Toward the Computer-Automated Design of Sophisticated Systems

by Enabling Structural Organization

Gregory S. HornbyAdaptive Control & Evolvable Systems GroupUniversity of California Santa CruzNASA Ames Research Centerhornby@email.arc.nasa.gov

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Introduction

Computer-automated design (CAD) systems have produced simple designs, such as:

• How to scale to produce entire complex systems?– Look to Engineering and Natural systems for inspiration.

• Both produce things with the characteristics of:– Modularity, Regularity & Hierarchy (MR&H).– => structural organization.

• To improve scalability of CAD systems, they must also be able to produce designs with structural organization (MR&H).

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Why Representation?

A CAD system consists of:– Search Algorithm (SA) for exploring the design space.– Representation for encoding designs.– Fitness/cost Function for scoring designs.

Which part of a CAD system is responsible for MR&H?– Should be independent of the fitness function.– SA is limited to what can be encoded.– Consequently dependent on the

Representation.

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Achieving Scalable Representations

• To improve structural organization of CAD systems:– Definitions of MR&H.– Metrics for measuring (and clearly defining) MR&H.

• These definitions and metrics are based on the properties of representations.

• Representations are a kind of programming language and thus have the fundamental properties of:– Combination: eg. Strings, Trees, Graphs.– Control Flow: Conditionals, Iteration.– Abstraction: Labels, Parameters, Recursion.

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Metrics for MR&H

We define MR&H by giving metrics for them:• Modularity: a module is an encapsulated group of

elements that can be manipulated together.– Measured by counting # of labeled procedures and

iterative loops.

• Regularity: amount of reuse.– Measured as: (size of design) / (size of design encoding).– In AIC terms: (size of string) / (size of string encoding)

• Hierarchy: Levels of nested modules.– The Hierarchy of an encoding is maximum depth of nested

modules.

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The 5 Representations

We compare 5 different representations by enabling different combinations of MR&H:

• Modularity(M):– Just Abstraction.

• Reuse(R):– Iteration, recursion.

• Hierarchy(H):– Nested procedures and

iterative loops.

• None: a tree of construction operators, no features.

• M: modularity thru labeled procedures, no reuse.

• MR: modularity & reuse. Iteration & abstraction but no nested loops or proc calls.

• MH: modularity & hierarchy. Abstraction, and nested abstraction but no recursion.

• MRH: modularity, reuse & hierarchy. Nested iteration and recursive abstraction enabled.

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Example Encoding with MRH

Genotype: Intermediate phenotype:

Graphical version:

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Evolved Tables

Table fitness = height*surface*volume / material

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Evolution in Action

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Evolving tables: fitness = height*surface area*stability/material.

No MRH enabled: MRH enabled:

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Comparing Complexity Measures

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Comparing Complexity Measures

None:

MR&H:

Fit:25mil, AIC:4999, M:0, R:1, H:1

Fit:60mil, AIC:495, M:34, R:10, H:9

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Using MR&H for a Single # Measure of Structural Organization…

None M MH MR MRH

Fitness

(*10^6)

4.82 6.78 7.82 14.60 18.00

MRH (len of vector)

1.73 7.4 12.8 10.8 37.2

M*R*H 0 14.2 65.6 69.8 2792

M*R*H

Assem

0 0.0079 0.026 0.0098 4.2

M*R*H

AIC

0 0.0079 0.026 0.031 0.34

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Conclusion

Hypothesis: To improve scalability need modularity, regularity and hierarchy (MR&H).

• MR&H are enabled in the representation by combination, control-flow & abstraction.

• Defined metrics for MR&H.

Compared representations with different combinations of MR&H enabled:– Best performance came with all of MR&H enabled.

– Measuring MR&H gives more intuitive value of complexity (structural organization) than AIC, or other measures.

Future improvements in scalability may come from adding other features of programming languages (objects?).