Thesis (MEng)--Stellenbosch University, 2015. / ENGLISH ABSTRACT: A method for multi-objective optimisation using the cross-entropy
method (MOO CEM) was recently developed by Bekker & Aldrich
(2010) and Bekker (2012). The method aims to identify the nondominated
solutions of multi-objective problems, which are often dynamic
and stochastic. The method does not use a statistical ranking
and selection technique to account for the stochastic nature of the
problems it solves. The research in this thesis aims to investigate
possible techniques that can be incorporated into the MOO CEM.
The cross-entropy method for single-objective optimisation is studied
first. It is applied to an interesting problem in the soil sciences and
water management domain. The purpose of this was for the researcher
to grasp the fundamentals of the cross-entropy method, which will be
needed later in the study.
The second part of the study documents an overview of multi-objective
ranking and selection methods found in literature. The first method
covered is the multi-objective optimal computing budget allocation
algorithm. The second method extends upon the first to include the
concept of an indifference-zone. Both methods aim to maximise the
probability of correctly selecting the non-dominated scenarios, while
intelligently allocating simulation replications to minimise required
sample sizes. These techniques are applied to two problems that
are represented by simulation models, namely the buffer allocation
problem and a classic single-commodity inventory problem. Performance
is measured using the hyperarea indicator and Mann-Whitney
U-tests. It was found that the two techniques have significantly different
performances, although this could be due to the different number
of solutions in the Pareto set.
In the third part of the document, the aforementioned multi-objective
ranking and selection techniques are incorporated into the MOO CEM.
Once again, the buffer allocation problem and the inventory problem
were chosen as test problems. The results were compared to experiments
where the MOO CEM without ranking and selection was used.
Results show that the MOO CEM with ranking and selection has
various affects on different problems. Investigating the possibility of
incorporating ranking and selection differently in the MOO CEM is
recommended as future research. Additionally, the combined algorithm
should be tested on more stochastic problems. / AFRIKAANSE OPSOMMING: 'n Metode vir meerdoelige optimering wat gebruik maak van die kruisentropie-
metode (MOO CEM) is onlangs deur Bekker & Aldrich (2010)
en Bekker (2012) ontwikkel. Die metode mik om die nie-gedomineerde
oplossings van meerdoelige probleme te identifiseer, wat dikwels dinamies
en stogasties is. Die metode maak nie gebruik van 'n statistiese
orden-en-kies tegniek om die stogastiese aard van die problem aan te
spreek nie. Die navorsing in hierdie tesis poog om moontlike tegnieke
wat in die MOO CEM opgeneem kan word, te ondersoek.
Die kruis-entropie-metode vir enkeldoelwit optimering is eerste bestudeer.
Dit is toegepas op 'n interessante probleem in die grondwetenskappe
en waterbestuur domein. Die doel hiervan was om die navorser
die grondbeginsels van die kruis-entropie metode te help verstaan, wat
later in die studie benodig sal word.
Die tweede gedeelte van die studie verskaf 'n oorsig van meerdoelige
orden-en-kies metodes wat in die literatuur aangetref word. Die eerste
metode wat bespreek word, is die optimale toedeling van rekenaarbegroting
vir multi-doelwit optimering algoritme. Die tweede metode
brei uit oor die eerste metode wat die konsep van 'n neutrale sone
insluit. Beide metodes streef daarna om die waarskynlikheid dat die
nie-gedomineerde oplossings korrek gekies word te maksimeer, terwyl
dit ook steekproefgroottes probeer minimeer deur die aantal simulasieherhalings
intelligent toe te ken. Hierdie tegnieke word toegepas
op twee probleme wat verteenwoordig word deur simulasiemodelle,
naamlik die buffer-toedelingsprobleem en 'n klassieke enkelitem voorraadprobleem.
Die prestasie van die algoritmes word deur middel van
die hiperarea-aanwyser en Mann Whitney U-toetse gemeet. Daar is
gevind dat die twee tegnieke aansienlik verskillend presteer, alhoewel dit as gevolg van die verskillende aantal oplossings in die Pareto versameling
kan wees.
In die derde gedeelte van die dokument, is die bogenoemde meerdoelige
orden-en-kies tegnieke in die MOO CEM geïnkorporeer. Weereens
is die buffer-toedelingsprobleem en die voorraadprobleem as toetsprobleme
gekies. Die resultate was met die eksperimente waar die
MOO CEM sonder orden-en-kies gebruik is, vergelyk. Resultate toon
dat vir verskillende probleme, tree die MOO CEM met orden-en-kies
anders op. 'n Ondersoek oor 'n alternatiewe manier om orden-en-kies
met die MOO CEM te integreer is as toekomstige navorsing voorgestel.
Bykomend moet die gekombineerde algoritme op meer stogastiese
probleme getoets word.
| Identifer | oai:union.ndltd.org:netd.ac.za/oai:union.ndltd.org:sun/oai:scholar.sun.ac.za:10019.1/97072 |
| Date | 03 1900 |
| Creators | Von Lorne von Saint Ange, Chantel |
| Contributors | Bekker, James, 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 | 151 pages : illustrations |
| Rights | Stellenbosch University |
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