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A simplicial homology algorithm for Lipschitz optimisation
Dissertation (MEng)--University of Pretoria, 2017.
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| Format: | Thesis |
| Language: | English |
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University of Pretoria
2018
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| _version_ | 1867613560455036928 |
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| access_status_str | Open Access |
| author2 | Endres, Stefan |
| author_browse | Endres, Stefan |
| author_facet | Endres, Stefan |
| collection | Thesis |
| dc_rights_str_mv | © 2018 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 (MEng)--University of Pretoria, 2017. |
| format | Thesis |
| id | oai:repository.up.ac.za:2263/65186 |
| institution | University of Pretoria (South Africa) |
| language | English |
| last_indexed | 2026-06-10T12:38:04.955Z |
| license_str | Other — see source repository |
| provenance_str_mv | Harvested via OAI-PMH from UPSpace — University of Pretoria Institutional Repository |
| publishDate | 2018 |
| publishDateRange | 2018 |
| publishDateSort | 2018 |
| 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:2263/65186 A simplicial homology algorithm for Lipschitz optimisation Endres, Stefan UCTD Global optimisation SHGO Computational homology Engineering, built environment and information technology theses SDG-07 Engineering, built environment and information technology theses SDG-09 Engineering, built environment and information technology theses SDG-17 Dissertation (MEng)--University of Pretoria, 2017. The simplicial homology global optimisation (SHGO) algorithm is a general purpose global optimisation algorithm based on applications of simplicial integral homology and combinatorial topology. SHGO approximates the homology groups of a complex built on a hypersurface homeomorphic to a complex on the objective function. This provides both approximations of locally convex subdomains in the search space through Sperner's lemma (Sperner, 1928) and a useful visual tool for characterising and e ciently solving higher dimensional black and grey box optimisation problems. This complex is built up using sampling points within the feasible search space as vertices. The algorithm is specialised in nding all the local minima of an objective function with expensive function evaluations e ciently which is especially suitable to applications such as energy landscape exploration. SHGO was initially developed as an improvement on the topographical global optimisation (TGO) method rst proposed by T orn (1986; 1990; 1992). It is proven that the SHGO algorithm will always outperform TGO on function evaluations if the objective function is Lipschitz smooth. In this dissertation SHGO is applied to non-convex problems with linear and box constraints with bounds placed on the variables. Numerical experiments on linearly constrained test problems show that SHGO gives competitive results compared to TGO and the recently developed Lc-DISIMPL algorithm (Paulavi cius and Zilinskas, 2016) as well as the PSwarm and DIRECT-L1 algorithms. Furthermore SHGO is compared with the TGO, basinhopping (BH) and di erential evolution (DE) global optimisation algorithms over a large selection of black-box problems with bounds placed on the variables from the SciPy (Jones, Oliphant, Peterson, et al., 2001{) benchmarking test suite. A Python implementation of the SHGO and TGO algorithms published under a MIT license can be found from https://bitbucket.org/upiamcompthermo/shgo/. mi2026 Chemical Engineering MEng Unrestricted SDG-07: Affordable and clean energy SDG-09: Industry, innovation and infrastructure SDG-17: Partnerships for the goals 2018-06-20T11:44:59Z 2018-06-20T11:44:59Z 2018 2017 Dissertation Endres, S 2017, A simplicial homology algorithm for Lipschitz optimisation, MEng Dissertation, University of Pretoria, Pretoria, viewed yymmdd <http://hdl.handle.net/2263/65186> A2018 http://hdl.handle.net/2263/65186 en © 2018 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 Global optimisation SHGO Computational homology Engineering, built environment and information technology theses SDG-07 Engineering, built environment and information technology theses SDG-09 Engineering, built environment and information technology theses SDG-17 A simplicial homology algorithm for Lipschitz optimisation |
| title | A simplicial homology algorithm for Lipschitz optimisation |
| title_full | A simplicial homology algorithm for Lipschitz optimisation |
| title_fullStr | A simplicial homology algorithm for Lipschitz optimisation |
| title_full_unstemmed | A simplicial homology algorithm for Lipschitz optimisation |
| title_short | A simplicial homology algorithm for Lipschitz optimisation |
| title_sort | simplicial homology algorithm for lipschitz optimisation |
| topic | UCTD Global optimisation SHGO Computational homology Engineering, built environment and information technology theses SDG-07 Engineering, built environment and information technology theses SDG-09 Engineering, built environment and information technology theses SDG-17 |
| url | http://hdl.handle.net/2263/65186 |