A new look at the topographical global optimization method and its application to the phase stability analysis of mixtures

Henderson, Nélio; Rêgo, Marroni de Sá; Sacco, Wagner F.; Rodrigues, Raimundo A.

doi:10.1016/j.ces.2015.01.029

Cited by 23 publications

(32 citation statements)

References 61 publications

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“…The TGO method is briefly reviewed in Chapter 2 closely following the formalism developed by Henderson et al (2015). In Chapter 3 we provide numerical examples of TGO which is then used as an informal experimental motivation for extending the algorithm.…”

Section: Structurementioning

confidence: 99%

“…Henderson et al (2015) also presents the algorithm in an introductory fashion. It is in essence an iterative clustering algorithm that maps the hypersurface of the objective function into a topography matrix (called a t-matrix) and then finds a certain number of starting points referred to as local minimisers.…”

Section: Chaptermentioning

confidence: 99%

“…Algorithms such as the basin-hopping global optimisation algorithm are typically used to find these points (Wales, 2015). The graph extracted from the topographical global optimisation (TGO) (Henderson et al, 2015;Törn, 1986;Törn, 1990;Törn & Viitanen, 1992) topograph (as described in Chapter 2) is unsatisfactory in some ways. Primarily because several starting points in the same locally convex domain can be generated even when enough information from the objective function sampling is known to prevent this from occurring.…”

Section: Synopsismentioning

confidence: 99%

“…Higher dimensional simplices can be represented and directed in a similar manner, for example a triangle consisting of three vertices v i , v j and Sacco, and Rodrigues, 2015;Törn, 1986;Törn, 1990;Törn & Viitanen, 1992) which is a clustering algorithm that finds several local minima from which the (probable) global minimum is found. It is often desirable to find all the local minima of the objective function for example in applications such as energy landscape exploration of potential models wherein mapping the local minima of the potential functions can provide valuable insights into the system.…”

Section: Synopsismentioning

confidence: 99%

“…The Topographical Global Optimisation (TGO) was originally conceived by Törn (1990) and Henderson et al (Henderson et al, 2015;Henderson, de Sá Rêgo, and Imbiriba, 2017) introduced new formalisms and empirical methods to determine hyperparameters described in this section. Henderson et al (2015) also presents the algorithm in an introductory fashion.…”

Section: Chaptermentioning

confidence: 99%

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A simplicial homology algorithm for Lipschitz optimisation

2018

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Un ni iv ve er rs si it ty y o of f P Pr re et to or ri ia a SynopsisThe 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 efficiently 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 finding all the local minima of an objective function with expensive function evaluations efficiently 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 first proposed by Törn (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 (Paulavičius anď Zilinskas, 2016) as well as the PSwarm and DIRECT-L1 algorithms. Furthermore SHGO is compared with the TGO, basinhopping (BH) and differential 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/.

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Section: Structurementioning

confidence: 99%

Section: Chaptermentioning

confidence: 99%

Section: Synopsismentioning

confidence: 99%

Section: Synopsismentioning

confidence: 99%

Section: Chaptermentioning

confidence: 99%

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A simplicial homology algorithm for Lipschitz optimisation

2018

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Equilibrium Study of Carbon Dioxide Reforming of Methane to Syngas

Li,

Wang

2024

Energy Tech

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Fugacity coefficients for the components in the gas mixture are determined using the Soave–Redlich–Kwong (SRK) equation of state. The Gibbs free energy minimization method is employed to determine the equilibrium composition of the components for CO2 reforming of CH4 to syngas. To utilize CO2 efficiently and avoid carbon deposition, CO2 composition in the initial feed should not be greater than 1 (nCH4,0 = 1), and the reaction is preferably operated at atmospheric pressure. Setting nCH4,0:nCO2,0 to 1:1, and increasing nO2,0 in the feed from 0 to 1.0 to adjust the initial composition, results in a decrease in the syngas equilibrium yield, and a increase in both nCO2,e and nH2O,e. The temperature required for complete carbon deposition removal decreased. Considering the effective utilization of CO2 at nCH4,0:nCO2,0 1:1, it is recommended to set nO2,0 in the feed to less than 0.5.

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