| Resumen |
Many real-world applications can be expressed as multi-objective optimization problems (MOPs), i.e., problems where several objectives are being considered concurrently. One characteristic of such problems is that the solution set, the so-called Pareto set, forms a (k1)-dimensional entity where k is the number of
objectives involved in the MOP. Since this set can except for trivial examples not be computed analytically, the question arises how to compute a suitable ?nite size approximation of the Pareto set, respectively its image, the Pareto front. In many applications it is advantageous to present the decision maker a set of solutions that are (ideally) evenly spread along the Pareto front in order to give him/her a good overview of the possible alternatives for the realization of the project.
In this talk, we address a particular three objective optimization problem that is related to the design of PID controllers and where such an even distribution of the solutions along the Pareto front is desired. To this end, we use the recently developed evolutionary multi-objective algorithm (EMOA) SMS_DPPSA that aims for averaged Hausdor? approximations of the Pareto front of a given MOP. Averaged Hausdor? approximations come very close to such even distributions as described above for general MOPs, and even yield such approximations in case the Pareto front is linear. Visual observations and a comparison to other state-of-the-art EMOAs indicate that SMS_DPPSA is indeed a good cho |
