Update README.md

README.md

@@ -3,9 +3,11 @@
 **Newer versions of the MOEA Framework, starting with version 3.4, include a significantly faster hypervolume implementation.  This project is being archived and may not receive further updates.**
 
 This project contains a collection of open-source codes for computing the hypervolume of a Pareto set.  The codes may have been modified
-from their original sources in order to standardize their interfaces.  All codes posted here are compatible with the
-[MOEA Framework](http://www.moeaframework.org).  Refer to section 10.1 in the MOEA Framework Beginner's Guide for additional information
-on using external hypervolume calculators.
+from their original sources in order to standardize their interfaces.  Please refer to the documentation and license information included with
+each implementation for additional details.
+
+The setup instructions below show how to compile and configure each implementation with the [MOEA Framework](http://www.moeaframework.org).  
+Refer to section 10.1 in the MOEA Framework Beginner's Guide for additional information.
 
 ## WFG Setup
 
@@ -53,18 +55,17 @@ If compiling on Windows, please note the `.exe` extension might be added to the
 
 ## Performance
 
-The performance of any hypervolume calculation is dependent on the number of objectives (dimensions).  Below is a very rough comparison of the performance of each approach, starting with the 4-objective DTLZ2 reference set:
-
-    Built-in:  0.618 seconds
-    WFG:       0.576 seconds
-    HOY:       0.561 seconds
-
-And for the 6-objective DTLZ2 reference set:
-
-    Built-in:  64.854 seconds
-    WFG:        0.660 seconds
-    HOY:        2.430 seconds
-
-Note: the built-in calculation is the hypervolume calculation included in the MOEA Framework by default.  Due to differences in licensing, the WFG
-and HOY codes can not be distributed within the MOEA Framework.  However, following the instructions above, you can enable the WFG or HOY
-calculations for your personal use.
+The performance of any hypervolume calculation is dependent on the number of objectives (dimensions) and the number of points in the Pareto front.
+Below is a very rough comparison of the performance of these implementations:
+
+Data Set    | Objectives | Built-in | ./wfg2  | ./hv
+----------- | ---------- | -------- | ------- | ------
+DTLZ2.2D.pf | 2          | 252 ms   | 275 ms  | 273 ms
+DTLZ2.3D.pf | 3          | 251 ms   | 293 ms  | 280 ms
+DTLZ2.4D.pf | 4          | 296 ms   | 322 ms  | 303 ms
+DTLZ2.6D.pf | 6          | 468 ms   | 359 ms  | 682 ms
+DTLZ2.8D.pf | 8          | 5.8 sec  | 1.5 sec | 101 sec
+
+This leads to a few conclusions:
+1. The built-in implementation is close in performance to its natively compiled variant WFG.  We only begin to see a difference with 8+ objectives.
+2. Users performing many hypervolume calculations with 8+ more objectives could still benefit from using the compiled WFG implementation