Bat algorithm for Topology Optimization in Microelectronic Applications

Bat Algorithm for Topology Optimizationin Microelectronic Applications

Xin-She Yang, Mehmet Karamanoglu and Simon Fong

@ FGCT2012

Yang,Karamanoglu,Fong (NPL) Bat Algorithm @ FGCT2012 1 / 14

Introduction Topology/Shape Design

Topology/Shape Design

Given a geometry (say, a rectangle), how to distribute two differentmaterials, with thermal conductivities K1 and K2, respectively, so as tomeet a specific design problem for heat transfer applications?

To maximize |TA − TB |?


Introduction Should we use different methods for different problems?

Should we use different methods for different problems?

Changing the landscape:Space mapping, surrogate, trust-region, dimension reduction ...


Introduction Bat Algorithm, Developed by Xin-She Yang (in 2010)

Bat Algorithm, Developed by Xin-She Yang (in 2010)

BBC Video

Microbats use echolocation for hunting

Ultrasonic short pulses as loud as 110dB with a short period of 5 to20 ms. Frequencies of 25 kHz to 100 kHz.

Speed up the pulse-emission rate, and increase loudness, whenhoming at a prey.


Introduction Bat Algorithm (Yang 2010)

Bat Algorithm (Yang 2010)

Acoustics of bat echolocation

λ =v

f∼ 2 mm to 14 mm.

Rules used in the bat algorithm:

fi = fmin + (fmax − fmin)β, β ∈ [0, 1],

vt+1i = v t

i + (xti − x∗)fi , xt+1

i = xti + vt

i .

Variations of Loudness and Pulse Rate

At+1i ← αAt

i , α ∈ (0, 1],

r t+1i = r0

i [1− exp(−γt)].


Introduction Bat Algorithm (Yang 2010)

Bat Algorithm (Yang 2010)

Acoustics of bat echolocation

λ =v

f∼ 2 mm to 14 mm.

Rules used in the bat algorithm:

fi = fmin + (fmax − fmin)β, β ∈ [0, 1],

vt+1i = v t

i + (xti − x∗)fi , xt+1

i = xti + vt

i .

Variations of Loudness and Pulse Rate

At+1i ← αAt

i , α ∈ (0, 1],

r t+1i = r0

i [1− exp(−γt)].


Introduction Advantages

Advantages

Dynamic exploration and exploitation

Simple to implement, and it searches for optimality using frequencytuning.

Initially, BA focuses on more explorative moves, and then switch tomore exploitation when optimality is approaching.

Balance between exploration and exploitation is not static, it isdynamic!


Introduction Variants and Applications

Variants and Applications

Continuous optimization

Binary bat algorithm for image processing and classifications

Spam filtering

Training neural networks

Multobjective bat algorithm

Clustering ...


Introduction Speed Reducer/Gear Box Design

Speed Reducer/Gear Box Design

Mixed-Integer Programming:

Continuous variables and integers.


Introduction

f (x1, x2, x3, x4, x5, x6, x7) = 0.7854x1x22 (3.3333x2

3 + 14.9334x3 − 43.0934)

−1.508x1(x26 + x2

7 ) + 7.4777(x36 + x3

7 ) + 0.7854(x4x26 + x5x

27 ),

subject to

g1 = 27x1x2

2 x3− 1 ≤ 0, g2 = 397.5

x1x22 x2

3− 1 ≤ 0,

g3 =1.93x3

4

x2x3d41− 1 ≤ 0, g4 =

1.93x35

x2x3d42− 1 ≤ 0,

g5 = 1110x3

6

√(745x4

hx3)2 + 16.9× 106 − 1 ≤ 0,

g6 = 185x3

7

√(745x5

hx3)2 + 157.5× 106 − 1 ≤ 0,

g7 = x2x340 − 1 ≤ 0, g8 = 5x2

x1− 1 ≤ 0,

g9 = x112x2− 1 ≤ 0, g10 = 1.5x6+1.9

x4− 1 ≤ 0,

g11 = 1.1x7+1.9x5

− 1 ≤ 0.

Simple bounds are 2.6 ≤ x1 ≤ 3.6, 0.7 ≤ h ≤ 0.8, 17 ≤ x3 ≤ 28,7.3 ≤ x4 ≤ 8.3, 7.8 ≤ x5 ≤ 8.3, 2.9 ≤ x6 ≤ 3.9, and 5.0 ≤ x7 ≤ 5.5. zmust be integers.


Introduction

The best solution obtained by BA is

fmin = 2993.7495888,

withx∗ = (3.5, 0.7, 17, 7.3, 7.8, 3.34446445, 5.285350625),

which is better than the solution in the literature (Cagnina et al., 2008)

f∗ = 2996.348165.


Introduction Topology/Shape Design in Microelectronic Applications

Topology/Shape Design in Microelectronic Applications


Introduction Optimal Topology

Optimal Topology

Distributions of two materials (left) and temperature (right). The material(K2 � K1) in the middle has lower conductivity so that |TA − TB | ismaximum.

Temperature: Red=high, blue=low.Yang,Karamanoglu,Fong (NPL) Bat Algorithm @ FGCT2012 12 / 14

Introduction Change of Objective Leads to Different Topology

Change of Objective Leads to Different Topology

Now the objective is to maximize |TA − TB | where A and B are on thehorizontal middle axis.

Temperature: Red=high, blue=low.


Introduction Bibliography

Bibliography

A. Evgrafov, K. Maute, R. G. Yang and M. L. Dunn, Topology optimizationfor nano-scale heat transfer, Int. J. Num. Methods in Engrg., 77 (2),285-300 (2009).

X. S. Yang, A New Metaheuristic Bat-Inspired Algorithm, in: NatureInspired Cooperative Strategies for Optimization (NISCO 2010) (Eds. J. R.Gonzalez et al.), Studies in Computational Intelligence, Springer Berlin, 284,Springer, 65-74 (2010).

X. S. Yang, bat algorithm for multi-objective optimisation, Int. J.Bio-Inspired Computation, Vol. 3, 267-274 (2011).

X. S. Yang, Engineering Optimization: An Introduction With MetaheuristicApplications, John Wiley and Sons, USA, (2010).

V. V. Zhirnov, R. K. Cavin, J. A. Hutchby, G. I. Bourianoff, Limits to binarylogic switch scaling - a gedanken model, Proc. of the IEEE, 91(11),1934-1939 (2003).

Thank you very much :)Yang,Karamanoglu,Fong (NPL) Bat Algorithm @ FGCT2012 14 / 14

Education

Bat algorithm for Topology Optimization in Microelectronic Applications