biologically inspired algorithm

8/4/2019 Biologically Inspired Algorithm

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Biologically InspiredBiologically InspiredComputationComputation

Mohamed A ElMohamed A El-- SharkawiSharkawiThe CIA labThe CIA lab

Department of ElectricalDepartment of ElectricalEngineeringEngineering

University of WashingtonUniversity of WashingtonSeattle, WA 98195Seattle, WA 98195-- 25002500

[email protected]@ee.washington.eduhttp://http://cialab. ee.washington. educialab. ee.washington. edu

M. A. El-Sharkawi, BIA 3

... the Babbling of Old Fools ?... the Babbling of Old Fools ?


!! To an uninspired scientist with a hammer,To an uninspired scientist with a hammer,

everything looks like a naileverything looks like a nail

!! If at first, the idea is not absurd, then there is noIf at first, the idea is not absurd, then there is no

hope for ithope for it

Albert Einstein

Seek new ideas even if out of theSeek new ideas even if out of the

ordinaryordinary


Seek new ideas even if you areSeek new ideas even if you are

unsure of their appealunsure of their appeal

!! If we knew what it was we were doing, itIf we knew what it was we were doing, it

would not be called research, would it?would not be called research, would it?


Wild Idea is a Sign of brillianceWild Idea is a Sign of brilliance

!! Imagination is more importantImagination is more important

than knowledge.than knowledge.

For knowledge is limited to all weFor knowledge is limited to all we

now know and understand,now know and understand,

while imagination embraces thewhile imagination embraces the

entire world, and all there ever willentire world, and all there ever will

be to know and understandbe to know and understand

!! Logic will get you from A to B.Logic will get you from A to B.

Imagination will take youImagination will take you

everywhereeverywhere


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History of Computation


5K YR Ago

RHIND

PAPYRUS

RHIND

PAPYRUS

RHIND

PAPYRUS


Driven by necessity we have progressed from

using fingers


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to tables


to abacus

to mechanical machines


to slide rules

to more mechanical machines


to calculators


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to computers


Impact of Modern ComputingPower

! Staggering impact on our ability to

Compute through iterations

Create amazingly complex algorithms


New Wave of Computing

! Moores law is still true computers double their power every 18

month.

! Computationally intensive techniqueshard to implement a few years agoare now feasible. Among these techniques are the so

called biologically inspired algorithms(BIA).


Biologically Inspired AlgorithmsBiologically Inspired Algorithms


Biologically Inspired SystemsBiologically Inspired Systems

! Philosophers argued that with allhuman achievements in science andengineering, nature still providesthe best systems that can ever befashioned.


Biologically Inspired SystemsBiologically Inspired Systems

This is trueeven if wecompare the

most complexmachine withthe simplestform of abiological cell.


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AndAndheeeeereheeeeeressAlbertAlbert

!! When the solution isWhen the solution is

simple, God is answering.simple, God is answering.

Albert Einstein


BIA or Biocomputation

! The use ofbiological processesorbehavior as metaphor, inspiration, orenabler in developing new computingtechnologies

! The field is highly multidisciplinary,Engineers, computer scientists, molecularbiologists, geneticists, mathematicians,physicists, and others.


Main steps of BiologicallyMain steps of BiologicallyInspired SystemsInspired Systems

! Observe and study: Observeanimal and human behaviors

and Study biological structures

! Mimic: Acquired knowledge may help us mimic

nature and develop better engineeringsystems and machines.


The ABCThe ABCs of BIAs of BIA(Bezdek)(Bezdek)

AArtificialrtificial BBiologicaliological CComputationalomputational


BIA SystemsBIA Systems!! Neural NetworksNeural Networks!! Evolutionary AlgorithmsEvolutionary Algorithms!! Fuzzy SystemsFuzzy Systems

!! Swarm IntelligenceSwarm Intelligence!! BoidsBoids!! Particle SwarmParticle Swarm!! DNA ComputingDNA Computing!! Artificial LifeArtificial Life!! Intelligent AgentsIntelligent Agents

!!


Nature is a Powerful Paradigm

! Brain""""Neural Networks

! Evolution theory""""Evolutionary Algorithms

! Flocking birds""""Particle Swarm Optimization,Boids

! Insects""""Swarm Intelligence

!

!


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Why BIA?Why BIA?

# May require little or no knowledge of the physicalsystem they emulate.

# System is developed by observations and intuition.

# Can find substance in data bases throughstochastic search.

# Can be self- tuned using raw experiential data.

# Noise tolerant and robust.

# Objectives no longer need to be in restrictivemathematical forms.

# Nonlinearity is no longer a disabling constraint.


Key ImprovementsKey Improvements

$The performance of BIAs is betterunderstood and appreciated.#NN can have an explanation facilities

and is no longer a black boxes.#Stability criteria for fuzzy control, long

lacking, can be established# Convergence is improved and global

optimization within a predeterminedspace can be achieved.


Conventional Model basedConventional Model based

SystemSystem

Sensors

-Model

Desired

Parameteror StateEstimation

DecisionModel


NonNon--Model based SystemModel based System

Process

Process

Engine

Engine

Data

from

Sen

sors

Data

from

Sen

sors

DesiredDesired

DecisionDecision


Classical Control: Design

System

inputs

Control

Inputs

Constraints


Classical Control: Operation

System

inputs

Control

Inputs

Constraints


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Intelligent Control

System

inputs

Control

Inputs

Constraints


Intelligent Control

System

inputs

Control

Inputs

Constraints


Neural Networks




InputPat

terns

OutputDe

cision

Connections

Input layer

Hidden layer

Output layer


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InputPattern

s

OutputDecisio

n

Connections adjustment

Input layer

Hidden layer

Output layer


InputPatterns

OutputDecision

Connections (Fixed)

Input layer

Hidden layer

Output layer


ElEl--Sharkaw

i

Sharkaw

i

NN TrainingNN Training


NN Training:NN Training:El-Sharkawis Quintuplets

NotEl

NotEl--Sharkawi

Sharkawi


ElEl--Sharkawi

Sharkawi

Testing of Trained NNTesting of Trained NN


NotEl

NotEl--Shar

kawi

Shar

kawi

Testing of Trained NNTesting of Trained NN


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Almost !Almost !

Evolutionary AlgorithmsEvolutionary Algorithms


Evolutionary Algorithm

! Single Search Technique (SST) could be trapped

in undesirable minima

! Convergence of SST depends on the selected

initial condition


Evolutionary Algorithm vs SST

Single Search Evolutionary Search


Population Pool

1 0 0 1 11 1 1 11 0 0 000 0 11 1 1 0 00 0

...

Byte 1 Byte 2 Byte n

1

00 1 11 1 1 11 0 0 0 00 0 11 110 0 0 0

...

1 0 0 1 11 1 111 0 0 000 0 11 1 1 0 0

00

...

1 0 01

1

1 1 1 11 0 00 00 0 1

1

1 10 000

...

0

individual

#1

#2

#3

#K

2 n


Fitness Evaluation

#1

#2

#3

Individuals

1 0 0 111 0

00 111 0

1 0 0 11 1 0

1 0 01 11 0

0

#n

FitnessComputations

f(.) Normalize

Ranked Individuals

#q

#p0 0 11 1 0

1 0 0 11 1 0

#p

#q

0

0 0 11 1 00

1 0 0 11 1 0

#1 1 0 0 111 0

1 0 01 11 0#3

#n 1 0 0 11 1 0

#2 00 111 00


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Crossover

#p

#q

0 0 11 1 00

1 0 0 11 1 0

Crossover0

0 1

1 1

0

0

1 0

0 1

1 1

0#p

#q

Crossover point


Success of Crossover

11111111 00000001 00000001 11111111

00000001 00000001 11111111 11111111

Global OptimalityGlobal Optimality

Smartness Beauty


Experiment


Fuzzy Systems


AndAndheeeeereheeeeeressAlbertAlbert

!! The only real valuableThe only real valuable

thing is intuition.thing is intuition.

Albert Einstein


Universe (X)

Subset A

Subset B

Subset C

Crisp Set/SubsetCrisp Set/Subset

1=A1=B

1=C

0=A


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9

8

10

On a scale of

one to 10, how

goodwas the

dive?

! close, heavy, light, big, small, smart, fast, slow,

hot, cold, tallandshort.

9.5


! Fuzzy Probability

! Example #1 Billy has 9 toes. The

probability Billy has 10

toes is zero.

The fuzzy membership

of Billy in the set of

people with 10 toes is

nonzero.


Example #2 A bottle of liquid has a probability of

of being rat poison and of being pure

water. A second bottles contents, in the fuzzy

set of liquids containing lots of rat

poison, is .

The meaning of for the two bottles

clearly differs significantly and would

impact your choice should you be

dying of thirst.

(cite: Bezdek)

#1

#2


Fuzzy ConflictsFuzzy Conflicts

Tall Short


Fuzzy ConflictsFuzzy Conflicts

Tall ShortTall or Short?Tall or Short?


Fuzzy AssociationFuzzy Association

4

5

6

7

Very Tall

Tall

Medium

Short

Very Short


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! Based on intuition and judgment

! No need for a mathematical model

! Provides a smooth transition betweenmembers and nonmembers

! Relat ively simple, fast and adaptive

! Less sensitive to system fluctuations

! Can implement design objectives, dif ficult toexpress mathematically, in linguistic ordescriptive rules.


Applications DomainApplications Domain

! Fuzzy Logic

! Fuzzy Modeling

Neuro-Fuzzy System! Fuzzy Control

Intelligent Control

Hybrid Control

! Fuzzy Pattern Recognition


SomeSomeInteresting ApplicationsInteresting Applications

! Smooth ride control

! Camcorder auto-focus and jiggle control

! Braking systems

! Copier quality control

! Rice cooker temperature control

! High performance drives

! Air-conditioning systems


Swarm Intelligence

Swarm IntelligenceSwarm Intelligence


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Swarm IntelligenceSwarm Intelligence

=CoordinationCoordination withoutwithout

Direct CommunicationDirect Communication


Swarm Intelligence

! Appears in swarms of certain insectspecies

! Interactions is indirect (stigmergy)

! Complex forms of social behaviorcan achieve a number of tasks


SWIN - Stigmergy

! Stigmergy means communicationthrough the environment

Pheromone laying : pheromone attractsants who lay even more pheromone

Task- relatedstigmergy: e. g. termite nestbuilding


Pheromone Trails


Features

! Distributed andMulti- agentsearch

! Uses stigmergy (communicationthrough the environment) for agentinteraction

! Adaptive

! Uses reinforcement learning

! Randomness """" robustness


Example of Swarm IntelligenceExample of Swarm Intelligence

Application to Complex SystemsApplication to Complex Systems(Routing in Data Networks)(Routing in Data Networks)


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Routing in Data NetworksRouting in Data Networks

!Why is it so complex? Distributed problem, requires coordination of a

number of nodes, which might not have direct

communication

Must cope with node failures

Must re-adjust routes that get congested


Existing Schemes

! Wired

Distance vector (Bellman-Ford)

Linkstate (Dijkstras)

OSPF (Internet Standard linkstate-based)

! Wireless

Table-driven (all nodes have routing tables to all

destinations)

On-demand (routing tables are created on demand)


Swarm Advantages in Routing

Yes for distributed BF,

but not for link-state.

Yes, packets can be

re-routed if links fail

Robustness

Slow adaptationYes, adapts to

congestionpatterns

Load balancing

Some, but may cause

oscillations. Can be slow.

Yes, can be very fastAdaptive

Some of them(e.g

Bellman Ford)

YesDistributed

Non-Swarm-basedSwarm- based


AntNetAntNet

! Introduced by Di Caro and Dorigo

! Designed for packet switching networks

! Uses ants who affect routing based on

trip times to destination

! This is not done directly, but through a

processed quantity


ANTNET: Routing TablesANTNET: Routing Tables

G

D

0.720.28

0.850.15

FB

Next Hop

Destination

Sum of row=1

Probability thatnext-hop is B ifdestination is D

F D

n

BK

Current


A

B

C

D

G

E

F

AB 0.23

BC 0.11

AB 0.23

CD 0.14

BC 0.11AB 0.23

DE 0.15

CD 0.14

BC 0.11

AB 0.23

Forward AntsForward Ants


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A

B

C

D

G

E

F

AB 0.23

BC 0.11

AB 0.23

CD 0.14

BC 0.11

AB 0.23

DE 0.15

CD 0.14

BC 0.11

AB 0.23

Backward AntsBackward Ants


Information Carried byInformation Carried by

Backward AntBackward Ant

! Trip-time table

Contains trip-time estimate to every destination

G

D

0.010.18

0.020.24

VarianceMean

Time

Destination


Why Forward and Backward

! Routing tables are updated only by ants

who were successful in reaching

destination

! If a ant is lost, it will not generate a

backward ant

next-hops that were not successful will not

be updated


The Algorithm-Essential steps

! Launch forward ant

! Find path randomly, but based onrouting table probabilities

! Remember the path and the arrival timesfor forward ant

! Backward ants trace path in reverse

! While at that, they update routing tables


AntNet: Table updates

Pdfis theprobability of choosing nodefas next-hop, when the destinationis d

N is the set of neighbors of the current node

fis the next-hop node

n are all the other neighbor nodes

+ and - are the positive and negative reinforcement, respectively

r= weighting factor (step size)

Nn,fn,P)'r(

)P)('r(

PP

PP

dn

df

dndn

dfdf

=

=

+=

+=

+

+

1

11


Weighting Factor

T= trip time from current node to the destination

= average ofT

c= scaling factor (usually 2)


16/29


AntNet

! Equation are based on negative feedback:

Positive reinforcement (+) should besmaller as probabilities get larger and viceversa

Negative reinforcement (-) should be largeras probabilities get larger and vice versa


AntNet

! Problem: Tcould be unreliable (high

variance)

! Solution: Use over ratio to adjust r

! Why? Because high / means Tis

unreliable and vice versa


r = T/ > 0.5r = T/ < 0.5

Adjusting r

a

e

a

e

+

Good time Bad time

! Add nonlinearity: r"(r )h

! Why? To manipulate the learning rate r

! Choice of h: usually 2 (heuristic)

T unreliable

T reliable

Monotonicallydecreasingfunction


Wireless Issues

! Broadcast advantage

When node transmits, it can be heard by all nodes in itsrange

! Energy constraints

Routing must take into account energy

Energy can also be adjusted by adjusting range

! Noise andbandwidth requirements also affectenergy and range

! Node mobility : nodes can move in and out ofrange


Swarm ControlSwarm Control


ObjectiveObjective

! To move a group of vehicles (rovers,

robots, underwater vehicles)

independently to achieve common or

distributed objectives.


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Artificial Potential Field (APF)Artificial Potential Field (APF)

! The motion of the vehicle is governed by a

minimum of two fields: attractive andrepulsive fields.

! Attractive field: a force that moves thevehicle toward the target position.

! Repulsive field: a force that moves thevehicle away from obstacles or areas that isbeing covered by other vehicles.


Target

destination

Obstacle

Vr

VaV

Vr

Va

V

Vr

Va

V


Attraction VelocityAttraction Velocity

Cartesian distance between the vehicle and the target

Da: distance between the vehicle and the target

: angle between the vehicle and the target

=

sin

cosDV aa


Repulsion VelocityRepulsion Velocity

Dr:distance between the vehicle and the obstacle.

: angle between the vehicle and the obstacle.

=

sincos

DV

r

r 1


Total VelocityTotal Velocity

! andare modulation parameters (can bedynamically changing)

For example: if the vehicle is to achieve astand-still state at the target point, is set tozero whenDa approaches zero.

! is the effect of other influences (otherrobots to avoid)

++= ra VVV


BoidsBoids


18/29


History ofHistory ofBoidsBoids (Flocking)(Flocking)

! Pioneered by Craig Reynolds

! Coherent flocking behavior using simple

rules was first demonstrated in the late

1980s .

To develop realistic motions of groups of

actors in computer animation.

Each actor (boid) has a scripted path

predetermined by the animator.


Flocking rules

! Basic rules (necessary and sufficient)

Cohesion: fly towards the center of your local flock mates.

Separation: keep a certain distance away from nearest flockmates.

Alignment: align your velocity vector with that of the localflock

! additional rules (for better flocking dynamics)

Evasion: avoid occupying the same local airspace as yournearest flockmate. Evasion is a localized form of separation.

Migration: fly towards a pre-specified location


Cohesion

! Move toward the

center of local

flockmates


Separation

! Steer to avoid collision

with local flockmates


Alignment

Steer towards the

average heading of

local flockmates


Evasion

Avoid occupying the

same local space as

your nearest

flockmate.


19/29


Migration

Fly towards a pre-

specified location


Final motion vector

Original velocity

Cohesion

Mitigation

Net velocity

Alignment

Evasion

Separation


Control Applications

! Simple behaviors for individuals and pairs: Seekand Flee

Pursue andEvade

Obstacle Avoidance

Path or wall Following

Flow Field Following

! Combined behaviors and groups: Crowd Path Following

Leader Following

Unaligned Collision Avoidance

Queuing(at a doorway)

Flocking(combining:separation


Tracking

Particle Swarm OptimizationParticle Swarm Optimization


Particle Swarm OptimizationParticle Swarm Optimization

=Coordination withCoordination withDirectDirectCommunicationCommunication


20/29

Particle Swarm Optimization

! Inventors: James Kennedy and RussellEberhart

! An Algorithm originally developed toimitate the motion of a Flock of Birds,or insects

! Assumes Information Exchange (SocialInteractions) among the search agents

! Basic Idea: Keep track of Global Best

Self Best

How does it work?

! Problem:Find X which minimizes f(X)

! Particle Swarm: Start:Start: Random set of solution vectors

Experiment:Experiment: Include randomness in the choiceof new states.

Remember:Remember: Encode the information aboutgood solutions.

Improvise:Improvise: Use the experience informationto initiate search in a new regions

PersonalBest at previous step

Currentmotion

Component in thedirection of personal best

Component in thedirection of previous motion

Component in thedirection of global best

New Motion

Global best


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PSO Modeling

! Each solution vector is modeled as The coordinatesof a bird or a particle in a

swarm flying through the search space

All the particles have a nonzero velocity andthus never stop flying and are alwayssampling new regions.

! Each particle remembers Where the global best and where the local

best are.


! The search is guided by The collective consciousness of the

swarm

Introducing randomness into thedynamics in a controlled manner

PSO Modeling


InertiaInertia

nonzero velocityPS never stop flying

Controlled randomness

Particle Swarm Dynamics

))()().(,0(

))()().(,0()(.)1(

2

1

kxkxar

kxkxarkvwkv

GroupBest

SelfBest

rr

rrrr

+

+=+

)()()1( kvkxkxrrr

+=+

The collective consciousnessof the swarm

Self consciousnessof the swarm


PSO

x is a solution vector particle and v is the velocityof this particle

a1

and a2 are two scalars,

w is the inertia

r(0,1) is a uniform random number generatorbetween 0 and 1

vgbvsb

vold

vnew


Design Parameters

! a1

and a2

!w: Should be between [0.9 and 1.2]

High values of w gives a global search

Low values of w gives a local search

! vmax: To be designed according to the

nature of the search surface.


The Art of Fitness Function! To move robots to boundary points

Metric: |f(x)- boundary value|


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Results - Case 1


The Art of Fitness Function! Distribute robots uniformly on the

boundary

Metric:|f(x)- boundary value| -Distance to closest neighbor

(to penalize proximity to neighbors)

Results - Case 2


The Art of Fitness Function! Distribute robots uniformly on the

boundary close to current state

Metric:|f(x)- boundary value| - Distance to

closest neighbor + Distance tocurrent state

(penalize proximity to neighbors, penalize distance from currentstate)

Results - Case 3


PSO ChallengesPSO Challenges

! Like any search technique, PSO could be

unsuccessful at distinguishing between global and

local minima

Local minimum is easier to find

If fitness function cannot amplify the difference

between global and local minima, PSO is likely

to stay in the local minima


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Modified PSOModified PSO

! Two-step PSO (or gradient-approximation)

! Cluster PSO


TwoTwo--Step PSOStep PSO

! Each particle takes two steps: short and long

Then decide on optimal step based on steeper

negative gradient

x0

xS

xL


TwoTwo--Step PSOStep PSO

! Better method at not overflying narrow

valleys

!Problems:

Particles may take the short step more often

than the long step, resulting in slower

convergence

Can still get trapped in local minima


Cluster PSOCluster PSO

! It is a hierarchical version of PSO:

PSO are arranged in clusters

Each cluster contains multiple agents

Each cluster has a centroid that acts,effectively, as a standard PSO agent

Each agent within the cluster is attractedto itspersonal best, the cluster best, andthe cluster centroid



vc

vgbvcbvabva

vcb

vcc



vc=wcvc+ac1(xcb-xcc) +ac2 (xgb-xcc)

va=wa va+a1(xab-xa)+a2 (xcb-xa) +a3 (xcc-xa)

xcc=xcc+vc

xa=xa+vc+va


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! Cluster PSO combines globally superior

ability of standard PSO in avoiding localminima with the locally efficient search

which can find narrow global minima.

MAYBE!

MultiobjectivesMultiobjectives Optimization &Optimization &

Pareto FrontsPareto Fronts


Conventional OptimizationConventional Optimization

! Any optimization problem can be framed as

finding the parameter minimizing a given

objective function

! findx* that minimizes y =f(x)

! Typically, one solution

x

f(x)

x*

f(x*)


Conventional OptimizationConventional Optimization

! Most optimization problems have several

(possibly conflicting) objectives.

! These problems are frequently treated as

Single-objective optimization problemsby

transforming all but one objective into

constraints.

Single cost function where all objectives are

weighted according to their importance.


Weighted Aggregation for MultiWeighted Aggregation for Multi--

Objective OptimizationObjective Optimization

! Objective: minimize the following functions

( ) ( ) ( )xf...,...,xf,xf n21

( ) ( ) ( ) ( )xfw......xfwxfwxJ nn+++= 2211

! Formulation: aggregate all functions in a weighted

fashion to form one cost index


Limitation of AggregatedLimitation of Aggregated

Optimization functionOptimization function

! Single aggregated function leads to onlyone solution.

! The relative importance must be selectedbefore hand and the final solution isdependent on the selection.

! Trade offs can not be easily evaluated.

! Solution is not possible fornonconvexsearch spaces.


25/29


TradeTrade--off Analysis (Example of Conflictingoff Analysis (Example of Conflicting

Objectives)Objectives)

! Designing ofdistributed controllers while

reducing the cost.

! Place functional blocks on a chip such that chip

area is minimized and power dissipation is also

minimized.

! Find the vehicle that covers the most distance in a

day while requiring the least energy.

! Placing enough sensors to monitor a system while

reducing the cost.


Simple Problem, Single solutionSimple Problem, Single solution

Find x* such that ( ) ( )xfxf i*

i for all i

f1(x*)

f2(x*)

f1

f2


Simple Problem, Multiple SolutionsSimple Problem, Multiple Solutions

Example: Operational AmplifierExample: Operational Amplifier

DC gain [dB]

transitfreq.[M

Hz]

bette

r

better


F

1f

2F

1f

2f

MultiMulti--Objective Optimization: Pareto FrontObjective Optimization: Pareto Front

better

better

minimize 21, ff

better

better

maximize 21, ff

Pareto FrontPareto Front


Goal of MultiGoal of Multi--ObjectiveObjective

Optimization (MOO)Optimization (MOO)

!Finding a set of decision variables that

satisfies constraints and

optimizes a vector of objectives.

! The term optimize means finding a

solution which would give values of all the

objective functions acceptable to the

designer


feasible region

Mathematical Formulation of MOOMathematical Formulation of MOO

! Find the vectorx* =[x1*, x2*, ...,xn*]T

which satisfies

m inequality constraints:

gi(x)>= 0, i=1,2,...,m

and p equality constraints:

hi(x) = 0, i=1,2,...,p

and optimizes the vector function;

f(x)=[f1(x), f2(x), ..., fk(x)]T


26/29


Terminologies used in MOOTerminologies used in MOO

!! The solution is dominant ifThe solution is dominant if

( ) ( )( ) ( ) ( )k...,......,,ixfxf

ixfxf

i

*

i

i

*

i

21oneleastatfor

and,allfor

biologically inspired algorithm

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