Thesis (PhD)--Stellenbosch University, 2012. / ENGLISH ABSTRACT: A difficult subclass of engineering optimisation problems is the class
of optimisation problems which are dynamic and stochastic. These
problems are often of a non-closed form and thus studied by means of
computer simulation. Simulation production runs of these problems
can be time-consuming due to the computational burden implied by
statistical inference principles. In multi-objective optimisation of engineering
problems, large decision spaces and large objective spaces
prevail, since two or more objectives are simultaneously optimised and
many problems are also of a combinatorial nature. The computational
burden associated with solving such problems is even larger than for
most single-objective optimisation problems, and hence an e cient
algorithm that searches the vast decision space is required. Many
such algorithms are currently available, with researchers constantly
improving these or developing more e cient algorithms. In this context,
the term \e cient" means to provide near-optimised results with
minimal evaluations of objective function values. Thus far research has
often focused on solving speci c benchmark problems, or on adapting
algorithms to solve speci c engineering problems.
In this research, a multi-objective optimisation algorithm, based on the
cross-entropy method for single-objective optimisation, is developed
and assessed. The aim with this algorithm is to reduce the number
of objective function evaluations, particularly when time-dependent
(dynamic), stochastic processes, as found in Industrial Engineering,
are studied. A brief overview of scholarly work in the eld of multiobjective
optimisation is presented, followed by a theoretical discussion
of the cross-entropy method. The new algorithm is developed, based
on this information, and assessed considering continuous, deterministic
problems, as well as discrete, stochastic problems. The latter include a
classical single-commodity inventory problem, the well-known buffer allocation problem, and a newly designed, laboratory-sized recon gurable
manufacturing system. Near multi-objective optimisation of two
practical problems were also performed using the proposed algorithm.
In the rst case, some design parameters of a polymer extrusion unit are
estimated using the algorithm. The management of carbon monoxide
gas utilisation at an ilmenite smelter is complex with many decision
variables, and the application of the algorithm in that environment is
presented as a second case.
Quality indicator values are estimated for thirty-four test problem
instances of multi-objective optimisation problems in order to quantify
the quality performance of the algorithm, and it is also compared to a
commercial algorithm.
The algorithm is intended to interface with dynamic, stochastic simulation
models of real-world problems. It is typically implemented in a
programming language while the simulation model is developed in a
dedicated, commercial software package.
The proposed algorithm is simple to implement and proved to be
efficient on test problems. / AFRIKAANSE OPSOMMING: 'n Moeilike deelklas van optimeringsprobleme in die ingenieurswese
is optimeringsprobleme van 'n dinamiese en stogastiese aard. Sulke
probleme is dikwels nie-geslote en word gevolglik met behulp van rekenaarsimulasie
bestudeer. Die beginsels van statistiese steekproefneming
veroorsaak dat produksielopies van hierdie probleme tydrowend is weens
die rekenlas wat genoodsaak word. Groot besluitnemingruimtes en
doelwitruimtes bestaan in meerdoelige optimering van ingenieursprobleme,
waar twee of meer doelwitte gelyktydig geoptimeer word, terwyl
baie probleme ook 'n kombinatoriese aard het. Die rekenlas wat met
die oplos van sulke probleme gepaard gaan, is selfs groter as vir die
meeste enkeldoelwit optimeringsprobleme, en 'n doeltre ende algoritme
wat die meesal uitgebreide besluitnemingsruimte verken, is gevolglik
nodig. Daar bestaan tans verskeie sulke algoritmes, terwyl navorsers
steeds poog om hierdie algoritmes te verbeter of meer doeltre ende
algoritmes te ontwikkel. In hierdie konteks beteken \doeltre end" dat
naby-optimale oplossings verskaf word deur die minimum evaluering
van doelwitfunksiewaardes. Navorsing fokus dikwels op oplossing van
standaard toetsprobleme, of aanpassing van algoritmes om 'n spesi eke
ingenieursprobleem op te los.
In hierdie navorsing word 'n meerdoelige optimeringsalgoritme gebaseer
op die kruis-entropie-metode vir enkeldoelwit optimering ontwikkel
en geassesseer. Die mikpunt met hierdie algoritme is om die aantal
evaluerings van doelwitfunksiewaardes te verminder, spesi ek wanneer
tydafhanklike (dinamiese), stogastiese prosesse soos wat dikwels in die
Bedryfsingenieurswese te egekom word, bestudeer word. 'n Bondige
oorsig van navorsing in die veld van meerdoelige optimering word gegee,
gevolg deur 'n teoretiese bespreking van die kruis-entropiemetode. Die
nuwe algoritme se ontwikkeling is hierop gebaseer, en dit word geassesseer
deur kontinue, deterministiese probleme sowel as diskrete, stogastiese probleme benaderd daarmee op te los. Laasgenoemde sluit
in 'n klassieke enkelitem voorraadprobleem, die bekende buffer-toedelingsprobleem,
en 'n nuut-ontwerpte, laboratorium-skaal herkon gureerbare
vervaardigingstelsel. Meerdoelige optimering van twee praktiese
probleme is met die algoritme uitgevoer. In die eerste geval word sekere
ontwerpparameters van 'n polimeer-uittrekeenheid met behulp van die
algoritme beraam. Die bestuur van koolstofmonoksiedbenutting in 'n
ilmeniet-smelter is kompleks met verskeie besluitnemingveranderlikes,
en die toepassing van die algoritme in daardie omgewing word as 'n
tweede geval aangebied.
Verskeie gehalte-aanwyserwaardes word beraam vir vier-en-dertig toetsgevalle
van meerdoelige optimeringsprobleme om die gehalte-prestasie
van die algoritme te kwanti seer, en dit word ook vergelyk met 'n
kommersi ele algoritme.
Die algoritme is veronderstel om te skakel met dinamiese, stogastiese
simulasiemodelle van regtew^ereldprobleme. Die algoritme sal tipies in
'n programmeertaal ge mplementeer word terwyl die simulasiemodel
in doelmatige, kommersi ele programmatuur ontwikkel sal word. Die
voorgestelde algoritme is maklik om te implementeer en dit het doeltre
end gewerk op toetsprobleme.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/71717 |
| Date | 12 1900 |
| Creators | Bekker, James |
| Contributors | Van Vuuren, J. H., Stellenbosch University. Faculty of Engineering. Dept. of Industrial Engineering. |
| Publisher | Stellenbosch : Stellenbosch University |
| Source Sets | South African National ETD Portal |
| Language | en_ZA |
| Detected Language | English |
| Type | Thesis |
| Format | 172 p. : ill. |
| Rights | Stellenbosch University |
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