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Parallel competing algorithms in global optimization
Dissertation (MSc)--University of Pretoria, 2000.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2022
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| _version_ | 1867613522037309441 |
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| access_status_str | Open Access |
| author2 | Groenwold, Albert A. |
| author_browse | Groenwold, Albert A. |
| author_facet | Groenwold, Albert A. |
| collection | Thesis |
| dc_rights_str_mv | © 2020 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. |
| description | Dissertation (MSc)--University of Pretoria, 2000. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/85359 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:37:28.861Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2022 |
| publishDateRange | 2022 |
| publishDateSort | 2022 |
| publisher | University of Pretoria |
| publisherStr | University of Pretoria |
| record_format | dspace |
| source_str | UPSpace — University of Pretoria Institutional Repository |
| spelling | oai:repository.up.ac.za:2263/85359 Parallel competing algorithms in global optimization Groenwold, Albert A. Bolton, H.P.J. UCTD Algorithms global optimization Dissertation (MSc)--University of Pretoria, 2000. Specialized techniques are needed to solve global optimization problems, due to the existence of multiple local optima or numerical noise in the objective function. The complexity of the problem is aggravated when discontinuities and constraints are present, or when evaluation of the objective function is computationally expensive. The global (minimization) programming problem is defined as finding the variable set for which the objective function obtains not only a local minimum, but also the smallest value, the global minimum. From a mathematical point of view, the global programming problem is essentially unsolvable, due to a lack of mathematical conditions characterizing the global optimum. In this study, the unconstrained global programming problem is addressed using a number of novel heuristic approaches. Firstly, a probabilistic global stopping criterion is presented for multi-start algorithms. This rule, denoted the unified Bayesian stopping criterion, is based on the single mild assumption that the probability of convergence to the global minimum is comparable to the probability of convergence to any other local minimum. This rule was previously presented for use in combination with a specific global optimization algorithm, and is now shown to be effective when used in a general multi-start approach. The suitability of the unified Bayesian stopping criterion is demonstrated for a number of algorithms using standard test functions. Secondly, multi-start global optimization algorithms based on multiple local searches, combined with the unified Bayesian stopping criterion, are presented. Numerical results reveal that these simple multi-start algorithms outperform a number of leading contenders. Thirdly, parallelization of the sequential multi-start algorithms is shown to effectively reduce the apparent computational time associated with solving expensive global programming problems. Fourthly, two algorithms simulating natural phenomena are implemented, namely the relatively new particle swarm optimization method and the well-known genetic algorithm. For the current implementations, numerical results indicate that the computational effort associated with these methods is comparable. Fifthly, the observation that no single global optimization algorithm can consistently outperform any other algorithm when a large set of problems is considered, leads to the development of a parallel competing algorithm infrastructure. In this infrastructure different algorithms, ranging from deterministic to stochastic, compete simultaneously for a contribution to the unified Bayesian global stopping criterion. This is an important step towards facilitating an infrastructure that is suitable for a range of problems in different classes. In the sixth place, the constrained global programming problems is addressed using constrained algorithms in the parallel competing algorithm infrastructure. The developed methods are extensively tested using standard test functions, for both serial and parallel implementations. An optimization procedure is also presented to solve the slope stability problem faced in civil engineering. This new procedure determines the factor of safety of slopes using a global optimization approach. Mechanical and Aeronautical Engineering MSc Unrestricted 2022-05-17T11:20:26Z 2022-05-17T11:20:26Z 2021/09/09 2000 Dissertation * https://repository.up.ac.za/handle/2263/85359 en © 2020 University of Pretoria. All rights reserved. The copyright in this work vests in the University of Pretoria. No part of this work may be reproduced or transmitted in any form or by any means, without the prior written permission of the University of Pretoria. application/pdf University of Pretoria |
| spellingShingle | UCTD Algorithms global optimization Parallel competing algorithms in global optimization |
| title | Parallel competing algorithms in global optimization |
| title_full | Parallel competing algorithms in global optimization |
| title_fullStr | Parallel competing algorithms in global optimization |
| title_full_unstemmed | Parallel competing algorithms in global optimization |
| title_short | Parallel competing algorithms in global optimization |
| title_sort | parallel competing algorithms in global optimization |
| topic | UCTD Algorithms global optimization |
| url | https://repository.up.ac.za/handle/2263/85359 |