The software download contains C source code that
takes R approximation sets as input, and outputs a
number of uniformly distributed points on the Jth attainment
surface (where J is in the range 1,...,R). Its purpose is to allow
straightforward plotting of (especially 3d) attainment surfaces in
gnuplot. Although it is most useful for 2- and 3-objective problems,
the code works for approximation sets of any dimension. The code
can handle mixed minimization/maximization problems.
Here, the input was a collection of 21 approximation sets (i.e. nondominated sets)
from 21 runs of an optimizer on a 3-objectives mixed minimization/maximization
The output can be any of the 21 attainment surfaces. Here, three of these surfaces, plotted using gnuplot, are shown.
1st (best) attainment surface:
11th (median) attainment surface:
21st (worst) attainment surface:
The concept of an attainment surface in multiobjective optimization is
introduced in the following two papers.
1. Carlos M. Fonseca and Peter J. Fleming. On the Performance Assessment and Comparison of Stochastic Multiobjective Optimizers. In Hans-Michael Voigt, Werner Ebeling, Ingo Rechenberg, and Hans-Paul Schwefel, editors, Parallel Problem Solving from Nature--PPSN IV, Lecture Notes in Computer Science, pages 584-593, Berlin, Germany, September 1996. Springer-Verlag.
2. Viviane Grunert da Fonseca, Carlos M. Fonseca, and Andreia O. Hall. Inferential Performance Assessment of Stochastic Optimisers and the Attainment Function. In Eckart Zitzler, Kalyanmoy Deb, Lothar Thiele, Carlos A. Coello Coello, and David Corne, editors, First International Conference on Evolutionary Multi-Criterion Optimization, pages 213-225. Springer-Verlag. Lecture Notes in Computer Science No. 1993, 2001.