View
46
Download
0
Category
Tags:
Preview:
DESCRIPTION
Bi-directional incremental evolution. Dr Tatiana Kalganova Electronic and Computer Engineering Dept. Bio-Inspired Intelligent Systems Group Brunel University. Outline. Evolutionary process Evolvable hardware Bi-directional incremental evolution: basic concept - PowerPoint PPT Presentation
Citation preview
Bi-directional incremental Bi-directional incremental evolutionevolution
Dr Tatiana KalganovaDr Tatiana Kalganova
Electronic and Computer Electronic and Computer Engineering Dept.Engineering Dept.
Bio-Inspired Intelligent Systems Bio-Inspired Intelligent Systems GroupGroup
Brunel UniversityBrunel University
OutlineOutline
Evolutionary processEvolutionary process Evolvable hardwareEvolvable hardware Bi-directional incremental Bi-directional incremental
evolution: basic conceptevolution: basic concept Bi-directional incremental Bi-directional incremental
evolution in evolvable hardwareevolution in evolvable hardware Some applications of bi-directional Some applications of bi-directional
incremental evolutionincremental evolution
What is an evolution?What is an evolution?
Evolution
Chromosome:DNA
Chromosome:DNA
Selection
CrossoverMutation
What is an evolvable What is an evolvable hardware (EHW)?hardware (EHW)?
The logic circuit is designed using The logic circuit is designed using evolutionary algorithmevolutionary algorithm
Y 3
Y 2
Y 0
x 0 x 1 x 2 x 3
Y 1
mult2.pla
15
62
3
4
7
Y 4
3
mult28
5
9
10
Y 5
Y 3
Y 2
mult212
Y 1
Y 0
7
11
mult21
x 0 x 1 x 2 x 3 x 4x 5
mult3.pla
mult24
mult22
mult26
chromosome
chromosome
Evolution
Selection
CrossoverMutation
Circuit design problem in Circuit design problem in evolvable hardwareevolvable hardware
Tested logic function
X1 X2 … XN Y1 Y2 … YM 0 0 … 1 1 0 … 0 0 1 … 1 0 1 … 0
. .
. .
. . 1 1 … 1 1 1 … 0
Logic circuit
Inputs X1 X2 … XN 0 0 … 1 0 1 … 1
.
.
. 1 1 … 1
Outputs Y1 Y2 … YM 0 1 … 1 0 1 … 1
.
.
. 1 1 … 0
Input1: Logic function Input2: Logic circuit Output: Test v's function
““Stalling” effect in Stalling” effect in evolutionary processevolutionary process
Circuit functionality fitness, F1
75
80
85
90
95
1001
316
631
946
1261
1576
1891
2206
2521
2836
3151
3466
3781
4096
4411
4726
The number of generations
Cir
cuit
fu
nct
ion
ali
ty
fitn
ess
, F
1
Circuit functionality fitness, F1
Mult2.pla - 5.000 generationsMult3.pla – 16.000.000 generationsMult4.pla - ? … 150.000.000.000 ?
““Stalling” effect in Stalling” effect in evolutionary processevolutionary process
REASON:REASON: the task is too complex the task is too complex to solve at once. to solve at once.
SOLUTION:SOLUTION: introduce the new introduce the new evolutionary process once the evolutionary process once the “stalling” effect is appeared“stalling” effect is appeared
IMPLEMENTATION:IMPLEMENTATION: the new fitness the new fitness function is used for each function is used for each evolutionary processevolutionary process
Bi-directional Incremental Bi-directional Incremental EvolutionEvolution
IDEA:IDEA: two directions of evolution to two directions of evolution to obtain the desired solutionobtain the desired solution
CONCEPT:CONCEPT: evolve the system from evolve the system from complex to simple and optimise using complex to simple and optimise using evolution from simple to complexevolution from simple to complex
REQUIREMENTS:REQUIREMENTS: knowledge of system knowledge of system evolved and identification of heuristicsevolved and identification of heuristics
SUCCESS:SUCCESS: use of simple different use of simple different evolutionary processes identified by evolutionary processes identified by various heuristicsvarious heuristics EXAMPLE:EXAMPLE: evolvable hardware evolvable hardware
Bi-directional Incremental Bi-directional Incremental EvolutionEvolution
Stage 1:Stage 1: Evolution Evolution towards a towards a modularised modularised systemsystem
IDEA:IDEA: Evolution Evolution performs from performs from complex system complex system to sub-systemsto sub-systems
Stage 2:Stage 2: Evolution Evolution towards an towards an optimised systemoptimised system
IDEA:IDEA: Evolution Evolution performs from performs from sub-systems to sub-systems to complex systemcomplex system
Bi-directional Incremental Bi-directional Incremental Evolution (BIE) in EHWEvolution (BIE) in EHW
Bidirectional Incremental EvolutionE
v ol
utio
n to
war
dsm
odul
aris
ed s
yste
m
Evo
lutio
n to
war
dsop
timis
ed s
yste
m
Complex circuit,S
...
Standardfunctional
decomposition
EHW-orienteddecomposition
Assembling
S1 S2 Sk
Simpler sub-circuits
Bi-directional Incremental Bi-directional Incremental Evolution (BIE) for EHWEvolution (BIE) for EHW
IdeaIdea
Evolve the system Evolve the system gradually using gradually using decomposition methodsdecomposition methods
1) Decompose the system into 1) Decompose the system into sub-systemssub-systems
2) Evolve each sub-system 2) Evolve each sub-system separatelyseparately
3) Assemble the complex 3) Assemble the complex systemsystem
4) Evolve the complex system4) Evolve the complex system
AdvantagesAdvantages• Evolving the Evolving the
circuits of the large circuits of the large number of number of variablesvariables
• Evolving the Evolving the circuits of any circuits of any complexitycomplexity
• No restrictions on No restrictions on the application the application tasktask
EVOLVE:an extrinsic EHW
Result: C b0 (T 0)
Keep the genotypeof the best
chromosomeC b0 (T 0)
Define an outputpartitioning vector, vo
and an productpartitioning vector, vp
Generate the truthtable, T 1I(n, | vp|),
O (|vo|, |vp|)
Generate the truthtable, T 2
I(n , p-| vp|),O (|vo|, p-| vp|)
Generate the truthtable, T 3I(n , |vp|),
O (m -|vo|, |vp|)
EVOLVE:an extrinsic EHW
Result: C b1(T 1)
T 0
IP (R )
IP (C b0(T 0)) EVOLVE:an extrinsic
EHWResult: C b3 (T 3)
T 1T 3
IP (R )fo(vo) and f io (v io)
for T 2 from T 0 arehigh ?
EVOLVE:an extrinsic
EHWResult: C b2 (T 2)
Fully functionalsolution for T 1 isgenerated. ( S 1)
IP (C b0(T 0))
Yes
NoEVOLVE:
an extrinsicEHW
Result: C b2 (T 2)
IP (R )
Fully functionalsolution for T 2 isgenerated ( S 2).
T 0=T 2C b0 (T 0)=C b2 (T 2)
fo(vo) and f io (v io)for T 3 from T 0 are
high ?
NoYes
EVOLVE:an extrinsic
EHWResult: C b3 (T 3)
IP (C b0(T 0))
Fully functionalsolution for T 3 isgenerated ( S 3).
EVOLVE:an extrinsic
EHWResult: C b3 (T 3)
IP (R )
T 0=T 3C b0 (T 0)=C b3 (T 3)
Generate thetruth table T 0 of
complexsystem, S 0
BIEBIEin EHWin EHW Gate
ArrayX
F
x 1x 2
x n
f1f2
fm
Evolved system
GateArray 1
X
x 1x 2
x n
f1f2
fm1
F1
GateArray sX
x 1x 2
x n
f1f2
fms
Fs
Output decomposition
GateArray 1
X 1
x 1x 2
x n1
h 1h 2
h k1
H 1
GateArray 2
X 2
x 1x 2
x n2
h 1h 2
h k2
H 2
Input decomposition
GateArray S f1
f2
fm
X s
x 1x 2
x ns
F
GateArray 1
x 1x 2
x n
f1f2
fm
GateArray s
X
x 1x 2
x n
f1f2
fm
Shannon decomposition
F
f1f2
fm
x 1x 2
x n
Evolved sub-systems
BIE:BIE:EHW-oriented EHW-oriented decompositiondecomposition
S i(n, m, p)(F 1 )
S 0 (7, 10, 128)(F 1 )
S 1 (7, 3, 128)(F 2 )
S 2 (7, 7, 128)(F 1 )
S 3 (7, 3, 128)(F 1 ), (F 2 )
S 4 (7, 4, 128)(F 1 )
S 8 (7, 1, 128)(F 1 ), (F 2 )
S 7 (7, 1, 128)(F 1 ), (F 2 )
S 5 (7, 1, 128)(F 1 ), (F 2 )
Diagram of evolving logicfunction of 7-inputs and 10outputs (z5xp1_d.pla) using
DCE with EHW-oriented outputdecomposition
S 6 (7, 3, 128)(F 1 )
Evolution towards amodularised system
Evolution towards anoptimised system
S 9 (7, 1, 128)(F 1 ), (F 2 )
BIE: sub-circuit allocationBIE: sub-circuit allocation
Evolution towards anoptimised system
Diagram of evolving logicfunction of 7-inputs and 10outputs (z5xp1_d.pla) usingincremental evolution withEHW-oriented output and
Shannon's decompositions
S 3 (7, 2, 64)(F 1 ), (F 2 )
Evolution towards amodularised system
S 6 (7, 1, 64)(F 2 )
S 7 (7, 1, 64)(F 1 ), (F 2 )
S 5 (7, 1, 128)(F 2 )
S 8 (7, 3, 128)(F 1 )
S 1 1 (7, 1, 64)(F 2 )
S 1 0 (7, 2, 64)(F 1 ), (F 2 )
S 9 (7, 2, 64)(F 2 )
S 1 2 (7, 1, 64)(F 1 ), (F 2 )
S 4 (7, 5, 128)(F 1 )
S 0 (7, 10, 128)(F 1 )
S i(n, m, p)(F 1 )
S 1 (7, 3, 128)(F 2 )
S 2 (7, 2, 64)(F 2 )
Direct and incremental Direct and incremental evolutionsevolutions
10 000 20 000 30 000 40 000 50 000 60 000 70 000 80 000
60
70
80
90
100S 0 S 2 S 3 S 4 S 5 S 6 S 7 S 8 S 9
Generations
Circ
uit
fu
nct
ion
alit
y
500
Performance of direct and bidirectional incremental evolutionStage 1: Synthesis of the fully functional circuit
IncrementalDirect
BIE in applicationsBIE in applications
Evolution of complex Evolution of complex combinational logic circuitscombinational logic circuits
Optimisation of control the Optimisation of control the fermentation processfermentation process
Prediction in investment appraisalPrediction in investment appraisal
BIE in prediction in BIE in prediction in investment appraisalinvestment appraisal
Problem:Problem:• Design an Intelligent System for Risk Design an Intelligent System for Risk
Classification of Stock Investment Classification of Stock Investment ProjectsProjects
Training networkTraining network
An effective bi-directional An effective bi-directional evolutionary strategy is evolutionary strategy is elaborated, as direct evolution fails elaborated, as direct evolution fails to rich a solution to the complex to rich a solution to the complex problem of optimising the weights problem of optimising the weights and shift terms in the fuzzy and shift terms in the fuzzy network over a set of investment network over a set of investment projects. projects.
BIEBIE
The strategy involves a decomposition The strategy involves a decomposition and an incremental part. and an incremental part.
The integral problem is first divided into The integral problem is first divided into subtasks of decreasing complexity by subtasks of decreasing complexity by partitioning accordingly the training set partitioning accordingly the training set of projects. of projects.
Then the subtasks are merged Then the subtasks are merged incrementally to optimise the integral incrementally to optimise the integral solution.solution.
Training partitioningTraining partitioning
{pro jec t 1 , p ro jec t 2 ,p ro jec t 3 ,p ro jec t 4 , p ro jec t 5 , p ro jec t 6 }
{pro jec t 1 }{pro jec t 2 , p ro jec t 3 ,p ro jec t 4 , p ro jec t 6 }
{pro jec t 6 }{pro jec t 2 , p ro jec t 3 ,
p ro jec t 4 }
{pro jec t 3 ,p ro jec t 4 }evo lu tion towards
decreasingcom plexity tasks
evo lu tion towardsincreasing
com plexity tasksfu ll-s ize tra in ing se t
{pro jec t 5 }firs t-leve lpartition ing
{pro jec t 2 , p ro jec t 3 ,p ro jec t 4 }
{pro jec t 2 , p ro jec t 3 ,p ro jec t 4 , p ro jec t 6 }
second-leve lpartition ing
{pro jec t 2 }th ird -leve lpartition ing
firstincrem enta l
leve l
secondincrem enta l
leve l
th irdincrem enta l
leve l
Training-set partitioning and increment during bidirectional incremental evolutionDecomposition part: the training set is partitioned at several levels, evolving the fuzzy network towards tasks with decreasing complexity.Incremental part: the training subsets are merged incrementally in reverse direction, evolving the network towards solving the integral problem.A dynamic objective function is applied at each decomposition and incremental level.
BIE resultsBIE results
Performance of bidirectional incremental evolution and direct evolution in maximum fitness per generationBlack line: bidirectional incremental evolution advances through several decomposition and incremental tasks and solves the general problem in 148,243 generations.Lighter line: direct evolution makes some initial progress and then stalls.
30000 60000 90000 120000 1500000
10
20
30
40
50
60
70
80
90
100
Generations
RF
NN
Fu
ncti
on
ality
20
00
0
projects 1,2,3,4,5,6
39
01
4
project 1
62
47
9
project 5
72
47
9
2,3,4,6 6
77
62
6
projects 2,3,4
12
76
26
342
234
2346
1,2,3,4,5,6
14
82
43
13
27
62
incr
emen
t
al p
art
decomposition part
direct evolution
bidirectional incremental evolution
Experimental resultsExperimental results
The bi-directional strategy evolves The bi-directional strategy evolves a fully functional fuzzy network in a fully functional fuzzy network in 148,243148,243 generations. generations.
Direct evolution reaches only Direct evolution reaches only 46.33%46.33% maximum fitness in maximum fitness in 500,000500,000 generations. generations.
Thus, the empirical results prove Thus, the empirical results prove decisively the efficiency of the decisively the efficiency of the developed evolutionary strategy.developed evolutionary strategy.
Some resultsSome results
In all applications mentioned In all applications mentioned earlier it has been obtained that earlier it has been obtained that the optimal solution has been the optimal solution has been obtained at least in 100 times obtained at least in 100 times quicker then using standard quicker then using standard evolutionevolution
The quality of evolved solution in The quality of evolved solution in this case remains the samethis case remains the same
BIE in applications: BIE in applications: SummarySummary
Design of complex combinational Design of complex combinational circuitscircuits
Use of Use of • Decomposition methodsDecomposition methods• Evolutionary strategyEvolutionary strategy
BIE in applications: BIE in applications: SummarySummary
Prediction in investment appraisalPrediction in investment appraisal
Use of Use of • Decomposition methodsDecomposition methods• Automatic re-scaling fitness functionAutomatic re-scaling fitness function• Neural networkNeural network• Fuzzy logicFuzzy logic
ConclusionConclusion
Bi-directional incremental evolution Bi-directional incremental evolution is the technique that can be used in is the technique that can be used in evolution of complex systemsevolution of complex systems
BIE allows to use evolutionary BIE allows to use evolutionary algorithms in both online and offline algorithms in both online and offline calculationscalculations
BIE can be used in large range of BIE can be used in large range of applicationsapplications
Recommended