A heuristic rejection criterion in interval global optimization algorithms

L. G. Casado, I. García, T. Csendes

Research output: Contribution to journalArticle

18 Citations (Scopus)

Abstract

This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.

Original languageEnglish
Pages (from-to)683-692
Number of pages10
JournalBIT Numerical Mathematics
Volume41
Issue number4
Publication statusPublished - Dec 2001

Fingerprint

Global optimization
Rejection
Global Optimization
Optimization Algorithm
Heuristics
Interval
Inclusion
Branch and Bound Algorithm
Global Minimum
Minimizer
Numerical Study
Objective function
Optimization Problem

Keywords

  • Branch-and-bound algorithm
  • Global optimization
  • Inclusion function

ASJC Scopus subject areas

  • Computer Graphics and Computer-Aided Design
  • Software
  • Applied Mathematics
  • Computational Mathematics

Cite this

A heuristic rejection criterion in interval global optimization algorithms. / Casado, L. G.; García, I.; Csendes, T.

In: BIT Numerical Mathematics, Vol. 41, No. 4, 12.2001, p. 683-692.

Research output: Contribution to journalArticle

@article{847100955b6f4d3a81f0015c0f955b59,
title = "A heuristic rejection criterion in interval global optimization algorithms",
abstract = "This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.",
keywords = "Branch-and-bound algorithm, Global optimization, Inclusion function",
author = "Casado, {L. G.} and I. Garc{\'i}a and T. Csendes",
year = "2001",
month = "12",
language = "English",
volume = "41",
pages = "683--692",
journal = "BIT Numerical Mathematics",
issn = "0006-3835",
publisher = "Springer Netherlands",
number = "4",

}

TY - JOUR

T1 - A heuristic rejection criterion in interval global optimization algorithms

AU - Casado, L. G.

AU - García, I.

AU - Csendes, T.

PY - 2001/12

Y1 - 2001/12

N2 - This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.

AB - This paper investigates the properties of the inclusion functions on subintervals while a Branch-and-Bound algorithm is solving global optimization problems. It has been found that the relative place of the global minimum value within the inclusion interval of the inclusion function of the objective function at the actual interval mostly indicates whether the given interval is close to a minimizer point. This information is used in a heuristic interval rejection rule that can save a big amount of computation. Illustrative examples are discussed and a numerical study completes the investigation.

KW - Branch-and-bound algorithm

KW - Global optimization

KW - Inclusion function

UR - http://www.scopus.com/inward/record.url?scp=0042318562&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042318562&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0042318562

VL - 41

SP - 683

EP - 692

JO - BIT Numerical Mathematics

JF - BIT Numerical Mathematics

SN - 0006-3835

IS - 4

ER -