Todays Menu Experiments in Modularity Universal Construction Machine

Today’s Menu • Experiments in Modularity • Universal Construction Machine

Regularity vs. Modularity • Regularity (structural) – Repeated/symmetric/self-similar patterns – Allows for compressed description – Introduced directly by developmental mechanisms, duplication/splicing operators – Can also result from environment pressure

Regularity vs. Modularity • Modularity (functional) – Decoupled parts serve different functions • Extreme: one of each module exhibits no regularity – Can be introduced directly from developmental mechanisms, grammars (e. g. trees) duplication/splicing operators – Can also result from environment pressure

Environment directs modularity How environmental changes provide pressure for functional modularity performance = individual × environment success = requirement : performance Arbitrary survival requirement Individual creature (transfer function) Environment building blocks

Rules of the game • • Fitness: number of requirements fulfilled Operators: Only uniform mutation of matrix (flat) Environment: Occasionally mutated Modularity: Number of nonzero elements (~block diagonal) Arbitrary survival requirement Individual creature (transfer function) Environment building blocks

Rules of the game • • Fitness: number of requirements fulfilled Operators: Only uniform mutation of matrix (flat) Environment: Occasionally mutated Modularity: Number of nonzero elements (~block diagonal) Arbitrary survival requirement Individual creature (transfer function) Environment building blocks

Implementation • • High mutation noise drowns effects Direct fitness proportionate too weak Boltzman T=0. 1 -0. 3 for F=0 -1 Population 500, steady state

Matrix Size 8 100 K Evaluation, Popsize 500, Boltz 0. 1 Red=change every 40000 evaluations Blue=change every 10000 evaluations Population not re-evaluated after change

Matrix Size 8 4 M Evaluation, Popsize 500 = 8000 Generations, Boltz 0. 1 Red=change every 40000 evaluations Blue=change every 10000 evaluations Population not re-evaluated after change

Matrix Size 8 4 M Evaluation, Popsize 500 = 8000 Generations, Boltz 0. 1 Red=change every 40000 evaluations Blue=change every 10000 evaluations Population re-evaluated after change

Average of 10 runs, over 10 samples Matrix Size 8 100, 000 Evaluation, Popsize 500 = 200 Generations, Boltz 0. 1 Blue, Red=change every ¥ evaluations (no change) Green, Magenta=change every 1000 evaluations (2 Generations) Population re-evaluated after change

Average of 10 runs, over 10 samples, Matrix Size 8 1, 000 Evaluation, Popsize 500 = 2000 Generations, Boltz 0. 1 Blue=change every ¥ evaluations (no change) Red=change every 100, 000 evaluations (no change in this experiment) Green =change every 10, 000 evaluations (20 Generations) Magenta=change every 1000 evaluations (2 Generations) Population re-evaluated after change

Average of 10 runs, over 10 samples, Matrix Size 8 100, 000 Evaluation, Popsize 500 = 200 Generations, Boltz 0. 1 Blue=change every ¥ evaluations (no change) Red=change every 100, 000 evaluations (no change in this experiment) Green =change every 10, 000 evaluations (20 Generations) Magenta=change every 1000 evaluations (2 Generations) Population re-evaluated after change, initialized at zero

Average of 10 runs, over 10 samples, Matrix Size 8 1, 000 Evaluation, Popsize 500 = 2000 Generations, Boltz 0. 2 Blue=change every ¥ evaluations (no change) Red=change every 100, 000 evaluations (no change in this experiment) Green =change every 10, 000 evaluations (20 Generations) Magenta=change every 1000 evaluations (2 Generations) Population re-evaluated after change

Axiomatic Design (Suh, 1990) • Theory for engineering design • Rests on two axioms: – Decoupling – Probability of success • All designs can be written as F=AD • Matrices and vectors are hierarchical and obtained top-down

Axiomatic Design • Maybe the axioms should be: – #1 Probability of success (regularity? ) – #2 Ability to maintain #1 over changing environments (adaptivity modularity) • Maybe this can be extended – #3 Ability to maintain #2 over time: acquisition of knowledge (identification and reuse of modules) across different runs

Universal Construction Machine • A machine that can make any other machine given resource and space – Alife – Mass customization • Implementation: 3 D printer with infinite resolution and variety of materials • Practical: 3 D doped plastic deposition – – – Undoped: for structure Doped with conductive material: wires Doped with ferrous material: magnetable Doped with oriented magnetic particles: magnets Doped with dyes: colors