Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm

Yrjö Seppälä, Tuomo Orpana

Research output: Contribution to journalArticleScientificpeer-review

11 Citations (Scopus)

Abstract

The CHAPS algorithm (CHAPS = Chance-Constrained Programming System) has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other. The CHAPS algorithm is based on the separation, linearization and iterative adjusting of linearization of chance-constrained deterministic equivalents by using the simplex method.

According to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance-constrained model. The positive result is partly due to the fact that the linearized model is very sparse. The algorithm requires six to eight CHAPS iteration runs in order to achieve sufficient accuracy in practice (10−5 –10−6). The algorithm converges linearly and its asymptotic error constant is 14.
Original languageEnglish
Pages (from-to)345 - 357
Number of pages13
JournalEuropean Journal of Operational Research
Volume16
Issue number3
DOIs
Publication statusPublished - 1984
MoE publication typeNot Eligible

Fingerprint

Chance Constrained Programming
Experimental Study
Linearization
Computer systems programming
Linear Optimization
Simplex Method
Several Variables
Random variables
Random variable
Linearly
Directly proportional
Chance constrained programming
Experimental study
Model
Sufficient
Optimization Problem
Converge
Iteration

Cite this

@article{20ca07023c2b48faad9fcb3f549860fb,
title = "Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm",
abstract = "The CHAPS algorithm (CHAPS = Chance-Constrained Programming System) has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other. The CHAPS algorithm is based on the separation, linearization and iterative adjusting of linearization of chance-constrained deterministic equivalents by using the simplex method.According to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance-constrained model. The positive result is partly due to the fact that the linearized model is very sparse. The algorithm requires six to eight CHAPS iteration runs in order to achieve sufficient accuracy in practice (10−5 –10−6). The algorithm converges linearly and its asymptotic error constant is 14.",
author = "Yrj{\"o} Sepp{\"a}l{\"a} and Tuomo Orpana",
year = "1984",
doi = "10.1016/0377-2217(84)90289-3",
language = "English",
volume = "16",
pages = "345 -- 357",
journal = "European Journal of Operational Research",
issn = "0377-2217",
publisher = "Elsevier",
number = "3",

}

Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm. / Seppälä, Yrjö; Orpana, Tuomo.

In: European Journal of Operational Research, Vol. 16, No. 3, 1984, p. 345 - 357.

Research output: Contribution to journalArticleScientificpeer-review

TY - JOUR

T1 - Experimental study on the efficiency and accuracy of a chance-constrained programming algorithm

AU - Seppälä, Yrjö

AU - Orpana, Tuomo

PY - 1984

Y1 - 1984

N2 - The CHAPS algorithm (CHAPS = Chance-Constrained Programming System) has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other. The CHAPS algorithm is based on the separation, linearization and iterative adjusting of linearization of chance-constrained deterministic equivalents by using the simplex method.According to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance-constrained model. The positive result is partly due to the fact that the linearized model is very sparse. The algorithm requires six to eight CHAPS iteration runs in order to achieve sufficient accuracy in practice (10−5 –10−6). The algorithm converges linearly and its asymptotic error constant is 14.

AB - The CHAPS algorithm (CHAPS = Chance-Constrained Programming System) has proved to be an efficient and accurate method for solving linear optimization problems which have several random variables distributed normally and independently of each other. The CHAPS algorithm is based on the separation, linearization and iterative adjusting of linearization of chance-constrained deterministic equivalents by using the simplex method.According to test results the solution time of the algorithm is directly proportional to the second power of the number of constraints of a linearized model corresponding to the chance-constrained model. The positive result is partly due to the fact that the linearized model is very sparse. The algorithm requires six to eight CHAPS iteration runs in order to achieve sufficient accuracy in practice (10−5 –10−6). The algorithm converges linearly and its asymptotic error constant is 14.

U2 - 10.1016/0377-2217(84)90289-3

DO - 10.1016/0377-2217(84)90289-3

M3 - Article

VL - 16

SP - 345

EP - 357

JO - European Journal of Operational Research

JF - European Journal of Operational Research

SN - 0377-2217

IS - 3

ER -