CS 285 MEMS Design usingGenetic Algorithms Carlo H. Séquin EECS Computer Science Division University of California, Berkeley
Genetic Algorithms • Pursue several design variations in parallel(many phenotypes in each generation) • Evaluate their “fitness” (how well they meet the various design objectives Pareto set) • Use best designs to “breed” new off-springs(by modifying / combining their genes) • Expectation: Good traits will stick around,bad solution will be weeded out ...
The “genome” is the ultimate parameterization of a design,given the proper procedureto interpret that code • Without the proper framework, the genome is meaningless. (e.g., human DNA on a planet in the Alpha-Centauri System)
An Experiment Let ME students design a MEMS resonator • Students (initially) had no IC experience • Good programmers • Excited about Genetic Algorithms
Micro-Electromechanical SystemsMEMS • Created with a somewhat enhanced fabrication technology used for integrated circuits. • Many nifty devices and systems have been built: motors, steerable mirrors, accelerometers, chemo sensors ...
The Design of a MEMS Resonator • Filters • Accelerometers • Gyroscopes Prevent horizontaloscillations ! Resonate vertically at desired frequency
Basic MEMS Elements Beam H-shaped center mass Anchor to substrate Comb drive
A General Set-Up for Optimization • Poly-line suspensions at 4 corners. • Adjust resonant frequency F • Get Kx Ky into OK ranges • Minimize layout area
Need an Electro-Mechanical Simulator ! “SUGAR” “SPICE for the MEMS World” (open source just like SPICE) DESIGN Fast,Simple,Capable. MEASUREMENT SIMULATION
A Possible Phenotype • Adjust resonant frequency to 10.0 ± 0.5 kHz • Bring Kx / Ky into acceptable range ( >10 ) • Minimize size of bounding box; core fixed
MEMS Actually Built and Measured
Genetic Algorithm in Action ! • Area = 0.181 mm2; Kx/Ky = 12
Use 4-Fold Symmetry ! • 1st-order compensation of fabrication variations
Using 4-fold Symmetry • Faster search ! Area = 0.171 mm2; Kx/Ky = 12
X,Y-Symmetry; Axis-Aligned Beams • Area = 0.211 mm2; Kx/Ky = 118
Introduce Serpentine Element • A higher-order composite subsystemwith only five parameters: N , Lh, Wh, Lv, Wv Wv Wh Lv Lh N=3
Proper Use of Serpentine Sub-Design • That is what we had in mind ...
Reduce X-dimension of layoutby introducing more serpentine loops Proper Use of Serpentine Element • Area = 0.143 mm2; Kx/Ky = 11
soft Kx flare out Trying to Reduce Area • Area = 0.131 mm2; Kx/Ky = 4 !!
Increasing Stiffness Kx • Connecting bars suppress horizontal oscillations • But branched suspensions may not be expressible in genome ( = underlying data structure ).
Using Cross-Linked Serpentines • Area = 0.126 mm2; Kx/Ky = 36 PROFESSIONAL DESIGN
Why Does the G.A. Not Find This ? • Lack of expressibility of genome. • Solution space too large, too rugged ... • Sampling is too sparse ! • Samples are not driven to local optima.
“Holey” Fitness Space • Open-ended engineering problems have complicated, higher-dimensional solution / fitness spaces.
20. Generation – drifting to higher ground 1. Generation – a random sampling 50. Generation – clustered near high mountains A Rugged Solution Space • No phenotype is on the top of a peak • Good intermediate solutions may get lost
What really happened here ? • Major improvement steps came by engineering insights. • Genetic algorithm found good solutions for the newly introduced configurations. • With few enough parameters & clear objectives, greedy optimization may be more efficient. • With complex multiple objectives, G.A. may have advantage of parallel exploration.
What Are Genetic Algorithms Good For ? • Exploring unknown territory • Generating a first set of ideas • Showing different subsystem solutions How can this be harnessed most effectively in an engineering design environment ?
Uncharted Territory • Task: Design a robot that climbs trees ! • How do you get started ??
Making G.A. Useful for Engineering Selection ofgood startingphenotypes Visualization • G.A. by itself is not a good engineering tool Suggestiveediting G.A. Selectivebreeding GreedyOptimization
OPASYNA Compiler for CMOS Operational AmplifiersH.Y. Koh, C.H. Séquin, P.R. Gray, 1990 Synthesizing on-chip operational amplifiers to given specifications and IC layout areas. 1. Case-based reasoning (heuristic pruning)selects from 5 proven circuit topologies. 2. Parametric circuit optimization to meet specs. 3. IC Layout generation based on macro cells.
MOS Operational Amplifier (1 of 5) Only five crucial design parameters !
Op-Amp Design (OPASYN, 1990) Multiple Objectives: • power dissipation (mW) • output voltage swing (V) • output slew rate (V/nsec) • open loop gain () • settling time (nsec) • unity gain bandwidth (MHz) • 1/f-noise (V*Hz-½) • total layout area (mm2) “Cost” of Design = weighted sum of deviations
Hard design constraints OPASYN Search Method Fitness Design-parameter space Cost Regular sampling followed by gradient ascent
MOS Op-Amp Layout • Following circuit synthesis & optimization, other heuristic optimization procedures produce layout with desired aspect ratio.
Synthesis in Established Fields • Filter design and MOS Op-Amp synthesishave well-established engineering practices. • Efficiently parameterized designs as wellasrobust and efficient design procedures exist. • Experience is captured in special-purpose programs and used for automated synthesis. • But what if we need to design something in “uncharted engineering territory” ?
