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Flexible Solvers and Emergent Answers

Lecture presentation for the Design Modelling Symposium in Berlin (10~12 oct 2011)

David Rutten

on 13 October 2011

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Transcript of Flexible Solvers and Emergent Answers

Flexible Solvers & Emergent Answers How stochastics and meta-heuristics can help us find solutions to parametrically defined problems David Rutten (Robert McNeel & Associates) Phase-Space
Topologies Lighting Cooling Price Installation Construction Cleaning Retail Sunlight & daylight Sunlight & Insulation Purchase & Transport Weight & Size Size & Accessibility Quality of view Location & Size ~50,000 lux ~1000 watts × m² € ~500 kg ~2 m² 0~100 % ~1 m 1 2 3 4 5 6 50 10 seconds 16.7 minutes 28 hours 116 days 3251 years 3.2 × 10 years 33 years Dimension Duration Brute-Force Runtimes Design parameters Fragment Property unit What do we mean by "best"? (100 samples per axis) (assuming 0.1 seconds per sample) The curse of
dimensionality 91 ~10 million rods & cones
~20 frames/second
~0.5 second ~100 million samples ————————— × Stochastics allow us to break free of the grid.
Heuristics allow us to do so in a clever way. Unstable Stable Filament Fractal Needle-in-a-haystack Incomplete → Fragmentary Discontinuous Multiple local optima Optimum Simulated Annealing Hot Frozen Cold Warm Phase-Space Progression of a single Simulated Annealing run Simulated Evolution Fitness Function must provide
a single number for every state. Generation 1 Generation 2 Generation 3 Generation X Limited run due to cooling schedule
Good at finding many local optima
Good at navigating rough landscapes Random Gene-complexes & Speciation Solution Selection determines which animals
are allowed to survive & mate. Mutations allow 'fresh' genes
to enter the population. Coalescence determines how genomes
are combined to produce offspring. Rejected Rejected Rejected More prone to getting stuck in local optima
Good at refining a solution
Allows user interaction Basins of attraction High-dimensional spaces Competing populations User/Solver Interaction Nearest neighbour Nearest 2 neighbours Nearest 3 neighbours Exact solution no
longer possible 50 parameters 10 possible distinct states in Phase-space { Each with a range from 0 to 100
Each with an accuracy of 4 decimal places {0.0000, 0.0001, 0.0002, ... , 99.9998, 99.9999, 100.0000} } 1 million possible values per parameter Observable universe contains roughly 10 cubic millimeters 300 90 Radius Position A C B E D {A + B + C + ... + Z } 2 2 2 2 Fitness Landscape of a Circle Fitter Phase-Space Fitness Parent Parent Offspring Parent Parent Offspring Construction of an evolutionary generation Quality Phase-Space "Pressure" due to existing runs First annealing run Second annealing run What then? (Position) (Size) What is a parametrically defined design? "A design where meaningful properties
are controlled through constants." x y Radius
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