Symbolic interval inference approach for subdivision direction selection in interval partitioning algorithms

Chandra Sekhar Pedamallu, Linet Özdamar, T. Csendes

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

In bound constrained global optimization problems, partitioning methods utilizing Interval Arithmetic are powerful techniques that produce reliable results. Subdivision direction selection is a major component of partitioning algorithms and it plays an important role in convergence speed. Here, we propose a new subdivision direction selection scheme that uses symbolic computing in interpreting interval arithmetic operations. We call this approach symbolic interval inference approach (SIIA). SIIA targets the reduction of interval bounds of pending boxes directly by identifying the major impact variables and re-partitioning them in the next iteration. This approach speeds up the interval partitioning algorithm (IPA) because it targets the pending status of sibling boxes produced. The proposed SIIA enables multi-section of two major impact variables at a time. The efficiency of SIIA is illustrated on well-known bound constrained test functions and compared with established subdivision direction selection methods from the literature.

Original languageEnglish
Pages (from-to)177-194
Number of pages18
JournalJournal of Global Optimization
Volume37
Issue number2
DOIs
Publication statusPublished - Feb 2007

Fingerprint

Subdivision
Partitioning
partitioning
Interval
Constrained optimization
Global optimization
Interval Arithmetic
Symbolic Computing
Constrained Global Optimization
Target
Convergence Speed
Test function
Inference
Speedup
Optimization Problem
Iteration

Keywords

  • Box-constrained global optimization
  • Interval branch and bound methods
  • Subdivision direction selection
  • Symbolic computing

ASJC Scopus subject areas

  • Applied Mathematics
  • Control and Optimization
  • Management Science and Operations Research
  • Global and Planetary Change

Cite this

Symbolic interval inference approach for subdivision direction selection in interval partitioning algorithms. / Pedamallu, Chandra Sekhar; Özdamar, Linet; Csendes, T.

In: Journal of Global Optimization, Vol. 37, No. 2, 02.2007, p. 177-194.

Research output: Contribution to journalArticle

@article{d2341d05b66a48c180804242b3d5c709,
title = "Symbolic interval inference approach for subdivision direction selection in interval partitioning algorithms",
abstract = "In bound constrained global optimization problems, partitioning methods utilizing Interval Arithmetic are powerful techniques that produce reliable results. Subdivision direction selection is a major component of partitioning algorithms and it plays an important role in convergence speed. Here, we propose a new subdivision direction selection scheme that uses symbolic computing in interpreting interval arithmetic operations. We call this approach symbolic interval inference approach (SIIA). SIIA targets the reduction of interval bounds of pending boxes directly by identifying the major impact variables and re-partitioning them in the next iteration. This approach speeds up the interval partitioning algorithm (IPA) because it targets the pending status of sibling boxes produced. The proposed SIIA enables multi-section of two major impact variables at a time. The efficiency of SIIA is illustrated on well-known bound constrained test functions and compared with established subdivision direction selection methods from the literature.",
keywords = "Box-constrained global optimization, Interval branch and bound methods, Subdivision direction selection, Symbolic computing",
author = "Pedamallu, {Chandra Sekhar} and Linet {\"O}zdamar and T. Csendes",
year = "2007",
month = "2",
doi = "10.1007/s10898-006-9043-y",
language = "English",
volume = "37",
pages = "177--194",
journal = "Journal of Global Optimization",
issn = "0925-5001",
publisher = "Springer Netherlands",
number = "2",

}

TY - JOUR

T1 - Symbolic interval inference approach for subdivision direction selection in interval partitioning algorithms

AU - Pedamallu, Chandra Sekhar

AU - Özdamar, Linet

AU - Csendes, T.

PY - 2007/2

Y1 - 2007/2

N2 - In bound constrained global optimization problems, partitioning methods utilizing Interval Arithmetic are powerful techniques that produce reliable results. Subdivision direction selection is a major component of partitioning algorithms and it plays an important role in convergence speed. Here, we propose a new subdivision direction selection scheme that uses symbolic computing in interpreting interval arithmetic operations. We call this approach symbolic interval inference approach (SIIA). SIIA targets the reduction of interval bounds of pending boxes directly by identifying the major impact variables and re-partitioning them in the next iteration. This approach speeds up the interval partitioning algorithm (IPA) because it targets the pending status of sibling boxes produced. The proposed SIIA enables multi-section of two major impact variables at a time. The efficiency of SIIA is illustrated on well-known bound constrained test functions and compared with established subdivision direction selection methods from the literature.

AB - In bound constrained global optimization problems, partitioning methods utilizing Interval Arithmetic are powerful techniques that produce reliable results. Subdivision direction selection is a major component of partitioning algorithms and it plays an important role in convergence speed. Here, we propose a new subdivision direction selection scheme that uses symbolic computing in interpreting interval arithmetic operations. We call this approach symbolic interval inference approach (SIIA). SIIA targets the reduction of interval bounds of pending boxes directly by identifying the major impact variables and re-partitioning them in the next iteration. This approach speeds up the interval partitioning algorithm (IPA) because it targets the pending status of sibling boxes produced. The proposed SIIA enables multi-section of two major impact variables at a time. The efficiency of SIIA is illustrated on well-known bound constrained test functions and compared with established subdivision direction selection methods from the literature.

KW - Box-constrained global optimization

KW - Interval branch and bound methods

KW - Subdivision direction selection

KW - Symbolic computing

UR - http://www.scopus.com/inward/record.url?scp=33846106858&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33846106858&partnerID=8YFLogxK

U2 - 10.1007/s10898-006-9043-y

DO - 10.1007/s10898-006-9043-y

M3 - Article

AN - SCOPUS:33846106858

VL - 37

SP - 177

EP - 194

JO - Journal of Global Optimization

JF - Journal of Global Optimization

SN - 0925-5001

IS - 2

ER -