The hypervolume indicator is a standard unary indicator that is frequently used to assess solution sets in multiobjective optimization. Initially introduced for performance assessment, i.e., for comparing the outcome sets of multiobjective optimization algorithms, it is nowadays also used within several evolutionary multiobjective optimization algorithms such as SMS-EMOA, the MO-CMA-ES, or ESP. It simply measures the volume of the space that is dominated by a solution set and bounded by a so-called reference point. The weighted hypervolume indicator is a generalization of this indicator and has been introduced in 2007 as a way to steer the search towards user-defined regions of the objective space with high weight. The algorithm W-HypE (Weighted Hypervolume Estimation Algorithm for Multiobjective Optimization) combines the idea of a weighted hypervolume indicator based search algorithm with Monte Carlo sampling of the indicator function to circumvent the high runtime of exact hypervolume computations when the number of objectives is high. This web page provides the PISA source code of W-HypE as well as links to related web pages.

The source code of W-HypE as proposed and used in the following papers can be found below. The code is provided under the standard PISA licence.

D. Brockhoff, J. Bader, L. Thiele, and E. Zitzler. Directed Multiobjective Optimization Based on the Weighted Hypervolume Indicator. Journal of Multi-Criteria Decision Analysis 20(5-6):291-317. Wiley, 2013.

D. Brockhoff, Y. Hamadi, and S. Kaci. Using Comparative Preference Statements in Hypervolume-Based Interactive Multiobjective Optimization. Accepted for publication at LION'2014. Springer, 2014.

The current version of the source code, fully implemented in Java, is 2.0. For the previous version 1.0, based on MATLAB and Java, see below. Requirements: Java 1.6 or higher.

The simplest way to use W-HypE is to run the following jar file, i.e., to start the W-HypE PISA selector by typing

where whype_param.txt is a text file specifying the random number generator seed, the number of samples, and the used weight function(s), PISA_ is the name of the standard PISA communications file, and the last argument gives the standard PISA waiting time.

Here you can find a former version of W-HypE which relies on MATLAB for the weighted hypervolume sampling and the calculation of the fitness. It was the version, originally used in the above JMCDA paper.

The first paper proposing the weighted hypervolume indicator. Implementations of the original bi-objective exact hypervolume computation code, can be found here.

E. Zitzler, D. Brockhoff, and L. Thiele. The Hypervolume Indicator Revisited: On the Design of Pareto-compliant Indicators Via Weighted Integration. In S. Obayashi et al., editors, Conference on Evolutionary Multi-Criterion Optimization (EMO 2007), volume 4403 of LNCS, pages 862-876, Berlin, 2007. Springer.

- An overview of the hypervolume indicator's computational complexity can be found on the web page of the 2013 SIMCO workshop
- A general web page about the hypervolume indicator
- PISA - A Platform and Programming Language Independent Interface for Search Algorithms