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Research Papers: Design Automation

P3GA: An Algorithm for Technology Characterization

[+] Author and Article Information
Edgar Galvan

Design Systems Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: e_galvan@tamu.edu

Richard J. Malak

Design Systems Laboratory,
Department of Mechanical Engineering,
Texas A&M University,
College Station, TX 77840
e-mail: rmalak@tamu.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received March 8, 2013; final manuscript received July 21, 2014; published online November 14, 2014. Assoc. Editor: Michael Kokkolaras.

J. Mech. Des 137(1), 011401 (Jan 01, 2015) (13 pages) Paper No: MD-13-1114; doi: 10.1115/1.4028101 History: Received March 08, 2013; Revised July 21, 2014; Online November 14, 2014

It is important for engineers to understand the capabilities and limitations of the technologies they consider for use in their systems. However, communicating this information can be a challenge. Mathematical characterizations of technical capabilities are of interest as a means to reduce ambiguity in communication and to increase opportunities to utilize design automation methods. The parameterized Pareto frontier (PPF) was introduced in prior work as a mathematical basis for modeling technical capabilities. One advantage of PPFs is that, in many cases, engineers can model a system by composing frontiers of its components. This allows for rapid technology evaluation and design space exploration. However, finding the PPF can be difficult. The contribution of this article is a new algorithm for approximating the PPF, called predictive parameterized Pareto genetic algorithm (P3GA). The proposed algorithm uses concepts and methods from multi-objective genetic optimization and machine learning to generate a discrete approximation of the PPF. If needed, designers can generate a continuous approximation of the frontier by generalizing beyond these data. The algorithm is explained, its performance is analyzed on numerical test problems, and its use is demonstrated on an engineering example. The results of the investigation indicate that P3GA may be effective in practice.

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Figures

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Fig. 1

Idealized interactions between system-level and discipline-level engineers

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Fig. 2

Illustrative example of the relationship between design details, x=[x1,x2]T, and their corresponding attribute values y=[y1,y2]T

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Fig. 3

Dependency relationships between discipline-level and system-level attributes for a hydraulic cylinder [4]. The preference ordering for values of discipline-level attribute b is unknown without further system-level information. In general, preferences can be nonmonotonic over the attribute domain.

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Fig. 4

Comparison between (a) CPD and (b) PPD. In this example, there are m=2 attribute, the feasible attribute set Yf⊂ℝ2

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Fig. 5

Illustration of dominance analysis on randomly generated design sites when CPD is (a) and is not (b) applicable

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Fig. 6

Flow chart of the P3GA. The shaded processes correspond to the novel concepts implemented in P3GA.

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Fig. 7

Illustration of kernel based SVDD. The SVDD is a test to determine whether a point is inside of the boundary.

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Fig. 8

Random population members in (a) the design space and their (b) attribute space image. The shaded region corresponds to the true feasible space in both domains.

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Fig. 9

An illustration of predictive PPD

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Fig. 10

Indicator Δp value as a function of number of generations for test problem 1, versions (a) and (b), at different values of the q parameter

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Fig. 11

Indicator Δp value as a function of number of generations for test problem 2, versions (a) and (b), at different values of the q parameter

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Fig. 12

Indicator Δp value as a function of number of generations for test problem 3, versions (a) and (b), at different values of the q parameter

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Fig. 13

Illustration of the P3GA results of a single trial for or test problem 2b at 100 generations. Illustrated is (a) the final p-nondominated points relative to the true PPF and (b) comparison of the true CPF at different parameter values, y1ε{0.25,0.50,0.75}, to the CPFs recovered from the P3GA data. Note that, in this case, the CPF is a cross section of the PPF at a specified parameter value.

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Fig. 14

Illustration of (a) the mean distance between the points, P, and the approximated PPF, S, at various generations

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