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extras/hypeIndicatorExact.m

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+% HYPEINDICATOREXACT calculates the HypE fitness
+%   HYPEINDICATOREXACT( POINTS, BOUNDS, K  ) calculates the HypE
+%   fitness for objective vectors POINTS. 
+%
+%   POINTS: objective vectors as rows, all to be minimized
+%   BOUNDS: reference point
+%   K:      parameter of HypE
+%
+%   Example: f =  hypeIndicatorExact( [1 3; 3 1], [4 4], 1 )
+
+function f = hypeIndicatorExact( points, bounds, k )
+    Ps = size(points,1);
+    if( k < 0 )
+        k = Ps;
+    end
+    actDim = size(points,2);
+    if( length(bounds) == 1 )
+        bounds = repmat(bounds, actDim, 1);
+    end
+    pvec = 1 : 1 : size(points,1);
+
+	alpha = [];
+    for i = 1 : k
+        j = 1:i-1;
+        alpha(i) = prod( (k-j) ./ (Ps - j ) )./i;
+    end  
+
+    f = hypesub( size(points,1), points, actDim, bounds, pvec, alpha, k );
+
+    function [h] = hypesub( l, A, actDim, bounds, pvec, alpha, k )
+        h = zeros(1,l);
+        [S,i] = sortrows(A,actDim);
+        pvec = pvec(i);
+        for i = 1 : size(S,1)
+            if( i < size(S,1) )
+                extrusion = S( i+1, actDim ) - S( i, actDim );
+            else
+                extrusion = bounds(actDim) - S( i, actDim );
+            end
+            if( actDim == 1 )
+                if( i > k )
+                    break;
+                end                
+                if( alpha >= 0 )
+                    h( pvec(1:i) ) = h( pvec(1:i) ) + extrusion * alpha(i);
+                end                
+            elseif( extrusion > 0 )
+                h = h + extrusion*hypesub( l, S(1:i,:), actDim - 1, ...
+                        bounds, pvec(1:i), alpha, k );            
+            end        
+        end

extras/hypeIndicatorSampled.m

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+% HYPEINDICATORSAMPLED calculates the HypE fitness
+%   HYPEINDICATORSAMPLED( POINTS, BOUNDS, K, NROFSAMPLES  ) 
+%   samples the HypE fitness values for objective vectors POINTS. 
+%
+%   POINTS:      objective vectors as rows, all to be minimized
+%   BOUNDS:      reference point
+%   K:           parameter of HypE
+%   NROFSAMPLES: nr of samples to be used
+%
+%   Example: f =  hypeIndicatorExact( [1 3; 3 1], [4 4], 1, 10000 )
+
+function F = hypeIndicatorSampled( points, bounds, k, nrOfSamples)
+    [nrP, dim] = size(points);
+    F = zeros(1,nrP);
+
+    alpha = zeros(1,nrP);
+    for i = 1 : k
+        j = 1:i-1;
+        alpha(i) = prod( (k-j) ./ (nrP - j ) )./i;
+    end  
+
+
+    if( length(bounds) == 1 )
+        bounds = repmat( bounds,1, dim );
+    end
+
+    BoxL = min(points);
+
+    S = rand(nrOfSamples,dim)*diag( bounds - BoxL) ...
+    + ones( nrOfSamples,dim)*diag(BoxL);
+
+    dominated = zeros( nrOfSamples, 1 );
+    for j = 1 : nrP
+        B = S - repmat(points(j,:),nrOfSamples,1);
+        ind = find( sum( B >= 0, 2) == dim);
+        dominated(ind) = dominated(ind) + 1;
+    end
+
+    for j = 1 : nrP
+        B = S - repmat(points(j,:),nrOfSamples,1);
+        ind = find( sum( B >= 0, 2) == dim);
+        x = dominated(ind);        
+        F(j) = sum(  alpha(x)  );
+    end    
+    F = F'*prod( bounds - BoxL)/nrOfSamples;
+
+
+