Bacterial Foraging Optimization - njavaid.com•optimal foraging policy •such terminology is especiallyjustified in case •where the models and policies have been ecologically validated

Bacterial Foraging Optimization

Presented by: Adia Khalid

PhD (Scholar)

Home Energy Optimization in Smart Grid

Supervised by: Dr. Nadeem Javaid

1

Introduction

Foraging strategies

Optimal foraging

Bacterial foraging algorithm

Home energy management

Price signals

Mapping

Agenda

2

Natural selection method

• eliminate animals with poor “foraging strategies”

Foraging strategies

• methods for locating, handling, and ingesting food

• favor those animals that have

• successful foraging strategies

• obtain enough food to enable them to reproduce

• after many generations poor foraging strategies are:

• either eliminated or

• shaped into good ones i.e.. Redesigned

such evolutionary principles have led scientists in the field of “foraging

theory” to hypothesize

• it is appropriate to model the activity of foraging as an optimization

process

Introduction (1\4)

Food Source

Food Quality

Food Capturing

Digesting Food

3

Passino, K. M. (2002). Biomimicry of bacterial foraging for distributed

optimization and control. IEEE control systems, 22(3), 52-67.

Introduction (2\4)

A foraging animal main focus:

• maximize the energy obtained per unit time spent foraging

• In the face of constraints presented by its own

• physiology

• e.g., sensing and cognitive capabilities

• environment

• e.g., density of prey, risks from predators, physical characteristics ofthe search area

Evolution has balanced these constraints

• sometimes referred to as

• optimal foraging policy

• such terminology is especially justified in case

• where the models and policies have been ecologicallyvalidated

4

Foraging focusEnergy

Maximization

Con

strain

ts

o Physiology

o Environment



Introduction (3\4)

Optimal Foraging:

• Optimal foraging theory formulates the foragingproblemas an optimization problem.

• Optimization models valid for social foraging

• where groups of animals cooperatively forage

• Here, we explain the biology and physics underlying thechemotactic (foraging) behavior of

• E.coli bacteria for optimization named as Bacterial ForagingOptimization

• Individual bacterium also communicates with others bysending signals

• During foraging of a real bacteria two basic operations

• Swim

• Tumble

• performed by a bacterium at the time of foraging by

• a set of tensile flagella

5

http://wikis.swarthmore.edu/mathbio/index.php?title=File:Optim

al_Foraging_Theory.jpg&limit=50



Introduction (4\4)

E.coli bacteria:

• the ones that are living in our intestines

Structure

• Diameter: 1μm

• Length: 2μm

• Flagellum:

• Chemotaxes

• movement in the presence of

• chemical attractants and

repellants

• Counterclockwise:

• Swim

• Clockwise:

• TumbleBactria chemotactic

Movement

6



Bacterial Foraging Algorithm (1\2)

7

Chemotaxis:

When a bacterium meets a favorable environment (rich in

nutrients and noxious free),

• it will continuous swimming in the same direction,if nutrient increase in the direction of swim

when it meets an unfavorable environment,• it will tumble, i.e., change the direction of swim

Reproduction:

After calculating fitness value for each bacteria,

• reproduction allows the bacteria to survive and

reproduce

Swarming:

E. Coli bacterium has a specific sensing actuation and

decision making mechanism

• On each move• It releases attracts to signal other bacteria to swarm towards its

Elimination and dispersal:

The chemotaxis provides a basis for local search and

reproduction speeds the convergence

• To avoid trap bacteria in local minimum

• Elimination-Dispersal is done

tumble run run

tumble run tumble

Nature Inspired meta-heurist algorithmA function that ranks

alternatives in search algorithmsat each branching

step based on available

information to decide which branch to follow

Heuristic means local

search, metaheuristic means generalized local search. ...

The main difference is that heuristicsare

problem-specific methods (created to solve a particular problem and probably nothing

else) while meta-heuristics are problem-independent methods that can be applied

to a wide range of problems.

The algorithm models bacterial

• Population: {i ϵ pop, where pop have 1:Np elements}

• Chemotaxis: {for j=1:Nc elements}

• Swarming: {for s=1:Ns elements}

• Reproduction: {for k=1:Nr elements}

• Elimination and Dispersal Steps: {for l=1:Ne step}

• Another parameter

• C: Step Size for the dimension

8

lkjPlkjJlkjiJlkjiJ i

cc ,,,,,),,,(),,,(

idltidlt

idltiClkjlkj

T

ii ,,,,1

1

1

,,,cN

j

i

health lkjiJJ

1

1

222 )1,()),(1,(100d

d

iii

cc dididiJ

Bacterial Foraging Algorithm (2\2)

BFA Mapping on Home Energy Management (HEM)

Target: We have to optimize the energy usage

• By scheduling the home appliances• Pass the on-peak hour load on off-peak hour

Home Energy Management (1/10)

9

BFA Mapping on Home Energy Management (HEM)Optimal Solution get form optimal search space

Search space

Population of group of bacteria's


10

BFA Parameters HEM Parameters Values

Population Possible solution 30

Bactrians with in a swarm Appliances 9

Bacterium status i.e. dead or alive Appliance’s ON or OFF status 1 or 0

Elimination steps Schedule 24 hour

Fitness Level i.e. min( ) Min (Cost) varyihealth

J

Cost depend on the power rate of an appliance and

price signals

Peak Load Reduction

• Demand Response

• encourage the user to make changes in their demand according to the price signals

Implementation is possibly implemented using some energy measuring consumption measuring meters:

• Bulk meter just save information with a single bulk

• Smart meter record electricity usage information frequently

[*]. Waterloo North Hydro, https://www.wnhydro.com/en/your-home/time-

of-use-rates.asp. Last visited: 20 May 2016.


11

Meter

Bulk meter

Flat rate Tiered rate

Smart meter

Time based rate

Dynamic

RTP CPP VPP CPR C/I rate

TOUPricing schemes:•Flat Rates - same rate during a given period of time

•E.g., 30-day bill cycle

•Tiered Rates - charge a different price based on blocks of usage

•e.g., first 500 kWh vs. next 500 kWh for 30-day billing cycle

•Time-based rate includes- Dynamic Rate and Time of Use

(TOU)

Dynamic Rate [*]

Real Time Price (RTP)

Critical Peak Pricing (CPP)

Curtailable/Interruptible (C/I)

Variable Peak Pricing (VPP)

Critical Peak Rebate (CPR)

Pricing Scheme[*]

• TOU: Prices set for the on-peak and off-peak hours,

• where hours divided into blocks and price for a particular block remain fixed

• RTP: Rates tariff based on the hourly bases usage of electricity

• Utilities regulates RTP in two parts

1) Base bill

calculated on the bases of define tariff for particular customer depend on

• customer baseline load (CBL)

2) Hourly prices apply according to the customer usage

• that is a difference between actual and CBL

𝑅𝑇𝑃 = ൝𝑃𝑟𝑖𝑐𝑒𝑈𝑛𝑖𝑡 , 𝑖𝑓 𝐿𝑜𝑎𝑑 ≤ 𝑙𝑖𝑚𝑖𝑡

𝑃𝑟𝑖𝑐𝑒𝑈𝑛𝑖𝑡 + 𝐸𝑥𝑡𝑟𝑎𝑐ℎ𝑎𝑟𝑔𝑒 , 𝑖𝑓 𝐿𝑜𝑎𝑑 > 𝑙𝑖𝑚𝑖𝑡……………….. (1)

• The C/I Option: Specifies conditions under which disturbance in service may occur

• A customer gives right to the Local Distribution Company (LDC) during the contract

• not the obligation to disturb the services

• In such situation LDC pays incentive to the customers through bill reduction




12

0

2

4

6

8

10

12

14

16

18

20

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

TOU

0

5

10

15

20

25

30

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

RTP

Pricing Scheme[*]

• VPP: hybrid TOU and RTP

𝑉𝑃𝑃𝑡𝑜𝑡𝑎𝑙 = 𝑉𝑃𝑃ℎ𝑜𝑢𝑟𝑜𝑛_𝑃𝑒𝑎𝑘

+ 𝑉𝑃𝑃ℎ𝑜𝑢𝑟𝑜𝑓𝑓_𝑃𝑒𝑎𝑘

……………. (2)

𝑉𝑃𝑃ℎ𝑜𝑢𝑟𝑜𝑓𝑓_𝑃𝑒𝑎𝑘 = 𝑇𝑂𝑈 ……………...(2a)

𝑉𝑃𝑃ℎ𝑜𝑢𝑟𝑜𝑛_𝑃𝑒𝑎𝑘 = 𝑅𝑇𝑃 ……………...(2b)

• CPP: Critical events may call during the specific period

• utilities observe high market price rate or during the power system emergency conditions

• Usually occur in hot summer weekdays

• Allow only 15 time per year

• CPR: During the critical event utilities increases the price for the specific time duration

• refunded it to customer

• when utilities observe any reduction in consumption




13

0

20

40

60

80

100

120

140

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

CPP

BFA Matlab Code


14

Bacterium\ Appliances Fitness Evolution

Vacuum

Cleaner

Water

Heater

Water

Pump

Dish

Washer

Refrigerator AC Ove

n

Washing

Machine

Cloth

Dryer

Jlast

1 0 0 1 0 1 1 1 1 101

0 1 1 1 1 0 0 0 0 100

1 1 1 1 1 0 0 1 1 99

1 0 1 1 0 0 1 1 0 100

for i=1:NP %

for j=1:D-1

if rand(1)>0.6

X=1;

else

X=0;

end

J(i)=sum(100*(x(k,j+1)-x(i,j)^2)^2+(x(i,j)-1)^2); % initial

fitness calculation

end

end

BFA Matlab Code


15


Vacuum

Cleaner

Water

Heater

Water

Pump

Dish

Washer

Refrigerator AC Ove

n

Washing

Machine

Cloth

Dryer

J

0 1 0 0 0 1 1 0 0 100

1 1 1 0 0 1 1 1 0 110

1 1 0 1 1 1 0 1 0 106

0 0 1 0 1 0 1 0 0 105

for l=1:Ne % 24 l=elimination of dispersal step

for k=1:Nr % 4 k=reproduction

for j=1:Nc % 3 Chemotaxis Loop %

for i=1:Np % for each bacteria

del=(rand(1,D)-0.5)*2;

x(i,:)=x(i,:)+(C/sqrt(del*del'))*del; % C=

0.4 %Direction of Tumble i.e. new position of bacterium

for d=1:D-1J(i)=sum(100*(x(i,d+1)-x(i,d)^2)^2+(x(i,d)-1)^2); %Fitness Evalutin

end

BFA Matlab Code


16


Vacuum

Cleaner

Water

Heater

Water

Pump

Dish

Washer

Refrigerator AC Ove

n

Washing

Machine

Cloth

Dryer

Jlast

0 0 0 1 0 0 1 1 1 100

1 1 0 0 0 1 1 0 1 110

1 1 0 1 1 1 0 1 0 106

0 0 1 0 1 0 1 0 0 105

for m=1:Ns % 2 swimming Step

if J(i)<Jlast(i)%Elimination and Dispersal Check

Jlast(i)=J(i);

x(i,:)=x(i,:)+C*(del/sqrt(del*del')); %Direction of Tumble i.e. new position of bacterium

for d=1:D-1

J(i)=sum(100*(x(i,d+1)-x(i,d)^2)^2+(x(i,d)-1)^2); %Fitness Function

end

else

Updated the

bacterium\ appliances

status

del=(rand(1,D)-0.5)*2;%Vector with random Direction

x(i,:)=x(i,:)+C*(del/sqrt(del*del'));

for d=1:D-1

J(i)=sum(100*(x(i,d+1)-x(i,d)^2)^2+(x(i,d)-1)^2);

end

end

end % end swimming Stepend % end of bacterial population

BFA Matlab Code


17

Bacterium\ Appliances Cost

Vacuum

Cleaner

Water

Heater

Water

Pump

Dish

Washer

Refrigerator AC Oven Washing

Machine

Cloth

Dryer

Cost

(cent)

0 0 0 1 0 0 1 1 1 48

1 1 0 0 0 1 1 0 1 30

1 1 0 1 1 1 0 1 0 45

0 0 1 0 1 0 1 0 0 50

for i=1:Np %% Check the Health

Cost_B(i)= power_Rate * Electricity_Price

end

end % end of reproduction step

Cost=min(Cost_B) % select best one

Minimum cost will be

selected

BFA Matlab Code


18


Vacuum

Cleaner

Water

Heater

Water

Pump

Dish

Washer

Refrigerator AC Oven Washing

Machine

Cloth

Dryer

J

1 1 0 1 0 1 1 1 0 103

1 0 0 1 0 0 1 0 1 106

0 1 0 1 0 1 0 1 1 100

0 1 1 1 1 0 0 0 0 109

%% random elimination dispersion

for j=1:Np

for i=1:D

if rand(1)>=Ped

x(j,i)=1;

else

x(j,i)=0;

end

for d=1:D-1

J(i)=sum(100*(x(i,d+1)-x(i,d)^2)^2+(x(i,d)-1)^2);

end

end

end

Schedule(l,:)=Cost;

end

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Documents

Bacterial Foraging Optimization - njavaid.com•optimal foraging policy •such terminology is especiallyjustified in case •where the models and policies have been ecologically validated