Abstract
In design situations where a single solution must be selected, it is often desirable to present the designer with a smart Pareto set of solutions—a minimal set of nondominated solutions that sufficiently represents the tradeoff characteristics of the design space. These sets are generally created by finding many well-distributed solutions and then either filtering out the excess ones or searching more closely in those regions that appear to have significant tradeoff. Such methods suffer from the inherent inefficiency of creating numerous solutions that will never be presented to the designer. This paper introduces the Smart Normal Constraint (SNC) method—a Pareto set generation method capable of directly generating a smart Pareto set. Direct generation is achieved by iteratively updating an approximation of the design space geometry and searching only in those regions capable of yielding new smart Pareto solutions. This process is made possible through the use of a new, computationally benign calculation for identifying regions of high tradeoff in a design space. Examples are provided that show the SNC method performing significantly more efficiently than the predominant existing method for generating smart Pareto sets.
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We would like to recognize the National Science Foundation (Grant CMMI-0954580) for funding this research.
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Appendix: Flowchart comparison of NC* and SNC methods
Appendix: Flowchart comparison of NC* and SNC methods
This chart gives the flow of the NC* and SNC methods, aligning corresponding steps horizontally. As shown here, the primary differences are (1) the greater number of steps included in the SNC method within each iteration (as a result of the Pareto frontier approximation being updated), (2) the introduction of two new steps in the SNC method (identified by stars in this figure), and (3) the application of the smart Pareto filter at the end of the NC* method, as opposed to the direct generation of a smart Pareto set by the SNC method. As in Table 1, the asterisk denotes that the NC* method has been implemented with the improvements of Messac and Mattson (2004) and Haddock et al. (2008) from Section 2.3 and used in conjunction with a smart Pareto filter, so as to draw attention to the novel aspects of the SNC method
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Hancock, B.J., Mattson, C.A. The smart normal constraint method for directly generating a smart Pareto set. Struct Multidisc Optim 48, 763–775 (2013). https://doi.org/10.1007/s00158-013-0925-6
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DOI: https://doi.org/10.1007/s00158-013-0925-6