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Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm
Sayed, A. 2025. Investigating the use of Copulas to improve the Multi-Objective Optimisation Cross-Entropy Method algorithm. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/d73a9204-f1a6-40e3-9947-53b38cbbafdf
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| Language: | English |
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Stellenbosch : Stellenbosch University
2025
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| _version_ | 1867614087938048000 |
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| access_status_str | Open Access |
| author | Sayed, Atiyyah |
| author2 | Bekker, J. F. |
| author_browse | Bekker, J. F. Sayed, Atiyyah |
| author_facet | Bekker, J. F. Sayed, Atiyyah |
| author_sort | Sayed, Atiyyah |
| collection | Thesis |
| dc_rights_str_mv | Stellenbosch University |
| description | Sayed, A. 2025. Investigating the use of Copulas to improve the Multi-Objective Optimisation Cross-Entropy Method algorithm. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/d73a9204-f1a6-40e3-9947-53b38cbbafdf |
| format | Thesis |
| id | oai:scholar.sun.ac.za:10019.1/132270 |
| institution | Stellenbosch University (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:46:28.519Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from SUNScholar — Stellenbosch University Repository |
| publishDate | 2025 |
| publishDateRange | 2025 |
| publishDateSort | 2025 |
| publisher | Stellenbosch : Stellenbosch University |
| publisherStr | Stellenbosch : Stellenbosch University |
| record_format | dspace |
| source_str | SUNScholar — Stellenbosch University Repository |
| spelling | oai:scholar.sun.ac.za:10019.1/132270 Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm Sayed, Atiyyah Bekker, J. F. Stellenbosch University. Faculty of Engineering. Dept. of Industrial Engineering. Copulas (Mathematical statistics) Mathematical optimization Algorithms Stochastic processes -- Mathematical models Computational intelligence UCTD Sayed, A. 2025. Investigating the use of Copulas to improve the Multi-Objective Optimisation Cross-Entropy Method algorithm. Unpublished masters thesis. Stellenbosch: Stellenbosch University [online]. Available: https://scholar.sun.ac.za/items/d73a9204-f1a6-40e3-9947-53b38cbbafdf Thesis (MEng)--Stellenbosch University, 2025. ENGLISH ABSTRACT: This study investigates the enhancement of the Multi-Objective Optimisation Cross-Entropy Method (MOO CEM) by incorporating copulas to improve its efficiency in solving discrete multi-objective optimisation problems, particularly within the context of industrial engineering. The Cross-Entropy Method (CEM) is a powerful tool for stochastic optimisation that has been successfully adapted to multi-objective problems. However, its application to discrete optimisation problems with numerous decision variables remains computationally intensive. Previous research by Bekker (2012) demonstrated that MOO CEM could achieve effective solutions with lower computational costs, but challenges remain, especially when correlations between decision variables are not fully accounted for. This study explores the potential of copulas, a statistical tool used to model dependencies between variables, to improve the MOO CEM’s sampling process and solution quality. Specifically, the research focuses on two main questions, namely 1. Whether or not correlation and copulas can be leveraged to enhance solution speed and quality. 2. Whether or not copulas can replace the truncated normal distribution used in MOO CEM’s sampling method to improve performance. The proposed methodology involves investigating these questions through a literature review, algorithm development, and testing on benchmark multi-objective optimisation problems. The thesis aims to contribute to the advancement of the MOO CEM by proposing an enhanced algorithm that reduces computational burden while improving the quality of Pareto front approximations. The results of this study suggest that integrating copulas into the MOO CEM can lead to significant improvements in the algorithm’s performance, offering potential benefits for both academic research and industrial applications. Key outcomes include a comparison of the original and enhanced MOO CEM algorithms, demonstrating the effectiveness of copula-based sampling in optimizing discrete, multi-objective problems. The findings also provide insights into the broader applicability of copulas in optimisation methods for Industrial Engineering and other complex decision-making domains. AFRIKAANSE OPSOMMING: In hierdie studie word die verbetering van die multi-doelwit optimering-algoritme met die kruisentropie metode (MOO CEM) ondersoek deur copulas te inkorporeer. Daar is gepoog om die doeltreffendheid van die metode te verbeter tydens die oplos van diskrete multi-doelwitoptimeringsprobleme, veral binne die konteks van bedryfsingenieurswese. Die kruis-entropie metode is ‘n kragtige instrument vir stogastiese optimering wat suksesvol aangepas is vir multidoelwitprobleme. Die toepassing daarvan op diskrete optimeringsprobleme met talle besluitnemingsveranderlikes bly egter berekeningsintensief. Vorige navorsing deur Bekker (2012) het getoon dat MOO CEM effektiewe oplossings kan behaal met laer berekeningskoste, maar uitdagings bly oor, veral wanneer korrelasies tussen besluitnemingsveranderlikes nie ten volle in ag geneem word nie. Hierdie studie verken die potensiaal van copulas, ‘n statistiese instrument wat gebruik word om afhanklikhede tussen veranderlikes te modelleer, om die MOO CEM se steekproefmetode en oplossingkwaliteit te verbeter. Die navorsing fokus spesifiek op twee hoofvrae: 1. Of korrelasie en copulas benut kan word om die spoed en kwaliteit van oplossings te verbeter. 2. Of copulas die afgeknotte normaalverdeling wat in MOO CEM se steekproefmetode gebruik word, kan vervang om die algoritme se werkverrigting te verbeter. Die voorgestelde metodologie behels die ondersoek van hierdie vrae deur ‘n literatuurstudie, algoritme-uitbreiding en toetsing op multi-doelwit-optimering toetsprobleme. Die studie mik om by te dra tot die verbetering van die MOO CEM deur ‘n aangepaste algoritme voor te stel wat die rekenlas verminder terwyl die gehalte van Pareto-front-benaderings verbeter word. Die resultate van hierdie studie dui daarop dat die integrasie van copulas in die MOO CEM tot beduidende verbeterings in die algoritme se werkverrigting kan lei, wat potensiële voordele bied vir beide akademiese navorsing en industriële toepassings. Sleuteluikomste sluit ‘n vergelyking van die oorspronklike en verbeterde MOO CEM-algoritme in, wat die doeltreffendheid van copula-gebaseerde monsterneming in die optimering van diskrete, multi-doelwitprobleme demonstreer. Die bevindinge bied ook insigte oor die breër toepasbaarheid van copulas in optimeringsmetodes vir bedryfsingenieurswese en ander komplekse besluitnemingsdomeine. Masters 2025-06-02T09:15:03Z 2025-06-02T09:15:03Z 2025-03 Thesis https://scholar.sun.ac.za/handle/10019.1/132270 en Stellenbosch University xii, 95 pages : illustrations application/pdf Stellenbosch : Stellenbosch University |
| spellingShingle | Copulas (Mathematical statistics) Mathematical optimization Algorithms Stochastic processes -- Mathematical models Computational intelligence UCTD Sayed, Atiyyah Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm |
| title | Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm |
| title_full | Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm |
| title_fullStr | Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm |
| title_full_unstemmed | Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm |
| title_short | Investigating the use of copulas to improve the multi-objective optimisation cross-entropy method algorithm |
| title_sort | investigating the use of copulas to improve the multi objective optimisation cross entropy method algorithm |
| topic | Copulas (Mathematical statistics) Mathematical optimization Algorithms Stochastic processes -- Mathematical models Computational intelligence UCTD |
| url | https://scholar.sun.ac.za/handle/10019.1/132270 |
| work_keys_str_mv | AT sayedatiyyah investigatingtheuseofcopulastoimprovethemultiobjectiveoptimisationcrossentropymethodalgorithm |