This paper describes a method for defining a coordinate system to parameterize a sampled Pareto frontier of a continuous multi-attribute design problem using a modified self-organizing map. By defining such a coordinate system, the design problem may be reformulated from y = f ( x ) to ( y , x ) = g ( ψ ) , where x is a vector of design variables, y is a vector of attributes, and ψ is a vector of barycentric coordinates. Exploration of the design problem using ψ as the independent variables has the following desirable properties: 1) Every vector ψ corresponds to a Pareto efficient design, and every Pareto efficient design has a corresponding ψ . 2) The number of ψ coordinates is equal to the number of attributes, regardless of the number of design variables. 3) Each attribute y i has a corresponding coordinate ψ i such that the sign of y i / ψ i is positive if the objective is to maximize y i and negative if the objective is to minimize y i (i.e., the attributes improve monotonically as their corresponding coordinates increase). This approach, named the “Pareto simplex self-organizing map” is easily implemented as a postprocessing step to sampling a Pareto frontier with multi-objective optimization. The construction of the coordinates and their use in design space exploration is demonstrated on a conceptual wing design problem.


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    Title :

    Representing Sampled Pareto Frontiers as Parameterized Continuous Manifolds Using Self-Organizing Maps


    Contributors:

    Published in:

    AIAA Journal ; 52 , 11 ; 2480-2490


    Publication date :

    2014-04-11


    Size :

    11 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English





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