STATISTICS OF THE PARETO FRONT IN MULTI-OBJECTIVE OPTIMIZATION UNDER UNCERTAINTIES

  • MOHAMED BASSI LERMA, Mohammed V University in Rabat, Mohammadia School of Engineers, Rabat, BP 765, Ibn Sina avenue, Agdal, Morocco
  • EDUARDO SOUZA DE CURSI LMN, EA 3828, INSA de Rouen-Normandie, BP 8, 76801 Saint-Etienne du Rouvray, France
  • EMMANUEL PAGNACCO LMN, EA 3828, INSA de Rouen-Normandie, BP 8, 76801 Saint-Etienne du Rouvray, France
  • RACHID ELLAIA LERMA, Mohammed V University in Rabat, Mohammadia School of Engineers, Rabat, BP 765, Ibn Sina avenue, Agdal, Morocco

Abstract

IN THIS PAPER WE ADDRESS AN INNOVATIVE APPROACH TO DETERMINE THE MEAN AND A CONFIDENCE INTERVAL FOR A SET OF OBJECTS ANALOGOUS TO CURVES AND SURFACES. THE APPROACH IS BASED ON THE DETERMINATION OF THE MOST REPRESENTATIVE MEMBER OF THE FAMILY BY MINIMIZING A HAUSDORFF DISTANCE.  THIS METHOD IS APPLIED TO THE ANALYSIS OF UNCERTAIN PARETO FRONTIERS IN MULTIOBJECTIVE OPTIMIZATION (MOO). THE DETERMINATION OF THE PARETO FRONT OF DETERMINISTIC MOO IS CARRIED BY MINIMIZING THE HYPERVOLUME CONTAINED BETWEEN THE FRONT AND THE UTOPIA POINT. WE GIVE SOME EXAMPLES AND WE APPLY THE APPROACH TO A TRUSS-LIKE STRUCTURE FOR WHICH CONFLICTING OBJECTIVE FUNCTIONS SUCH AS THE STRUCTURE MASS AND THE MAXIMUM DISPLACEMENT ARE BOTH TO BE MINIMIZED.

Published
2018-09-27
Section
Articles