Graphical tools for the analysis of bi-objective optimization algorithms
Manuel López‐Ibáñez, Thomas Stützle, Luís Paquete · 2010
A fundamentally different approach to the quality assessment of multi-objective SLS algorithms derives from the concept of attainment function. The attainment function extends the scalar concepts of mean and variance to random sets. The attainment function theory may completely characterize the statistical distribution of solutions in the objective space in terms of location, spread and mutual dependence. Moreover, statistical testing and inference are possible. However, the use of attainment functions is still rather limited in practice. We present here two practical applications of the first-order attainment function for analysing the output of SLS algorithms for bi-objective optimization problems. Programs implementing the techniques presented here are also available. Later, we discuss what would be necessary to extend this work for more than two objectives and for other types of analysis.