Documentation of obj4wings

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Function Synopsis

ObjVal = obj4wings(Chrom, P1, P2)

Help text

 OBJective function FOUR-WINGS.

 This function implements the continuous and discrete variant of the
 Four-Wings function. The continuous version is a unimodal function
 with niveaulines resembling conjugated hyperbolas. Because of the
 low slope the surface of the discrete version consists of wide
 plateaus. The area of the plateaus increase with their niveau. 
 
 This function is defined as stepfun4 function in:%
  Jain, Clusterbasierte Abbruchkriterien fuer den Evolutionaeren Test. 
     Diploma-thesis, Technical University of Berlin, Department of 
     Computer Science, chapter 5.1, 1999.

 Syntax: ObjVal = obj4wings(Chrom, P1, P2)

 Input parameters:
    Chrom     - Matrix containing the chromosomes of the current
                population. Each row corresponds to one individual's
                string representation.
                If Chrom == [NaN xxx]  or 
                   Chrom == [NaN xxx yyy], 
               then special values will be returned, see Output parameters
                   xxx == 1 (or []) return boundaries
                   xxx == 2 return title 
                      yyy == 0 return title of continuous variant
                      yyy == 1 return title of discrete variant
                   xxx == 3 return value of global minimum
    P1        - (Optional) Number indicating which variant is used,
                if Chrom is not NaN or []. 
                   P1 = 1  use discrete version
                   P1 = 0  use continuous version
                If P1 is omitted or P1 = [] the continuos version 
                   is used (P1 = 0).
    P2        - Additional parameter

 Output parameters:
    ObjVal    - Column vector containing the objective values of the
                individuals in the current population.
                if called with 
                   Chrom == [NaN xxx] or Chrom == [NaN xxx yyy], 
                then ObjVal contains
                   xxx == 1 (or []), matrix with the boundaries of 
                                     the varaibles
                   xxx == 2, text with the title of the function
                      yyy omitted: title of continuous variant
                      yyy = 0      title of continuous variant
                      yyy = 1      title of discrete variant
                   xxx == 3, value of global minimum

 Examples:

  % continuous variant of the Four-Wings function
  >> obj4wings(Chrom)

  % discrete variant of the Four-Wings function
  >> obj4wings(Chrom, 1)