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A method for developing systems that traverse the Pareto frontiers of multiple system concepts through modularity

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Abstract

Natural changes in customer needs over time often necessitate the development of new systems that satisfy the new needs. In a previous work by the authors, a 5-step multiobjective optimization-based method was presented to identify systems that anticipate, account for, and allow for these changes by moving from one Pareto design to another through module addition. Recognizing the potential for changes in needs to exceed the limits of a single Pareto frontier, the present paper introduces important advancements that extend development to modules connecting multiple disparate system concepts. As such, the search for suitable system designs is extended from a Pareto frontier that characterizes one system concept to a Pareto frontier that characterizes a set of system concepts. An expanded methodology is described, and a tri-objective hurricane and flood resistant residential structure example is used to demonstrate the method. The authors conclude that the developed method provides a new methodology for selecting platform and module designs in the presence of multiple system concepts, and is capable of identifying a set of modular system designs that are well-suited to satisfy changing needs over time.

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Abbreviations

δ :

Matrix dictating the desired progression that each module provides.

D a :

Set containing all design variable values of x a and x p.

D m :

Set containing all design variable values of x m and x p.

g :

Vector of inequality constraints.

h :

Vector of equality constraints.

J :

Aggregate objective function.

μ :

Vector of design objectives.

n d :

Number of designs comprising the adaptive design set.

\(n_{\hat{\mu}}\) :

Number of additional objective constraints needed to define anticipated regions of interest.

P (α) :

Vector of design objective values of the base design of a module.

P (β) :

Vector of design objective values of the target design of a module.

\(\bar{P}^{(i)}\) :

Vector of design objective values of a design when used with the i-th module.

ΔP (i) :

Vector of the change in design objective values from the base design to \(\bar{P}^{(i)}\).

p :

Vector of design parameters.

x :

Vector of design variables.

x a :

Vector of non-platform adjustable design variables.

x m :

Vector of non-platform design variables that characterize the design of modules.

x p :

Vector of platform design variables.

[](i) :

indicates current design/module.

[](k) :

indicates current design concept.

n [] :

indicates the number of [].

[] l :

indicates the lower limit of [].

[] u :

indicates the upper limit of [].

[]* :

indicates the optimal value of [].

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Acknowledgements

We would like to recognize the National Science Foundation Grant CMMI-0954580 for funding this research.

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Authors and Affiliations

  1. Department of Mechanical Engineering, Brigham Young University, Provo, UT, 84602, USA

    P. K. Lewis & C. A. Mattson

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  1. P. K. Lewis
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  2. C. A. Mattson
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Correspondence to C. A. Mattson.

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Lewis, P.K., Mattson, C.A. A method for developing systems that traverse the Pareto frontiers of multiple system concepts through modularity. Struct Multidisc Optim 45, 467–478 (2012). https://doi.org/10.1007/s00158-011-0735-7

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  • DOI: https://doi.org/10.1007/s00158-011-0735-7

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