Quantified pareto-optimal front comparisons using attainment surfaces

Fonseca and Fleming introduced attainment surfaces over twenty years ago. It was shown that two algorithms could be compared using a grand attainment surface. Grand attainment surfaces show the regions in which one algorithm statistically outperforms another. Knowles and Corne extended the work done by Fonseca and Fleming by introducing a quantitative measure based on the concepts of the grand attainment surfaces. This paper presents an argument that the intersection line generation approach used to calculate the quantitative measure is not well suited for all Pareto-optimal front shapes. An alternative, the weighted POF shaped intersection line generation approach is presented. The new approach is tested along with the old approach against 30 test cases. The results show that the newly proposed weighted POF shaped intersection line generation approach is well suited for all the tested POF shapes and subsequently yield more accurate results.