Research Papers

A Stochastic Tree-Search Algorithm for Generative Grammars

[+] Author and Article Information
Matthew I. Campbell1

Automated Design Laboratory, Department of Mechanical Engineering,  University of Texas at Austin, Austin, TX 78712-0292mc1@mail.utexas.edu

Rahul Rai

Department of Mechanical and Aerospace Engineering,  University at Buffalo (UB)-SUNY, Buffalo, NY 14260rahulrai@buffalo.edu

Tolga Kurtoglu

Palo Alto Research Center, 3333 Coyote Hill Road, Palo Alto, CA 94304kurtoglu@parc.com


Corresponding author.

J. Comput. Inf. Sci. Eng 12(3), 031006 (Aug 09, 2012) (11 pages) doi:10.1115/1.4007153 History: Received July 11, 2012; Revised July 12, 2012; Published August 09, 2012; Online August 09, 2012

This paper presents a new search method that has been developed specifically for search trees defined by a generative grammar. Generative grammars are useful in design as a way to encapsulate the design decisions that lead to candidate solutions. Since the candidate solutions are not confined to a single configuration or topology and thus useful in conceptual design, they may be difficult to computationally analyze. Analysis is achieved in this method by querying the user. A formal definition of a rule-based interactive tree-search is presented in this paper. The user interaction is kept to 30 pair-wise comparisons of candidates. From the data gathered from the comparisons, a stochastic decision-making process infers what candidate solutions best match the known optimal. The method is implemented and applied to a grammar for tying neckties. It is shown through 21 user experiments and 4000 automated experiments that the method consistently finds solutions within the 99.8 percentile. The computational complexity of the proposed algorithm is also studied. The implications of this method for conceptual design are expounded on in the conclusions.

Copyright © 2012 by American Society of Mechanical Engineers
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Figure 1

An example of a search tree that results from invoking a generative grammar on a seed

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Figure 2

Rules to tie a necktie knot (a) rules for beginning a tie knot, (b) rules for continuing a tie knot, and (c) rules for terminating a tie knot

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Figure 3

Application of rule sequence {13,8,9,11,10,7,15} creates a cross-knot in seven steps from initial Null seed

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Figure 4

A screenshot of GraphSynth depicting the list of rules (on the right) and two rules from the necktie grammar

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Figure 5

Pseudocode for the heuristic used in the interactive graph search algorithm

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Figure 6

The user feedback is provided via a pair-wise comparison of n designs (four in this case)

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Figure 7

An example of a search tree that results from invoking a generative grammar on a seed

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Figure 8

The number lines show corresponding values of p and Q

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Figure 9

The frequency of distance metric for the 35,498 necktie designs and the probability and cumulative density functions

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Figure 10

Results from the automated experiments. Average distance metric, f(d), and its percentile is shown for computed best designs for varying values of B (a), Q (b), and designer interaction dialog (c).

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Figure 11

Average distance metric computed for best designs generated at the end of each user feedback dialog




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