Walking Fish Group:

hypervolume project

We have developed a series of algorithms, both

  • for calculating the exact hypervolume of a non-dominated front, for use as a metric; and
  • for identifying the least-contributing point in a front, for use in selection, archiving, or diversity.

papers
code
data
PAPERS PUBLISHED IN THIS PROJECT

[WFGHV11] Wesley Cox and Lyndon While. Improving and Extending the HV4D Algorithm For Calculating Hypervolume Exactly. 29th Australasian Joint Conference on Artifical Intelligence, volume ???? of Lecture Notes in Computer Science, pages ?-?. Springer-Verlag, December 2016. []

[WFGHV10] Wesley Cox and Lyndon While. Improving the IWFG Algorithm For Calculating Incremental Hypervolume. 2016 IEEE Congress on Evolutionary Computation, pages 3969-3976. IEEE, July 2016. []

[WFGHV9] Lyndon While and Lucas Bradstreet. Applying the WFG Algorithm To Calculate Incremental Hypervolumes. 2012 IEEE Congress on Evolutionary Computation, pages 489-496. IEEE, June 2012. [download]

[WFGHV8] Lyndon While, Lucas Bradstreet, and Luigi Barone. A Fast Way of Calculating Exact Hypervolumes. IEEE Transactions on Evolutionary Computation volume 16, no 1, pages 86-95. IEEE, February 2012. [download]

[LucasThesis] Lucas Bradstreet. The hypervolume indicator for multi-objective optimisation: calculation and use. PhD thesis, The University of Western Australia, November 2011. [download]

[WFGHV6] Lucas Bradstreet, Lyndon While, and Luigi Barone. A Fast Many-objective Hypervolume Algorithm using Iterated Incremental Calculations. 2010 IEEE Congress on Evolutionary Computation, pages 179-186. IEEE, July 2010. [download]

[WFGHV7] Lucas Bradstreet, Luigi Barone, and Lyndon While. Updating Exclusive Hypervolume Contributions Cheaply. 2009 IEEE Congress on Evolutionary Computation, pages 538-544. IEEE, May 2009. [download]

[WFGHV3] Lucas Bradstreet, Lyndon While, and Luigi Barone. A Fast Incremental Hypervolume Algorithm. IEEE Transactions on Evolutionary Computation, volume 12, no 6, pages 714-723. IEEE, December 2008. [download]

[WFGHV5] Lucas Bradstreet, Lyndon While, and Luigi Barone. Incrementally Maximising Hypervolume for Selection in Multi-objective Evolutionary Algorithms. 2007 IEEE Congress on Evolutionary Computation, pages 3203-3210. IEEE, September 2007. [download]

[WFGHV4] Lucas Bradstreet, Lyndon While, and Luigi Barone. Maximising Hypervolume for Selection in Multi-objective Evolutionary Algorithms. 2006 IEEE Congress on Evolutionary Computation, pages 6208-6215. IEEE, July 2006. [download]

[WFGHV1] Lyndon While, Phil Hingston, Luigi Barone, and Simon Huband. A Faster Algorithm for Calculating Hypervolume. IEEE Transactions on Evolutionary Computation, volume 10, no 1, pages 29-38. IEEE, February 2006. [download]

[WFGHV2] Lyndon While, Lucas Bradstreet, Luigi Barone, and Phil Hingston. Heuristics for Optimising the Calculation of Hypervolume for Multi-objective Optimisation Problems. 2005 IEEE Congress on Evolutionary Computation, volume 3, pages 2225-2232. IEEE, September 2005. [download]

[WFGHV0] Lyndon While. A New Analysis of the LebMeasure Algorithm for Calculating Hypervolume. 3rd International Conference on Evolutionary Multi-Criterion Optimization, volume 3410 of Lecture Notes in Computer Science, pages 326-340. Springer-Verlag, March 2005. [download]

IMPLEMENTATIONS

WFG is one of the fastest known algorithms for calculating hypervolume as a metric, in the general case.

HV4DX is the fastest known algorithm for calculating hypervolume as a metric, for 4D data; and HV5DR is the fastest known algorithm for 5D data.

IWFG is the fastest known algorithm for identifying the least-contributing point in a front.

DATA

To generate a random non-dominated front, we initialise S = empty, generate an infinite list of points, and test each point p in turn, adding p to S only if {p} U S is a non-dominated front. Each objective value is in [0.1,10].
For each DTLZ front, we generated a representative sample containing 10,000 points. Then to generate a front we select points randomly from the sample.

THE DATA USED IN WFGHV1 and WFGHV2

randomlinearsphericaldiscontinuousdegenerate
3D zip zip zip zip zip rev
4D zip zip zip zip zip rev
5D zip zip zip zip zip rev
6D zip zip zip zip zip rev
7D zip zip zip zip zip rev
8D zip zip zip zip zip rev
9D zip zip zip zip zip rev
10D ---- ---- zip ---- zip ----
11D ---- ---- zip ---- zip ----
12D ---- ---- zip ---- zip ----
13D ---- ---- zip ---- zip ----



THE DATA USED IN WFGHV8

random spherical discontinuous degenerate
3D zip zip zip zip
4D zip zip zip zip
5D zip zip zip zip
6D zip zip zip zip
7D zip zip zip zip
10D zip zip zip zip
13D zip zip zip zip



THE DATA USED IN WFGHV10

randomsphericaldiscontinuous
1,000 pts zip zip zip



CONTACT INFORMATION

©2005-15 Walking Fish Group
lyndon.while@uwa.edu.au