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Binomial RTR with Linkage learning . Presenter: Tsung -Yu Ho 2011.09.22. A story about Niching . Signing Baseball Players. What is Niching ?. After regular season, every team’s manager is worried about signing Free Agent (FA). . [SALARY]. High. A. Pujols. P. Fielder. High. - PowerPoint PPT Presentation
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Binomial RTR with Linkage learning
Presenter: Tsung-Yu Ho2011.09.22
A story about Niching What is Niching ?
Signing Baseball PlayersAfter regular season, every team’s manager is worried about signing Free Agent (FA).
ABILITY
SALARY(Demand)
High
LowGoodBad
A. PujolsP. FielderR. Cano
J. ReyesH. BellJ. FrancisH. Kuroda王建民Matsui B. Webs
[SALARY]High
Low
2012 FAs
Reduce to one axis
Strategy?
Strategy for Keeping BestBoston Red Sox CEO Larry Lucchino says Yankees is the “ evil empire”
2012
FAs
2011
FAs2010
FAs
2009
FAs
2008
FAs
High
Low
Evil Empire
Strategy for Preserving LocalA movie “Moneyball” shows different strategy by using Implicit Function to find suitable player.
High
Low
Free Agents
Choose local windows
Use Implicit Function
MoneyballTeam
Discussion of StrategyBaseball management is a complicated game that hardly knows the optimal strategy. Here are two points that we should consider.
Keep current optima not always lead to find global optima. Allow some local solutions may improve the
performance.
The estimated metric is important For example, play’s salary is not a good judgment. There are many different metrics to make different
result.
Niching on Optimization
Optimization without Niching
Optimization with Niching Hierarchical
Flow Diagram
SGA
selection
Cross over
Model-based GA
+ Model-Building S XO
ModelBuildin
gRTR
CPF
Solve
Exponential
(hBOA)
Polynomial(CGA, ECGA)
Reason
Reason
ResultsShow
Show
1 2
34
5
RTRWeaknessAssumption Binomial
RTRModification
6
+ EDAs, result again CPF
Model-Building(1)Trap Functions, k=5
u(x) 0 51 2 3 4
FitnessFitness
1111110111100111001000010
10.8
00000
11111 xxxxx xxxxxx
00000 xxxxx xxxxxx
NumberXO
11000
00111
11111 xxxxx xxxxxx
00000 xxxxx xxxxxx
0.5N
0.5N
N
0
Increase 00000
Model-Building(2)Avoid disruption by XO
11111 00000 11111
1 1 1 1 1
0 0 0 0 0 0 0 0 0 0
00000 00000 11111
1 1 1 1 1
1 1 1 1 1
Pair-wise Linkage Learning after selection
0 0 0 0 0 ‘11’ = ‘1’
‘00’ = ‘0’
11111 00000 11111
00000 00000 11111
1 0 1 0 0 1
Model-Building with RTR
RTR keeps 000 and 111 in Hierarchical Problem
000
111 111
0 1 1
1
F1(000 111 111)
F2(011) > F2(111)
111
RTR Algorithm
Example少林寺招收新血 , 舉辦比武大會
希望提升整體實力 , 並維持等比例的武藝 .(A, B, C, D, E 表示武力等級 )
B A B C E DD C D D A D EB
(少林寺 ) (參賽者 )
Random
C
B
A
C
Example少林寺招收新血 , 舉辦比武大會
希望提升整體實力 , 並維持等比例的武藝 .(A, B, C, D, E 表示武力等級 )
B A B E DDC D D A D EB
(少林寺 ) (參賽者 )
Random
DDD
CB
Example少林寺招收新血 , 舉辦比武大會
希望提升整體實力 , 並維持等比例的武藝 .(A, B, C, D, E 表示武力等級 )
B B EDC E
(少林寺 ) (參賽者 )
A D
B A B C E DD
NEW
Original
Discussion of RTRModel-Building according to some distribution
Probability
Fitness
Probability
Fitness
Before selection and RTR
After selection and RTR
Lead to different model building
CPF(1)Concatenated parity function
Single BB, where F(ueven) =2 and F(uodd) = 0.
0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1
AfterSelection
(s=2)
0 0 0 0 0 0 0 1 1 0 1 1 1 1 0 1 1 0 1 0 1 1 0 1
P(00) = P(11) = P(10) = P(01) = 0.25No dependency between the pair
CPF(2)EDAs with pairwise linkage learning can not detect any k>1 linkage on CPF.
0 0 00 0 00 1 10 1 11 1 01 1 0
1 0 1 1 0 1
0 0 0 0 0 1 0 1 0 1 0 0 0 1 1 1 0 1 1 1 0 1 1 1
After RTR
Parent Population
Offspring Population
Window size = 4
0 0 0 0 0 0 0 1 1 1 1 0 0 1 1 1 0 1 1 1 0 1 1 1
Dependency increase
Spurious LinkageSpurious Linkage
Add linkage on the independent pair.RTR produce spurious linkage
Preserved local solutions change the expected distribution Model-building works on inaccuracy distribution and produces spurious linkage
However, selection can decrease the bias on distribution
EDAs with RTR solve most problems in polynomial timeException for hBOA on CPF
hBOA is a powerful EDA RTR is hard to understand It is mysterious?
Experiment ResultsTest EDAs on CPF
CGA, ECGA, and hBOACGA
No linkage learning, no RTR Polynomial time
ECGA has linkage learning, no RTR Polynomial time
hBOA Has linkage learning and RTR Exponential time
The difficulty of CPF EDAs(pairwise) can not learn linkage on CPF
CPF is a difficulty problem ?
CGA can solve CPF in polynomial time The performance of CGA is similar to SGA CPF is a easy problem ?
Summary What is real linkage for EDAs is unclear. If EDAs can solve CPF without any linkage structure in
polynomial time, CPF is like a one max problem.
Converge of CGA on CPF(1)
Too many Global Optima A (CPF problem
Drift 00 and 11 are global optima One of Shemata with bias will converge.
Converge of CGA on CPF(2)
F(uodd) > F(ueven)
1 1 1 0 0 1 0 1 0 1 0 0
Probability
0.25
0.250.25
0.25
Probability + bias
Unclear of RTR RTR use Hamming distance to detect two similar genes.
It has less relation in linkage-learning.
Trap Problem (k=4)
Fitness1.60.8
Distance = 2
0 1 0 0 1 1 1 1 0 1 1 1 0 0 0 0 1 1 0 1 0 1 1 1
0.6 1
0.8
0
0
0
Binomial distribution supports sequence of n independent elements.If we have n independent bits in the problem, binomial distribution of population can make sure no dependent linkage.In fact, because the bias, it is hard to form the idea distribution.However, niching can approach what we need.
Idea Distribution
Binomial DistributionProbability = Average Fitness of populationNumber = Population sizeParent + Offspring form binomial population.
Fitness
Binomial with linkage RTR is not meaningful for linkage learning Linkage can reduce to a single bit BB.The binomial distribution can be implemented on linkage structure.
1 1 0 1 0 1 10 1
1 1 0 1 0 1 10 1 3 BBs
9 BBs
Modification of RTRRTR use Hamming distance
111…111 000…000
Distance(i,j)
FHigh FLow
Distance(i,j) > EquDistance(Fi,Fj)
Modification consider fitness and distance
P
P P
Binomial RTR(1)Fitness-based
Fitness => Rank (r1, r2, r3, … rN) => Rank (0.01, 0.02, …, 0.98, 0.99)
Model-building based Match “most frequency shema” => +1
Because we don’t what is optima
0 0 0 0 0 1 1 1 0 1 1 1
(0 0 0) (0 0 0) (1 1 0) (1 1 1)
+1 +1 +1
Most Frequency Shema
ith population
ri =
Binomial RTR(2)
Parent (i)Population
1
51014
1
Offspring(j) Population
𝑃 (𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 (𝑖 , 𝑗 )=𝐸𝑞𝑢𝑖𝑏𝑖𝑙𝑒𝑛𝑡 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒(𝑟𝑖 ,𝑟𝑗))
ConclusionRTR is well-used for most EDAs because of its well performance.RTR has some weakness
Poor on allelic pairwise independent functions (CPF) Hard to understand the relation between with RTR Do not consider solution quality
BRTR has some advantage Similar as RTR Use binomial distribution to keep solution Consider both fitness and similarity.
