: Self-Adaptive Control

EAs Parameter Setting: Self-Adaptive Control

AdaptiveDeterministic

Before­­­­­­­­­the­run­­­­­­­­

ParameterTuning

ParameterControl

Self-Adaptive

ParameterSetting

Mutation­Step­for­Entire­Genome

Mutation­Steps­for­Each­Genome­Value

Duringthe run

August 24, 2000 70ECAI 2000

GAs Parameter Setting: Adaptive Control

GAs Parameter Setting: Adaptive Control

AdaptiveDeterministic

Before­­­­­­­­­the­run­­­­­­­­

ParameterTuning

ParameterControl

Self-Adaptive

- Feedback from the search is used to determine the direction and/or magnitude of the change in the parameter value.

- A Fuzzy Logic Controller

is used to obtain parameter changes in » Population­Size» Mutation­Rateas a function of » Genotypic­Diversity» Percentage­Completed­Trials

Duringthe run

ParameterSetting

August 24, 2000 71ECAI 2000

SC Hybrid Systems: FLC Tuning EASC Hybrid Systems: FLC Tuning EA

Probabilistic Models

NeuralNetworks

EvolutionStrategies

EvolutionaryPrograms

GeneticProgr.

EA parameterscontrolled

by FLC HYBRID SYSTEMS

MV-Algebras

FuzzyController

FuzzyLogic

Multivalued &Fuzzy Logics

Approximate Reasoning Approaches

GeneticAlgorithms

EvolutionaryAlgorithms

Search/Optimization Approaches

August 24, 2000 72ECAI 2000

Object-level­Problem

Fuzzy Logic Controlled GA (FLC-GA)

Object-level GA

Fuzzy LogicController

•­Genotypic Diversity• Percentage Completed Trials

KB

Population Size Mutation Rate

State Variables describingthe evolution stage­

Controlled GA parameters­

August 24, 2000 73ECAI 2000

• EA Model:­- Structure,­Parameters­

• EA Parameter Setting­- EA­Parameter­Tuning- EA­Parameter­Control

• An Application to Agile Manufacturing- Object-level­Representation­and­Complexity

• Solution- FLC­KB- Statistical­Experiments- Analysis­and­Summary­of­1200­Experiments

• Remarks

EA Parameter SettingEA Parameter Setting

August 24, 2000 74ECAI 2000

Global­optimization­of­design,­manufacturing,­supplierplanning­decisions­in­a­distributed­manufacturing­environment

Customer

Supplier

Manufacturing

Design

Tools

Tools

Data

Marketing

Tools Data

Virtual DesignEnvironment

EA Parameter Control: An Application

EA Parameter Control: An Application

DataTools

Data

Data Tools

August 24, 2000 75ECAI 2000

Design

Part­P1

Acceptable Alternates

Suppliers

P1 P2 Pk M

1

2

3

8

Genome

Gen

e A

llel

e S

ets

Crossover Operation Mutation

Parents

Offspring

1

2

3

6Part­P2

Part­Pk

Manufacturing Facilities

Parts, suppliers,and design DB

Mfg. DB

3)10( T

ijTTijij eCJmin

i,j

Object-level Optimization Problem

Object-level Problem RepresentationObject-level Problem Representation

August 24, 2000 76ECAI 2000

Search Space Size

• For EA Statistical Analysis:O(107)

• For EA Performance Validation:O(1018) and O(1021)

Object-level Problem ComplexityObject-level Problem Complexity

August 24, 2000 77ECAI 2000

• EA Model:­- Structure,­Parameters­

• EA Parameter Setting­- EA­Parameter­Tuning- EA­Parameter­Control

• An Application to Agile Manufacturing- Object-level­Representation­and­Complexity

• Solution- FLC­KB- Statistical­Experiments- Analysis­and­Summary­of­1200­Experiments

• Remarks

EA Parameter Setting - OutlineEA Parameter Setting - Outline

August 24, 2000 78ECAI 2000

Fuzzy­LogicController

Solution ArchitectureSolution Architecture

Object-level­GA

Manufacturing­Planning­Module

Untuned­GA

Fuzzy­LogicControlled­GA(Online­Control)

Object-level­GA

August 24, 2000 79ECAI 2000

Object-level­GA

Manufacturing­Planning­Module

Population Size: 50Generations: 250Crossover Rate: 0.6Mutation Rate: 0.001

Untuned GA (U-TGA)Untuned GA (U-TGA)

August 24, 2000 80ECAI 2000

Guidance for ExperimentsGuidance for Experiments

•Minimize high-level search space size for FLC-EA by

- Identify primary drivers (influences) of EA searchDOE determined that the two main drivers were:

Population Size (N) and Mutation Rate (Pm )

- Control primary drivers by few simple heuristic rulesBuilt two FLC controllers with heuristic rule sets and SFChanged on input (state variable) to capture evolution

stage

• Determining FLC firing rate- Take a control action every 10 generation

• Extensive & statistically significant empirical evidence- Use t-test and F-tests to analyze and improvements

August 24, 2000 81ECAI 2000

Object-level Problem

Object-level EA

Fuzzy LogicController

• Genotypic Diversity• Percentage

Completed Trials

KB

Population Size Mutation Rate

I/O­Scaling­Factors I/O­Termsets Rule­Sets

Fuzzy Logic Controller for EAs: Knowledge Base

Fuzzy Logic Controller for EAs: Knowledge Base

August 24, 2000 82ECAI 2000

• InputsGD­­­=­Genotypic­Diversity:

­­­­­­­Normalized­Average­Hamming­Distance

­

PFE­=­Percentage­Fitness­Evaluations:­­­ ­­­­­­­­­

­(Completed­#­Trials)­/­(Max­Allocated­#­Trials)

n

iji LengthGenome

ijd

nnGD

1,1)1(

2

where dij is the Hamming Distance GD range­is­[0,­1]­==­[Low,­High]

PFE range­is­[0,­1]­=­[Low,­High]

Fuzzy Controller for N and Pm: InputsFuzzy Controller for N and Pm: Inputs

August 24, 2000 83ECAI 2000

Object-level Problem

Object-level EA

Fuzzy LogicController

• Genotypic Diversity• Percentage

Completed Trials

KB

Population Size Mutation Rate

I/O­Scaling­Factors I/O Termsets Rule­Sets

Fuzzy Logic Controller for EAs: Knowledge Base

Fuzzy Logic Controller for EAs: Knowledge Base

August 24, 2000 84ECAI 2000

•Inputs:• GD: A(Very Low), B(Low), C(Medium), D(High), E(Very High)• PFE: A(Very Low), B(Low), C(Medium), D(High), E(Very High)

•Outputs (for both N and Pm):•A(Neg. High), B(Neg. Medium), C(No Change), D(Pos. Medium), E(Pos. High)

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1A B C D E

0 0.2 0.4 0.6 0.8 10

0.2

0.4

0.6

0.8

1A B C D E

Fuzzy Controller for N and Pm: Termsets

Fuzzy Controller for N and Pm: Termsets

August 24, 2000 85ECAI 2000

Object-level Problem

Object-level EA

Fuzzy LogicController

• Genotypic Diversity• Percentage

Completed Trials

KB

Population Size Mutation Rate

I/O­Scaling­Factors I/O­Termsets Rule Sets

Fuzzy Logic Controller for EAs: Knowledge Base

Fuzzy Logic Controller for EAs: Knowledge Base

August 24, 2000 86ECAI 2000

­GD = Genotypic Diversity: Normalized Average Hamming Distance

PFE = Percentage Fitness Evaluations: (Completed # Trials) / (Max Allocated # Trials)

N= Change in Population Size

GDPFEN

Genotypic Percentage Fitness Evaluation (PFE)Diversity (GD) Very Low Low Medium High Very High

Very Low Pos­High Pos­High Pos­High Pos­Medium No­Change

Low Pos­High Pos­High Pos­Medium No­Change Neg­Medium

Medium Pos­High Pos­Medium No­Change Neg­Medium Neg­High

High Pos­Medium No­Change Neg­Medium Neg­High Neg­High

Very High No­Change Neg­Medium Neg­High Neg­High Neg­High

Genotypic Percentage Fitness Evaluation (PFE)Diversity (GD) Very Low Low Medium High Very High

Very Low Pos­High Pos­High Pos­High Pos­Medium No­Change

Low Pos­High Pos­High Pos­Medium No­Change Neg­Medium

Medium Pos­High Pos­Medium No­Change Neg­Medium Neg­High

High Pos­Medium No­Change Neg­Medium Neg­High Neg­High

Very High No­Change Neg­Medium Neg­High Neg­High Neg­High

Exploitation StageReduce­population/­Refine­best­­

­­

Exploration StageIncrease­population/­broaden­search

Fuzzy Controller for Population Size:Rule Set

Fuzzy Controller for Population Size:Rule Set

August 24, 2000 87ECAI 2000

• Data Set for Experiments- Seven part classes corresponding to a

complexity of O(107)

• EA Structure: - Type: {Simple, Steady-State}- Chromosome Encoding: Integer- Fitness Function: Three type of cost

functions- Selection Method: Proportional Roulette- Crossover Operator: Uniform- Mutation Operator: Exponentially

Decreasing

Statistical Experiments: EA StructureStatistical Experiments: EA Structure

August 24, 2000 88ECAI 2000

• Set-Up for 1200 experiments:

- We­defined­4­EA­configurations(a) Untuned Simple EA (U-SEA)(b) FL Controlled Simple EA (FLC-SEA)(c) Untuned Steady State EA (U-SSEA)(d) FL Controlled Steady State EA (FLC-

SSEA)

Statistical Experiments: Set-UpStatistical Experiments: Set-Up

August 24, 2000 89ECAI 2000

• For each configuration we performed 300 experiments: - 20 runs for each pair of (Cost function, Max

number of Trials)- 15 different pairs of (Cost function, Max number

of Trials) - Three types of cost functions:

(1) J = C*T; (2) J = C*T2; (3) J = C*e(T-10)/3

- Five values of maximum number of Trials (to evaluate effect of different evolution lengths):

(i) 3,000; (ii) 5,000; (iii) 7,000; (iv) 9,000; (v) 11,000

Statistical Experiments: Set-Up (cont.)Statistical Experiments: Set-Up (cont.)

August 24, 2000 90ECAI 2000

• For each of the four configurations (a-d) we ran 20 experiments with the same parameters

• Then we considered the following measures:B­=­sample­average­over 20 experiments­of­Best­score­frequency­(number­of­time­cost­function­J­reached­its­minimal­value­-­known­a­priori­for­small­size­experiment)­

­=­average­of­population­best­=­standard­deviation­of­population­best

B

Statistical Experiments: MeasuresStatistical Experiments: Measures

August 24, 2000 91ECAI 2000

• We performed an ANOVA test (botht and F test - with p < 0.05 ) to see if:

Cost (U-SEA) >> cost ( FLCSEA)Cost (U-SEA) >> cost ( U-SSEA)Cost (U-SSEA) >> cost ( FLC-SSEA)

• We verified if the FLC caused the controlled EA to perform worse than its corresponding untuned EA, i.e.:

Cost (U-SEA) << cost ( FLC-SEA)

Cost (U-SSEA) << cost ( FLC-SSEA)

Statistical Experiments: AnalysisStatistical Experiments: Analysis

August 24, 2000 92ECAI 2000

Statistical Experiments: ResultsStatistical Experiments: Results

• For each cost function we ran 400 experiments (100 x EA type)

• For each EA type we ran 20 experiments for 5 different pop. sizes

• The entry in each cell is the number of significant changes found in the statistics of each of these five groups of experiments

C*T

C*T2

C*e(T-10)/3

J = Cost U-SEA FLC-SEA U-SSEA FLC-SSEAFunction B B B B

- - - - 4 3 - - - - 1 2- - - - 2 3 - - - - 1 3- 1 - - - 3 - 1 - - 1 2

Significant changes in

Total 7% 47% 60% 7% 20% 47%

Significant changes in

and in

August 24, 2000 93ECAI 2000

• EA Model:­- Structure,­Parameters­

• EA Parameter Setting­- EA­Parameter­Tuning- EA­Parameter­Control

• An Application to Agile Manufacturing- Object-level­Representation­and­Complexity

• Solution- FLC­KB- Statistical­Experiments- Analysis­and­Summary­of­1200­Experiments

• Remarks

EA Parameter SettingEA Parameter Setting

August 24, 2000 94ECAI 2000

RemarksRemarksRemarksRemarks

• FLC State Representation: [Evolution Stage] - Evolution time needs to be an explicit state

variable since we have different control goals during the EA’s stages.

- Diversity measures the evolutionary stage:

» Percentage­Fitness­Evaluations­(PFE)­

» Genotypic­Diversity­(GD)­

• FLC Control Variables: [EA Adaptable Parameters]

N= Change in Population Size Pm= Change in Mutation Rate

August 24, 2000 95ECAI 2000

Remarks (cont.)Remarks (cont.)

• Main Result

- By using the FLC with the above State and Control variables, we achieved a good improvement of the population average and an even better improvement of the population variance.

- No major negative effects on EA performance using FLC

August 24, 2000 96ECAI 2000

• Soft Computing Overview­ SC­Components:­PR,­FL,­NN,­EA

• Modeling with FL and EA

• Hybrid SC Systems-FLC­Parameter­Tuning­by­EA-EA­Parameter­Setting

• Conclusions

Hybrid SC and EA – Outline (4)Hybrid SC and EA – Outline (4)

August 24, 2000 97ECAI 2000

Synergy­in­SC:­Reasons­&­Approaches

• Hybrid Soft Computing­

- Leverages­tolerance for imprecision,­uncertainty,­and­incompleteness­-­intrinsic­to­the­problems­to­be­solved

- Generates­tractable, low-cost, robust­solutions­to­such­problems­by integrating knowledge and data­

• Tight Hybridization­

- Data-driven­Tuning­of­Knowledge-derived­Models» Translate­domain­knowledge­into­initial­structure­and­parameters

» Use­Global­or­local­data­search­to­tune­parameters

- Knowledge-driven­Search­Control» Use­Global­or­local­data­search­to­derive­models­(Structure­+­Parameters)

» Translate­domain­knowledge­into­an­algorithm’s­controller­to­improve/manage­solution­convergence­and­quality

August 24, 2000 98ECAI 2000

Synergy­in­SC:­Reasons­&­Approaches

• Loose Hybridization (Model Fusion)- Does­not­combine­features­of­methodologies­-­only­their­results

- Their­outputs­are­compared,­contrasted,­and­aggregated,­to­increase­reliability­

• Hybrid Search Methods- Intertwining­local­search­within­global­search- Embedding­knowledge­in­operators­for­global­search

• Future:- Circle­ of­ SC's­ related­ technologies­ will­ probably­ widen­beyond­its­current­constituents.­

- Push­ for­ low-cost­solutions­and­ intelligent­ tools­will­ result­in­ deployment­ of­ hybrid­ SC­ systems­ that­ efficiently integrate reasoning and search techniques.

August 24, 2000 99ECAI 2000

August 24, 2000 100ECAI 2000

FL Controllers tuned by EAs (cont.)• Historical Approaches (cont.):

- Kinzel et al. 94:» Chromosome­=­Rule­Table

» Point-radius­crossover­changing­3x3­rule­window­(similar­to­a­two-point­crossover­for­string­

representation)

» Order­of­tuning:­– Initialize­rulebase­according­to­heuristics– Apply­GAs­to­find­best­rule­table– Tune­membership­function­of­best­rule­set

- Herrera et al. 95:» Chromosome­=­concatenation­of­all­rules

» Real-valued­encoding,­Max-min­arithmetical­crossover

August 24, 2000 101ECAI 2000

Evolutionary Algorithms: ESEvolutionary Algorithms: ES•Evolutionary Strategies (ES)

- Originally proposed for the optimization of continuous functions

- (, )-ES and ( + )-ES» A­population­of­parents­generate­offspring» Best­offspring­are­selected­in­the­next­generation» (,­)-ES:­parents­are­excluded­from­selection» (­+­)-ES:­parents­are­included­in­selection

- Started as (1+1)-ES (Reschenberg) and evolved to ( + )-ES (Schwefel)

- Started with Mutation only (with individual mutation operator) and later added a recombination operator

- Focus on behavior of individuals

August 24, 2000 102ECAI 2000

Evolutionary Algorithms: EPEvolutionary Algorithms: EP

•Evolutionary Programming (EP) - Originally proposed for sequence predictiom

and optimal gaming strategies

- Currently focused on continuous parameter optimization and training of NNs

- Could be considered a special case of ( + )-ES without recombination operator

- Focus on behavior of species (hence no crossover)

- Proposed by Larry Fogel (1963)

August 24, 2000 103ECAI 2000

Evolutionary Algorithms: GAEvolutionary Algorithms: GA•Genetic Algorithms (GA)

- Perform a randomized search in solution space using a genotypic rather than a phenotypic

- Each solution is encoded as a chromosome in a population (a binary, integer, or real-valued string)» Each­string’s­element­represents­a­particular­feature­of­the­solution

- The string is evaluated by a fitness function to determine the solution’s quality» Better-fit­solutions­survive­and­produce­offspring» Less-fit­solutions­are­culled­from­the­population

- Strings­are­evolved­using­mutation­&­recombination­operators.- New­individuals­created­by­these­operators­form­next­generation­of­solutions­

- Started­by­Holland (1962; 1975)

August 24, 2000 104ECAI 2000

Evolutionary Algorithms: GPEvolutionary Algorithms: GP

•Genetic Programming (GP) - A special case of Genetic Algorithms

»Chromosomes­have­a­hierarchical­rather­than­a­linear­structure

»Their­sizes­are­not­predefined

»Individuals­are­tree-structured­programs

»Modified­operators­are­applied­to­sub-trees­or­single­nodes­

- Proposed­by­Koza (1992)

August 24, 2000 105ECAI 2000

•GA Structural Design Selections:- Parent­Selection­Method:

»{Proportional­Roulette,­Tournament,­Rank,­Uniform,­...­}

- Crossover­Operator:»{Once-cut,­Two-cuts,­Uniform,­BLX,­Parent­Weighted,­...}­

- Mutation­Operator:»Mutation­Rate:­{Exponentially­Decreasing,­Uniform,­..}­

»Value:­{Exponentially­Decreasing,­Uniform,­Normally­Distributed,­­…}­

GA Structure (cont.)GA Structure (cont.)

August 24, 2000 106ECAI 2000

•Other­possible­parameters­that­could­be­adjusted:

- T = Number of Trials = Ni

where­N­is­population­size­and­i=­1,­Max_Gen

= Mutation step­

­in­Normally­distributed­Mutation­value

- PS = Probability of Selection­

Parametrized­slope­of­probability­distribut.

- AS = Arity of Parents­

number­of­parents­in­recombination

GA Parameters (cont.)GA Parameters (cont.)

August 24, 2000 107ECAI 2000

­GD­­­ =­Genotypic­Diversity:­­­Normalized­Average­Hamming­Distance

­PFE­ =­Percentage­Fitness­Evaluations:­­­(Completed­#­Trials)­/­(Max­Allocated­#­Trials)

­Pm=­Change­in­Mutation­Rate

GDPFEPm

Genotypic Percentage Fitness Evaluation (PFE)Diversity (GD) Very Low Low Medium High Very High

Very Low Pos­High Pos­High Pos­Medium Pos­Medium No­Change

Low Pos­High Pos­Medium Pos­Medium No­Change No­Change

Medium Pos­Medium Pos­Medium No­Change No­Change No­Change

High Pos­Medium No­Change No­Change No­Change No­Change

Very High No­Change No­Change No­Change No­Change No­Change

Genotypic Percentage Fitness Evaluation (PFE)Diversity (GD) Very Low Low Medium High Very High

Very Low Pos­High Pos­High Pos­Medium Pos­Medium No­Change

Low Pos­High Pos­Medium Pos­Medium No­Change No­Change

Medium Pos­Medium Pos­Medium No­Change No­Change No­Change

High Pos­Medium No­Change No­Change No­Change No­Change

Very High No­Change No­Change No­Change No­Change No­Change

Fuzzy Controller for Mutation Rate: Rule SetFuzzy Controller for Mutation Rate: Rule Set

August 24, 2000 108ECAI 2000

• GA Parameters- N­ =­Base­Population­size:­ 50- Pc­ =­Crossover­rate:­ 0.600- Pm =­Mutation­rate: 0.005- G­ =­Generation­Gap 100%­replacement­

-­Simple­GA­(SGA)

25%­replacement

­ -­Steady­State­GA­(SSGA)

- S­ =­Selection­Strategy: Elitist

Statistical Experiments: Set-Up (cont.)

Statistical Experiments: Set-Up (cont.)

August 24, 2000 109ECAI 2000

J = C*e(T-10)/3

Summary of 1200 ExperimentsSummary of 1200 Experiments

Max Numb U-SGA FLC-SGA U-SSGA FLC-SSGATrials B B B B

3000 0% 1788.8 71 0.040 20% 1729 81 0.047 70% 1685 63 0.037 80% 1677 58 0.034

5000 5% 1767.9 103 0.058 35% 1705 74 0.043 75% 1682 63 0.037 80% 1673 47 0.028

7000 35% 1710.3 81 0.047 45% 1680 41 0.025 60% 1739 108 0.062 95% 1665 45 0.027

9000 20% 1748.8 102 0.058 50% 1676 46 0.027 80% 1695 82 0.048 85% 1689 70 0.041

11000 50% 1719.5 88 0.051 75% 1668 40 0.024 75% 1709 98 0.058 95% 1665 45 0.027

Max Numb U-SGA FLC-SGA U-SSGA FLC-SSGATrials B B B B

3000 0% 1788.8 71 0.040 20% 1729 81 0.047 70% 1685 63 0.037 80% 1677 58 0.034

5000 5% 1767.9 103 0.058 35% 1705 74 0.043 75% 1682 63 0.037 80% 1673 47 0.028

7000 35% 1710.3 81 0.047 45% 1680 41 0.025 60% 1739 108 0.062 95% 1665 45 0.027

9000 20% 1748.8 102 0.058 50% 1676 46 0.027 80% 1695 82 0.048 85% 1689 70 0.041

11000 50% 1719.5 88 0.051 75% 1668 40 0.024 75% 1709 98 0.058 95% 1665 45 0.027

Max Numb U-SGA FLC-SGA U-SSGA FLC-SSGATrials B B B B

3000 5% 352.5 20.9 0.059 15% 341.3 12.0 0.035 50% 343.8 23.0 0.067 75% 332.4 4.6 0.014

5000 30% 338.6 8.0 0.024 30% 337.7 7.9 0.023 60% 336.2 11.6 0.034 85% 331.8 4.1 0.012

7000 20% 339.7 1.9 0.005 30% 338.8 1.7 0.005 70% 341.3 5.2 0.015 70% 336.3 3.4 0.010

9000 30% 343.2 15.74 0.046 50% 333.9 5.0 0.015 80% 335.2 15.3 0.046 60% 334.6 5.6 0.017

11000 65% 337.0 15.3 0.045 60% 331.7 3.5 0.010 65% 336.9 15.3 0.045 65% 336.9 15.3 0.045

Max Numb U-SGA FLC-SGA U-SSGA FLC-SSGATrials B B B B

3000 5% 352.5 20.9 0.059 15% 341.3 12.0 0.035 50% 343.8 23.0 0.067 75% 332.4 4.6 0.014

5000 30% 338.6 8.0 0.024 30% 337.7 7.9 0.023 60% 336.2 11.6 0.034 85% 331.8 4.1 0.012

7000 20% 339.7 1.9 0.005 30% 338.8 1.7 0.005 70% 341.3 5.2 0.015 70% 336.3 3.4 0.010

9000 30% 343.2 15.74 0.046 50% 333.9 5.0 0.015 80% 335.2 15.3 0.046 60% 334.6 5.6 0.017

11000 65% 337.0 15.3 0.045 60% 331.7 3.5 0.010 65% 336.9 15.3 0.045 65% 336.9 15.3 0.045

Max Numb U-SGA FLC-SGA U-SSGA FLC-SSGATrials B B B B

3000 0% 655.05 90.2 0.138 5% 638.2 87.7 0.137 15% 592.0 53.0 0.090 80% 554.3 14.9 0.027

5000 10% 625.1 95.0 0.152 25% 600.8 47.6 0.079 35% 597.1 91.5 0.153 55% 570.8 24.7 0.043

7000 20% 606.84 97.9 0.161 20% 566.4 22.3 0.039 70% 563.6 22.8 0.040 65% 566.0 23.7 0.042

9000 30% 569.14 29.8 0.052 50% 573.9 41.8 0.073 85% 556.3 17.7 0.032 50% 573.2 24.9 0.043

11000 25% 608.35 129.4 0.213 40% 573.0 35.7 0.062 60% 568.4 24.4 0.043 70% 563.6 22.7 0.040

Max Numb U-SGA FLC-SGA U-SSGA FLC-SSGATrials B B B B

3000 0% 655.05 90.2 0.138 5% 638.2 87.7 0.137 15% 592.0 53.0 0.090 80% 554.3 14.9 0.027

5000 10% 625.1 95.0 0.152 25% 600.8 47.6 0.079 35% 597.1 91.5 0.153 55% 570.8 24.7 0.043

7000 20% 606.84 97.9 0.161 20% 566.4 22.3 0.039 70% 563.6 22.8 0.040 65% 566.0 23.7 0.042

9000 30% 569.14 29.8 0.052 50% 573.9 41.8 0.073 85% 556.3 17.7 0.032 50% 573.2 24.9 0.043

11000 25% 608.35 129.4 0.213 40% 573.0 35.7 0.062 60% 568.4 24.4 0.043 70% 563.6 22.7 0.040

7% 47% 60% 7% 20% 47%

Significant change in Significant change in

J = C*T

J = C*T2

J = C*T2J = C*e(T-10)/3

August 24, 2000 110ECAI 2000

Next Steps: Controlling Other Parameters

• Run-time Controlled GAs Parameters:- Population size:

» larger­size:­increase­parallel­search­in­solution­space

» smaller­size:­focus­on­current­existing­regions

- Probability mutation:

» Higher­prob.­of­mutation­disrupts­current­solutions­-­exploration­» Lower­probability­of­mutation­favors­current­solutions­-­exploitation

• Other Possible Run-time Controllable GAs Parameters:- Customized mutation operators:

» ­Variable­amount­of­changes­– smaller­for­good­solutions,­larger­for­bad­ones

- Fitness function:

» Evolving­fitness­function­(variable­weights­in­multi-criteria­aggregating­function)

DONE

DONE

August 24, 2000 111ECAI 2000

GAs controlled by FL (cont.)- Probability of Selection:

» Parametrized­slope­distribution­ranging­from:– Uniform­probability:­ignore­fitness­function­and­perform­random­

selection­of­parents­-­extreme­case­of­exploration,­to­

– Proportional­selection­with­rescaling­and­other­intermediate­strategies­-­compromise­between­exploration­and­exploitation­cases,­and

– Ranking:­always­select­the­best­N­and­ignore­the­rest­-­extreme­case­of­exploitation

» Probability­as­function­of­fitness­and­genotypical­distance­with­other­solutions­-­enforcing­diversity­and­favoring­exploration

- Probability of crossover:

» Constraints­applicability­to­mostly­good­solutions

- Customized-crossover operators­(for­real-coded­GAs):

» Selection­of­crossovers­based­on­T-norms­and­T-conorms­causes­offsprings­to­take­more­extreme­values­(exploration)

» Selection­of­crossovers­based­on­aggregating­operators­causes­offsprings­to­take­average­values­(exploitation)

August 24, 2000 112ECAI 2000

Frequency of Control Actions

Control­Action:­mutation­rate­changed­every­10­generations

population­size­change­every­generation

Mutation Rate

Mutation­rates­drops­exponentially­after­a­control­action­that­increases­it

Inference Engine Parameters

Left­Hand­Side­(LHS)­evaluation:­ Minimum operator

Rule­Firing: Minimum operator

Rule­Output­Aggregation: Maximum operator

Defuzzification: Center of Gravity (COG)

Fuzzy Controller for N and Pm: Control Parameters

Fuzzy Controller for N and Pm: Control Parameters

August 24, 2000 113ECAI 2000

• OutputsN =­Change­in­Population­Size­(Mult.­Factor)­

Pm=­Change­in­Mutation­Rate­(Mult.­Factor)

N range is [0.5, 1.5] == [Neg High, Pos High]- so that NC corresponds to 100% of previous Pop Size

N range­is­[0.5,­1.5]­==­[Neg­High,­Pos­High]so­that­NC­corresponds­to­100%­of­previous­Pop­Size

Population­Size­is­clamped­within­[25,­150]

Pm range­is­[0.5,­1.5]­==­[Neg­High,­Pos­High]­so­that­NC­corresponds­to­100%­of­previous­Pm

Mutation­Rate­is­clamped­within­[0.005,­0.10]

Fuzzy Controller for N and Pm: OutputsFuzzy Controller for N and Pm: Outputs

August 24, 2000 114ECAI 2000

• Develop Collection of Quasi-independent Models

• Each Model Generates:- Output Value­(Vi ) - Prediction- Confidence parameter (Ci ) derived from training stats.­- Introspection

• Intelligent Fusion Rules- Consider discrepancies among Output values (v)- Consider dynamic confidence value (c) associated with each output

Loc Val AIGEN

AICOMP

FUSIONRULES

Living­AreaAddress­(GeoCoded­)

Lot­Size#­Beds#­Baths,­...

PoolConditions...

eL eG

eC

eF

Example of Fusion for Mortgage Collateral Evaluation

ei =­{­Vi­,­Ci }

Fusion of Reasoning ModelsFusion of Reasoning Models

August 24, 2000 115ECAI 2000

Synergy­in­SC:­Reasons­&­Approaches

•­SC­Leverages­Knowledge­and­Data­to­Derive­the­Model

•­Model­=­Structure­+­Parameters­(&­Search)

•­Data-driven­Tuning­of­Knowledge-derived­Models-Translate­domain­knowledge­to­initial­structure­&­parameters-Use­Global­or­local­data­search­to­tune­parameters

•­Knowledge-driven­Search­Control

-Use­Global­or­local­data­search­to­derive­models­(Structure­+­Parameters)

-Translate­domain­knowledge­into­an­algorithm’s­controller­to­improve/manage­solution­convergence­and­quality

•­Hybrid­Search­Methods-Embedding­local­search­within­global­search-Embedding­knowledge­in­operators­for­global­search-Fusion­of­models­to­increase­accuracy­and­reliability