By Ping-Chu Hung Advisor: Ying-Ping Chen

 Introduction: background and objectives  Review of ECGA  ECGA for integer variables ◦ Experiments and performances  ECGA for real numbers  ECGA on characteristic determination  Future work and conclusions 2

 Flow Chart of GAs  Building blocks: the key to success Individuals Good Individuals (Parents) Good Individuals (Parents) evaluation and selection crossover and mutation 3

 If a function can be decomposed into several nonlinear sub-functions, we say that variables in the same sub-function have linkage between them.  A building block is a set of variables that have linkage between them.  The key for GAs to success is keeping good schema and abandon bad schema  In practical use, schemas are often broken by crossover 4

 Flow Chart of EDAs  ECGA(1999) is one of the most advanced EDAs Individuals Good Individuals (Parents) Good Individuals (Parents) evaluation and selection Probability Model Probability Model modeling sampling 5

 GAs and EDAs are commonly based on binary strings  To solve integer and real number problems, we intuitively encode variables as binary strings  Variables encoded as binary strings will induce extra linkages  GAs are incapable of solving linkage problems, but how about EDAs? 6

 Extend ECGA to different variable types ◦ Integer: modify the probability model ◦ Real value: based on iECGA, split-on-demand  Evaluate the performance of iECGA ◦ iECGA outperforms ECGA in integer deception problems  Apply real-coded ECGA on a real-world application ◦ Characteristic determination problem 7

 Introduction: background and objectives  Review of ECGA  ECGA for integer variables ◦ Experiments and performances  ECGA for real numbers  ECGA on characteristic determination  Future work and conclusions 8

 A probability model contains two factors ◦ How to represent probability models? ◦ How to judge the quality of probability models?  ECGA ◦ Represent models as marginal product models (MPMs) ◦ Judge models by minimum description length (MDL) principle 9

[0,3][1][2] AlleleCountAlleleCountAlleleCount Population [1,2][0][3] AlleleCountAlleleCountAlleleCount

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 Flow Chart of ECGA Individuals Good Individuals (Parents) Good Individuals (Parents) evaluation, tournament selection MPMs modeling sampling 12 Greedy MPM search MDL as criterion Building-block- wise Crossover

 Introduction: background and objectives  Review of ECGA  ECGA for integer variables ◦ Experiments and performances  ECGA for real numbers  ECGA on characteristic determination  Future work and conclusions 13

 Given an integer ranged from 0 to 15, the integer will be encoded as a four-bit binary string  These four bits intuitively form a building block  If several integers have linkage between them, ECGA have to solve a two-level linkage problem 14

 Individuals as integer vectors  Modified MPM  Modified model complexity [0,1][2] AlleleCountAlleleCount Population

 To test the effect of encoding, we have two kinds of objective function ◦ No linkage at integer level, but linkage at bit level ◦ Linkage at both level  Comparison between iECGA, ECGA, and integer coded GA 16

 No linkage at integer level, but linkage at bit level  f ₁(x) is deceptive function in bit level. Fitness of f ₁(x) is the number of 1’s in binary form of x 17

 Linkage at both level (u is the upperbound) 18

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size of BBsorder of BBs BB at bit levelBB at integer level f₁f₁ 4 bits1 1 f₂f₂ 28 bits2 f₃f₃ 3 bits39 bits3 f₄f₄ 2 bits48 bits4 20

 Population size:  Crossover ◦ Uniform crossover in GA ◦ BB-wise crossover in ECGA and iECGA  Mutation ◦ No mutation in ECGA and iECGA ◦ Mutation rate 0.1 in GA  Selection ◦ Tournament selection  Modeling ◦ Maximum building-block size in ECGA: 15 bits 21

Fitness Function bits 22

Fitness Function bits 23

Fitness Function bits 24

Fitness Function bits 25

Convergence speed for Fitness Function 4 26

 Why iECGA performs better than GA? ◦ Good schemas are preserved ◦ Higher convergence speed  Why ECGA fails in integer domain? ◦ Greedy MPM search is incapable to find out hierarchical building blocks ◦ The linkage between integers may not propagate to the bit level  Why function 3 is harder than others? functioncardinalityorder of BBs f₂f₂ f₃f₃ f₄f₄

 Introduction: background and objectives  Review of ECGA  ECGA for integer variables ◦ Experiments and performances  ECGA for real numbers  ECGA on characteristic determination  Future work and conclusions 28

Real-number Individuals Real-number Individuals Good Real-Number Individuals Good Real-Number Individuals tournament selection tournament selection Good Integer Individuals Good Integer Individuals Split-on- Demand (Chen et. al., 2006) Split-on- Demand (Chen et. al., 2006) random sampling random sampling MPM model greedy MPM search 29

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(0,0) (3,5) (1,4) 32

higher density in better area 33

 Introduction: background and objectives  Review of ECGA  ECGA for integer variables ◦ Experiments and performances  ECGA for real numbers  ECGA on characteristic determination  Future work and conclusions 34

 When we design and fabricate a new solid state device, the extrinsic properties can be measured, but the intrinsic properties are unknown ◦ Measure extrinsic properties first ◦ Then evaluate intrinsic properties  Why we need intrinsic properties? ◦ For simulation software ◦ Control the quality of the poly-Si film 35

Put voltage on gate 36

 What we can measure? ◦ Given a V G, we can measure an E a  What we want to get? ◦ The values of N d, S d, E td, N t, E tt 37

101 (V G, E a ) pairs Real-coded ECGA 5 variables objective value calculate approximate value of Ea sum up the difference between approximate value and experimental value 38 Objective Function

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 What we can measure? ◦ Given a V G, we can measure an E a  What we want to get? ◦ The values of N d, S d, E td, N t, E tt, N i, E it 41

ELA 42

SSL 43

FLA 44

SPC 45

 The equivalent circuit of gate/SiO ₂/poly-Si structure bulkinterface oxide 46

 What we can measure? ◦ Given a frequency ω and a gate bias V G, we can measure the value of C eq  Properties of interface (D it, τ it ) ◦ Independent of frequencies, but depend on gate biases  Properties of bulk (D s, τ s ) ◦ Independent of both frequencies and gate biases 47

22 variables: 2 common bulk properties and 20 interface properties 70 input values: 7 frequencies vs. 10 gate biases 48

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 Introduction: background and objectives  Review of ECGA  ECGA for integer variables ◦ Experiments and performances  ECGA for real numbers  ECGA on characteristic determination  Future work and conclusions 50

 Hierarchical building blocks  Overlapped building blocks  Mutation operator ◦ Building-block-wise mutation operator on ECGA  Other representations ◦ Gray code 51

 Extend ECGA to different variable types ◦ Integer: modify the probability model ◦ Real value: based on iECGA, split-on-demand  Evaluate the performance of iECGA ◦ iECGA outperforms ECGA in integer deception problems  Apply real-coded ECGA on a real-world application ◦ Characteristic determination problem 52