Design Mode Analysis of Pareto Solution Set for Decision-Making Support

Algorithm 2

Design mode analysis focusing on granularity.

    (1) Generate a design dataset = () of size N.

   (2) Scale the dataset such that all decision variables have

   zero mean and unit variance.

   (3) Initialize total approximation error E = .

   (4) Set a threshold η for E.

   (5) Initialize layer counter i = 1.

   (6) while  E > η do

   (7)  Initialize the number of clusters in current layer

    .

   (8)  Initialize the counter of the clusters in new layer k = 1.

   (9)  Initialize E = 0.

 (10)  for  j = 1 to H  do

  (11)    Extract the design mode by applying PCA to .

 (12)    Calculate the component loading for each

       design mode.

 (13)    Choose a base design , or calculate

       a mean vector of .

 (14)    Choose p design modes so as to satisfy cumulative

       proportion of the variance P ≥ 0.80.

 (15)    Perform Design Approximation (mentioned above)

       for all the designs in .

(16)     Add (approximation error for ) to

       the total error: E = E + .

 (17)    Divide the cluster into two clusters and

        by using data clustering.

 (18)     k = k + 2

 (19)  end  for

(20)  i = i + 1.

 (21) end  while