Toward the Computer-Automated Design of Sophisticated Systems by Enabling Structural Organization Gregory S. Hornby Adaptive Control & Evolvable Systems Group University of California Santa Cruz NASA Ames Research Center

Ames Research Center 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). Evolved gait for Sony’s AIBO. Over 20,000 sold: Evolved X-band antenna for NASA’s ST5 mission. Three are in space:

Ames Research Center 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.

Ames Research Center 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.

Ames Research Center 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.

Ames Research Center 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.

Ames Research Center Example Encoding with MRH Genotype:Intermediate phenotype: Graphical version:

Ames Research Center Evolved Tables Table fitness = height*surface*volume / material

Ames Research Center Evolution in Action Evolving tables: fitness = height*surface area*stability/material. No MRH enabled: MRH enabled:

Ames Research Center Comparing Complexity Measures

Ames Research Center 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

Ames Research Center Using MR&H for a Single # Measure of Structural Organization… NoneMMHMRMRH Fitness (*10^6) MRH (len of vector) M*R*H M*R*H Assem M*R*H AIC

Ames Research Center 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?).