It is widely believed that in order to solve large-scale global optimization problems, an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if first-order information on the objective function is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in absence of some kind of global information on the problem, is a ‘blind’ procedure, aimed at placing observations as evenly as possible in the search domain. Often, this procedure reduces to uniform random sampling (like in Multistart algorithms or in techniques based on clustering). In this paper, we propose a new framework for global exploration which tries to guide random exploration towards the region of attraction of low-level local optima. The main idea originated by the use of smoothing techniques (based on Gaussian convolutions): the possibility of applying a smoothing transformation not to the objective function but to the result of local searches seems to have never been explored yet. Although an exact smoothing of the results of local searches is impossible to implement, in this paper we propose a computational approximation scheme which has proven to be very efficient and (maybe more important) extremely robust in solving large-scale global optimization problems with huge numbers of local optima and, in particular, for problems displaying a ‘funnel’ structure.

Local Optima Smoothing for Global Optimization / ADDIS B.; LOCATELLI M.; F. SCHOEN. - In: OPTIMIZATION METHODS & SOFTWARE. - ISSN 1055-6788. - STAMPA. - 20:(2005), pp. 417-437. [10.1080/10556780500140029]

Local Optima Smoothing for Global Optimization

SCHOEN, FABIO
2005

Abstract

It is widely believed that in order to solve large-scale global optimization problems, an appropriate mixture of local approximation and global exploration is necessary. Local approximation, if first-order information on the objective function is available, is efficiently performed by means of local optimization methods. Unfortunately, global exploration, in absence of some kind of global information on the problem, is a ‘blind’ procedure, aimed at placing observations as evenly as possible in the search domain. Often, this procedure reduces to uniform random sampling (like in Multistart algorithms or in techniques based on clustering). In this paper, we propose a new framework for global exploration which tries to guide random exploration towards the region of attraction of low-level local optima. The main idea originated by the use of smoothing techniques (based on Gaussian convolutions): the possibility of applying a smoothing transformation not to the objective function but to the result of local searches seems to have never been explored yet. Although an exact smoothing of the results of local searches is impossible to implement, in this paper we propose a computational approximation scheme which has proven to be very efficient and (maybe more important) extremely robust in solving large-scale global optimization problems with huge numbers of local optima and, in particular, for problems displaying a ‘funnel’ structure.
2005
20
417
437
ADDIS B.; LOCATELLI M.; F. SCHOEN
File in questo prodotto:
File Dimensione Formato  
OptMetSoftw2005.pdf

Accesso chiuso

Tipologia: Versione finale referata (Postprint, Accepted manuscript)
Licenza: Tutti i diritti riservati
Dimensione 378.1 kB
Formato Adobe PDF
378.1 kB Adobe PDF   Richiedi una copia

I documenti in FLORE sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificatore per citare o creare un link a questa risorsa: https://hdl.handle.net/2158/222337
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 50
  • ???jsp.display-item.citation.isi??? 37
social impact