title: Surrogate-Assisted Evolutionary Algorithms for Wind Farm Layout Optimisation Problem

authors: Zheng, Chen

subjects: surrogate-assisted evolutionary optimisation

abstract: Due to the increasing need for computationally expensive optimisation in many real-world applications, surrogate-assisted evolutionary algorithms have attracted growing attention. In the literature, surrogate-assisted evolutionary approaches have been successful in highly computational expensive optimisation problems. However, surrogates have not been used with the Wind Farm Layout Optimisation Problem (WFLOP) before.

In this work, an evolutionary approach using surrogate modelling techniques to reduce the computational cost of the WFLOP is studied. The WFLOP mainly focuses on finding the optimal geographical placement of wind turbines within a wind farm in order to maximise power generation. But evaluating wind farm layout is very computationally expensive. The purpose of using surrogates is to approximate the real evaluation function of an evolutionary algorithm, but the surrogates can be computed more efficiently. The aim of this study is try to discover whether if surrogate-assisted evolutionary approach is effective on the WFLOP.

An analytical wake model is used to calculate the velocity deficits in the downstream generated by individual turbines. A set of initial offline experiments was conducted based on a dataset of wind farm layouts sampled from the space of all layouts, using biased random walk. These experiments were designed to discover which features lead to construction of an accurate surrogate model. According to the results of these experiments, polar coordinates (sorted according to distance) as features are selected for learning. A multilayer perceptron (MLP) neural network and a tree-based regression model (M5P) are chosen as the surrogate models to approximate the real fitness function in conjunction with an (mu, lambda) evolutionary strategy. Two previously presented BlockCopy operators are used in the evolutionary strategy. The surrogate models are managed using a modified version of the Pre-selection strategy and the Best strategy.

Our evaluation used four benchmark wind farm scenarios with dimensionality ranging from 200 to 1420 dimensions. The evaluation results show that our preliminary MLP and M5P surrogate models did not improve the optimisation results over traditional evolutionary strategies due to scalability issues. The scalability is a known weakness of many surrogate-assisted evolutionary approaches for the reason that most of them are designed for low-dimensionality problems. However, the research should continue on this topic because of its importance to renewable energy.

text: Surrogate-Assisted Evolutionary Algorithms for Wind Farm Layout Optimisation Problem Due to the increasing need for computationally expensive optimisation in many real-world applications, surrogate-assisted evolutionary algorithms have attracted growing attention. In the literature, surrogate-assisted evolutionary approaches have been successful in highly computational expensive optimisation problems. However, surrogates have not been used with the Wind Farm Layout Optimisation Problem (WFLOP) before.

In this work, an evolutionary approach using surrogate modelling techniques to reduce the computational cost of the WFLOP is studied. The WFLOP mainly focuses on finding the optimal geographical placement of wind turbines within a wind farm in order to maximise power generation. But evaluating wind farm layout is very computationally expensive. The purpose of using surrogates is to approximate the real evaluation function of an evolutionary algorithm, but the surrogates can be computed more efficiently. The aim of this study is try to discover whether if surrogate-assisted evolutionary approach is effective on the WFLOP.

An analytical wake model is used to calculate the velocity deficits in the downstream generated by individual turbines. A set of initial offline experiments was conducted based on a dataset of wind farm layouts sampled from the space of all layouts, using biased random walk. These experiments were designed to discover which features lead to construction of an accurate surrogate model. According to the results of these experiments, polar coordinates (sorted according to distance) as features are selected for learning. A multilayer perceptron (MLP) neural network and a tree-based regression model (M5P) are chosen as the surrogate models to approximate the real fitness function in conjunction with an (mu, lambda) evolutionary strategy. Two previously presented BlockCopy operators are used in the evolutionary strategy. The surrogate models are managed using a modified version of the Pre-selection strategy and the Best strategy.

Our evaluation used four benchmark wind farm scenarios with dimensionality ranging from 200 to 1420 dimensions. The evaluation results show that our preliminary MLP and M5P surrogate models did not improve the optimisation results over traditional evolutionary strategies due to scalability issues. The scalability is a known weakness of many surrogate-assisted evolutionary approaches for the reason that most of them are designed for low-dimensionality problems. However, the research should continue on this topic because of its importance to renewable energy.

year: 2016

title: Identities in the Algebra of Partial Maps

authors: Jackson, Marcel

subjects: mathematics

abstract: We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

text: Identities in the Algebra of Partial Maps We consider the identities of a variety of semigroup-related algebras modelling the algebra of partial maps. We show that the identities are intimately related to a weak semigroup deductive system and we show that the equational theory is decidable. We do this by giving a term rewriting system for the variety. We then show that this variety has many subvarieties whose equational theory interprets the full uniform word problem for semigroups and consequently are undecidable. As a corollary it is shown that the equational theory of Clifford semigroups whose natural order is a semilattice is undecidable.

year: 2006

title: Reo Rua Pukapuka Pikitia: Whānau drawing on their community cultural wealth to create strategies for developing Te Reo Rangatira

authors: Brouwer, Jacqui

abstract: The use of Te Reo Māori in Early Childhood Education in Aotearoa New Zealand is mandated in the ECE curriculum. Research shows that picturebooks are powerful tools in language learning, but there is a lack of research concerning the use of bilingual picturebooks by whānau to support Māori language learning in a New Zealand kindergarten. This research presents findings from a 4-week programme in which five whānau members were introduced to several types of dual language picturebooks (Reo Rua Pukapuka Pikitia, RRPP) in a Puna Pukapuka Pikitia (PPP). Whānau explored RRPP and suggested how they could bring Reo Rangatira from RRPP into their homes to support language learning. Their suggestions aligned with Ellis’s principles of effective language teaching (Ellis, 2010) including the development of formulaic phrases, following the ways in which tamariki naturally learn language, encouraging opportunities for tamariki to speak and listen, as well as having interactions linked to RRPP.

text: Reo Rua Pukapuka Pikitia: Whānau drawing on their community cultural wealth to create strategies for developing Te Reo Rangatira The use of Te Reo Māori in Early Childhood Education in Aotearoa New Zealand is mandated in the ECE curriculum. Research shows that picturebooks are powerful tools in language learning, but there is a lack of research concerning the use of bilingual picturebooks by whānau to support Māori language learning in a New Zealand kindergarten. This research presents findings from a 4-week programme in which five whānau members were introduced to several types of dual language picturebooks (Reo Rua Pukapuka Pikitia, RRPP) in a Puna Pukapuka Pikitia (PPP). Whānau explored RRPP and suggested how they could bring Reo Rangatira from RRPP into their homes to support language learning. Their suggestions aligned with Ellis’s principles of effective language teaching (Ellis, 2010) including the development of formulaic phrases, following the ways in which tamariki naturally learn language, encouraging opportunities for tamariki to speak and listen, as well as having interactions linked to RRPP.

year: 2023