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

Authors

  • 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.

Downloads

Published

2018-09-27

Issue

Vol. 15 No. 11 (2018)

Section

Articles

License

Authors who publish with this journal agree to the following terms:

 

  1. Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License [CC BY] that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  2. Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  3. Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).