LAUSR

In spite of being introduced over twenty-five years ago, Fonseca and Fleming’s attainment surfaces have not been widely used. This article investigates some of the shortcomings that may have led to the lack of adoption of this performance measure. The quantitative measure based on attainment surfaces, introduced by Knowles and Corne, is analyzed. The analysis shows that the results obtained by the Knowles and Corne approach are influenced (biased) by the shape of the attainment surface. Improvements to the Knowles and Corne approach for bi-objective pof comparisons are proposed. Furthermore, assuming M objective functions, an M-dimensional attainment-surface-based quantitative measure, named the porcupine measure, is proposed for comparing the performance of multi-objective optimization algorithms. A computationally optimized version of the porcupine measure is presented and empirically analyzed.