Bat algorithm for Topology Optimization in Microelectronic Applications

Bat Algorithm for Topology Optimization
in 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 diﬀerent
materials, with thermal conductivities K1 and K2 , respectively, so as to
meet 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 to
20 ms. Frequencies of 25 kHz to 100 kHz.
Speed up the pulse-emission rate, and increase loudness, when
homing at a prey.


Introduction Bat Algorithm (Yang 2010)

Bat Algorithm (Yang 2010)

Acoustics of bat echolocation
v
λ = ∼ 2 mm to 14 mm.
f
Rules used in the bat algorithm:

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

vt+1 = vit + (xt − x∗ )fi ,
i i xt+1 = xt + vt .
i i i


Introduction Bat Algorithm (Yang 2010)

Bat Algorithm (Yang 2010)

Acoustics of bat echolocation
v
λ = ∼ 2 mm to 14 mm.
f
Rules used in the bat algorithm:

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

vt+1 = vit + (xt − x∗ )fi ,
i i xt+1 = xt + vt .
i i i

Variations of Loudness and Pulse Rate
At+1 ← αAt ,
i i α ∈ (0, 1],
rit+1 = ri0 [1 − exp(−γt)].


Introduction Advantages

Advantages

Dynamic exploration and exploitation
Simple to implement, and it searches for optimality using frequency
tuning.
Initially, BA focuses on more explorative moves, and then switch to
more exploitation when optimality is approaching.
Balance between exploration and exploitation is not static, it is
dynamic!


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

2 2
f (x1 , x2 , x3 , x4 , x5 , x6 , x7 ) = 0.7854x1 x2 (3.3333x3 + 14.9334x3 − 43.0934)
2 2 3 3 2 2
−1.508x1 (x6 + x7 ) + 7.4777(x6 + x7 ) + 0.7854(x4 x6 + x5 x7 ),
subject to
27 397.5
g1 = 2
x1 x2 x3
− 1 ≤ 0, g2 = 2 2
x1 x2 x3
− 1 ≤ 0,
1.93x 3 1.93x5 3
g3 = x x d44 − 1 ≤ 0, g4 = 4
x2 x3 d2
− 1 ≤ 0,
2 3 1

g5 = 110x 3 ( 745x4 )2 + 16.9 × 106 − 1 ≤ 0,
1
hx3
6
1 745x5 2
g6 = 85x 3 ( hx3 ) + 157.5 × 106 − 1 ≤ 0,
7
g7 = x403 − 1 ≤ 0,
2x
g8 = 5x12 − 1 ≤ 0,
x
x1
g9 = 12x2 − 1 ≤ 0, g10 = 1.5xx4
6 +1.9
− 1 ≤ 0,
g11 = 1.1xx57 +1.9
− 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. z
must be integers.


Introduction

The best solution obtained by BA is

fmin = 2993.7495888,

with
x∗ = (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 | is
maximum.

Temperature: Red=high, blue=low.

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 the
horizontal middle axis.

Temperature: Red=high, blue=low.

Introduction Bibliography

Bibliography
A. Evgrafov, K. Maute, R. G. Yang and M. L. Dunn, Topology optimization
for 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: Nature
Inspired 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 Metaheuristic
Applications, John Wiley and Sons, USA, (2010).
V. V. Zhirnov, R. K. Cavin, J. A. Hutchby, G. I. Bourianoﬀ, Limits to binary
logic switch scaling - a gedanken model, Proc. of the IEEE, 91(11),
1934-1939 (2003).

Thank you very much :)

Bat algorithm for Topology Optimization in Microelectronic Applications

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