International Journal of Mathematical Modelling and Numerical Optimisation http://www.inderscience.com/browse/index.php?journalID=352&year=2012&vol=3&issue=1/2 Inderscience Publishers Ltd en-uk International Journal of Mathematical Modelling and Numerical Optimisation 2040-3607 2040-3615 © 2012 Inderscience Publishers Ltd editor@inderscience.com https://www.inderscience.com/images/files/coverImgs/ijmmno_scoverijmmno.jpg http://www.inderscience.com/browse/index.php?journalID=352&year=2012&vol=3&issue=1/2 http://www.inderscience.com/link.php?id=44711 The present paper introduces the GATE algorithm, which was specifically designed to lessen the cost of GAs for engineering design problems. The main strength of the algorithm is to find a good design using a relatively low number of function evaluations. The heart of the algorithm is a new heuristic called territorial core evolution (TE). TE regulates the mean step and the permitted search area of the GAs' random search operators, depending on the state of convergence of the algorithm. As a result, more global or more local searches are made when necessary to better fit the specificities of each problem. GATE, which was initially calibrated using a Gaussian landscape generator as test case, is shown to be very efficient to solve that kind of topology, especially for large scale problems. Application of the GATE algorithm to various classical test cases allows a better understanding of the strengths and limitations of this algorithm. GATE: a genetic algorithm designed for expensive cost functions
Stéphane Dominique; Jean-Yves Trépanier; Christophe Tribes
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 5 - 29
The present paper introduces the GATE algorithm, which was specifically designed to lessen the cost of GAs for engineering design problems. The main strength of the algorithm is to find a good design using a relatively low number of function evaluations. The heart of the algorithm is a new heuristic called territorial core evolution (TE). TE regulates the mean step and the permitted search area of the GAs' random search operators, depending on the state of convergence of the algorithm. As a result, more global or more local searches are made when necessary to better fit the specificities of each problem. GATE, which was initially calibrated using a Gaussian landscape generator as test case, is shown to be very efficient to solve that kind of topology, especially for large scale problems. Application of the GATE algorithm to various classical test cases allows a better understanding of the strengths and limitations of this algorithm.

]]> 10.1504/IJMMNO.2012.044711 International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 5 - 29 Stéphane Dominique; Jean-Yves Trépanier; Christophe Tribes Department of Mechanical Engineering, École Polytechnique de Montréal, 2500, chemin de Polytechnique, Montréal (Québec), H3T 1J4, Canada. ' Department of Mechanical Engineering, École Polytechnique de Montréal, 2500, chemin de Polytechnique, Montréal (Québec), H3T 1J4, Canada. ' Department of Mechanical Engineering, École Polytechnique de Montréal, 2500, chemin de Polytechnique, Montréal (Québec), H3T 1J4, Canada optimisation genetic algorithms territorial core evolution large scale design problems academic test cases engineering design. 2012-01-04T23:20:50-05:00 3 1/2 5 29 2012-01-04T23:20:50-05:00 http://www.inderscience.com/link.php?id=44712 Fuzzy reliability-based optimisation tasks feature high-dimensional and highly non-linear response surfaces. Due to the computational expense, metamodels have to be applied, which are capable to approximate these response surfaces appropriately. In this paper, two complementary approaches of simulation-driven sequential metamodels are introduced for a fuzzy reliability-based optimisation. First, a function decomposition for a fuzzy reliability-based optimisation is worked out. It enables to build metamodels for the space of design variables and the space of uncertain variables separately. Second, local metamodels are applied to approximate the response surface adaptively. Thereby, the pointwise local approximations are controlled by the fuzzy reliability-based optimisation algorithm. In consequence, the function evaluation, e.g., finite element analysis, is only performed in regions of interest. Simulation-driven sequential metamodels for fuzzy reliability-based optimisation tasks
Stephan Pannier; Wolfgang Graf
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 30 - 44
Fuzzy reliability-based optimisation tasks feature high-dimensional and highly non-linear response surfaces. Due to the computational expense, metamodels have to be applied, which are capable to approximate these response surfaces appropriately. In this paper, two complementary approaches of simulation-driven sequential metamodels are introduced for a fuzzy reliability-based optimisation. First, a function decomposition for a fuzzy reliability-based optimisation is worked out. It enables to build metamodels for the space of design variables and the space of uncertain variables separately. Second, local metamodels are applied to approximate the response surface adaptively. Thereby, the pointwise local approximations are controlled by the fuzzy reliability-based optimisation algorithm. In consequence, the function evaluation, e.g., finite element analysis, is only performed in regions of interest.

]]> 10.1504/IJMMNO.2012.044712 International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 30 - 44 Stephan Pannier; Wolfgang Graf Institute for Structural Analysis, Technische Universität Dresden, 01062 Dresden, Germany. ' Institute for Structural Analysis, Technische Universität Dresden, 01062 Dresden, Germany local metamodels fuzzy reliability optimisation FRBO simulation metamodelling local response surface approximation sequential metamodels finite element analysis FEA. 2012-01-04T23:20:50-05:00 3 1/2 30 44 2012-01-04T23:20:50-05:00 http://www.inderscience.com/link.php?id=44713 To overcome the excessive CPU cost of evolutionary algorithms (EAs) which make use of demanding evaluation models, metamodel-assisted EAs (MAEAs) have been devised and used in either single-objective (SOO) or multi-objective (MOO) problems. MAEAs are based on low-cost surrogate evaluation models that screen out non-promising individuals during the evolution and exclude them from the expensive, problem-specific evaluation. This paper proposes a new technique that further reduces the computational cost of MAEAs. This technique is based on the principal-component-analysis (PCA) of the non-dominated individuals (in MOO) within each generation, to identify dependences among the design variables and, through appropriate rotations, use this piece of information to efficiently 'drive' the application of the evolution operators. The proposed technique is used to perform the multi-operating point design of a matrix hydraulic turbine, where each evaluation is based on a 3D computational fluid dynamics (CFD) code; this is a highly constrained optimisation problem with many objectives, which is herein handled as a two-objective one. Some convincing mathematical function minimisation problems are also worked out using PCA-driven EAs; it is, thus, shown that the PCA-driven evolution operators can be used with or without metamodels. Design of a matrix hydraulic turbine using a metamodel-assisted evolutionary algorithm with PCA-driven evolution operators
Stylianos A. Kyriacou; Simon Weissenberger; Kyriakos C. Giannakoglou
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 45 - 63
To overcome the excessive CPU cost of evolutionary algorithms (EAs) which make use of demanding evaluation models, metamodel-assisted EAs (MAEAs) have been devised and used in either single-objective (SOO) or multi-objective (MOO) problems. MAEAs are based on low-cost surrogate evaluation models that screen out non-promising individuals during the evolution and exclude them from the expensive, problem-specific evaluation. This paper proposes a new technique that further reduces the computational cost of MAEAs. This technique is based on the principal-component-analysis (PCA) of the non-dominated individuals (in MOO) within each generation, to identify dependences among the design variables and, through appropriate rotations, use this piece of information to efficiently 'drive' the application of the evolution operators. The proposed technique is used to perform the multi-operating point design of a matrix hydraulic turbine, where each evaluation is based on a 3D computational fluid dynamics (CFD) code; this is a highly constrained optimisation problem with many objectives, which is herein handled as a two-objective one. Some convincing mathematical function minimisation problems are also worked out using PCA-driven EAs; it is, thus, shown that the PCA-driven evolution operators can be used with or without metamodels.

]]> 10.1504/IJMMNO.2012.044713 International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 45 - 63 Stylianos A. Kyriacou; Simon Weissenberger; Kyriakos C. Giannakoglou Andritz HYDRO, RD, Lunzerstrasse 78, 4031 Linz, Austria; National Technical University of Athens, Parallel CFD and Optimisation Unit, P.O. Box 64069, Athens 15710, Greece. ' Andritz HYDRO, RD, Lunzerstrasse 78, 4031 Linz, Austria. ' National Technical University of Athens, Parallel CFD and Optimisation Unit, P.O. Box 64069, Athens 15710, Greece optimisation evolutionary algorithms EAs metamodelling correlated design variables hydraulic turbines turbine design principal component analysis PCA computational fluid dynamics CFD constrained optimisation. 2012-01-04T23:20:50-05:00 3 1/2 45 63 2012-01-04T23:20:50-05:00 http://www.inderscience.com/link.php?id=44714 The main obstacle in simulation-driven design optimisation of microwave structures is the high computational cost of high-fidelity electromagnetic (EM) simulation. In this paper, we discuss two computationally efficient design optimisation methodologies that exploit variable-fidelity electromagnetic models. The first technique is based on sequential optimisation of coarse-discretisation EM models. The optimal design of the current model is used as an initial design for the finer-discretisation one. The final design is then obtained in the refinement procedure that uses a polynomial approximation of the coarse-discretisation EM data. The unavoidable misalignment between the polynomial and the high-fidelity model is corrected using space mapping. The second technique also exploits coarse-discretisation EM model, however, the discrepancy between the lowand high-fidelity models is accounted for by appropriate adjustment of the design specifications. Our techniques are straightforward to implement and computationally efficient because the optimisation burden is shifted to the coarse-discretisation models. They are also applicable to virtually any type of microwave structures which is demonstrated using several design examples, including microstrip bandpass filter, planar ultrawideband antenna and a coplanar-waveguide-to-microstrip transition. Variable-fidelity simulation-driven design optimisation of microwave structures
Slawomir Koziel; Stanislav Ogurtsov; Leifur Leifsson
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 64 - 81
The main obstacle in simulation-driven design optimisation of microwave structures is the high computational cost of high-fidelity electromagnetic (EM) simulation. In this paper, we discuss two computationally efficient design optimisation methodologies that exploit variable-fidelity electromagnetic models. The first technique is based on sequential optimisation of coarse-discretisation EM models. The optimal design of the current model is used as an initial design for the finer-discretisation one. The final design is then obtained in the refinement procedure that uses a polynomial approximation of the coarse-discretisation EM data. The unavoidable misalignment between the polynomial and the high-fidelity model is corrected using space mapping. The second technique also exploits coarse-discretisation EM model, however, the discrepancy between the lowand high-fidelity models is accounted for by appropriate adjustment of the design specifications. Our techniques are straightforward to implement and computationally efficient because the optimisation burden is shifted to the coarse-discretisation models. They are also applicable to virtually any type of microwave structures which is demonstrated using several design examples, including microstrip bandpass filter, planar ultrawideband antenna and a coplanar-waveguide-to-microstrip transition.

]]> 10.1504/IJMMNO.2012.044714 International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 64 - 81 Slawomir Koziel; Stanislav Ogurtsov; Leifur Leifsson Engineering Optimization and Modeling Center, School of Science and Engineering, Reykjavik University, Menntavegur 1, 101 Reykjavik, Iceland. ' Engineering Optimization and Modeling Center, School of Science and Engineering, Reykjavik University, Menntavegur 1, 101 Reykjavik, Iceland. ' Engineering Optimization and Modeling Center, School of Science and Engineering, Reykjavik University, Menntavegur 1, 101 Reykjavik, Iceland computer-aided design CAD electromagnetic simulation adaptive design specifications variable fidelity optimisation surrogate modelling microwave design design optimisation electromagnetic models microwave structures. 2012-01-04T23:20:50-05:00 3 1/2 64 81 2012-01-04T23:20:50-05:00 http://www.inderscience.com/link.php?id=44715 This paper discusses the viability of using a metamodelling technique in conjunction with a controlled random search algorithm (CRSA) for global optimisation of costly functions. CRSA is a stochastic, population-set based algorithm, capable of performing global optimisation tasks efficiently. The metamodel technique is based on the iterative construction of response surfaces with radial basis functions (inverse multiquadrics) using the points exactly evaluated during the optimisation process. Cyclic search patterns for metamodel constrained optimisations are iteratively used for determining candidate points using CRSA. The methodology is tested on some Dixon-Szeg Metamodelling approach using radial basis functions, stochastic search algorithm and CFD – application to blade cascade design
Edna R. Da Silva; Nelson Manzanares-Filho; Ramiro G. Ramirez Camacho
International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 82 - 97
This paper discusses the viability of using a metamodelling technique in conjunction with a controlled random search algorithm (CRSA) for global optimisation of costly functions. CRSA is a stochastic, population-set based algorithm, capable of performing global optimisation tasks efficiently. The metamodel technique is based on the iterative construction of response surfaces with radial basis functions (inverse multiquadrics) using the points exactly evaluated during the optimisation process. Cyclic search patterns for metamodel constrained optimisations are iteratively used for determining candidate points using CRSA. The methodology is tested on some Dixon-Szeg

]]> 10.1504/IJMMNO.2012.044715 International Journal of Mathematical Modelling and Numerical Optimisation, Vol. 3, No. 1/2 (2012) pp. 82 - 97 Edna R. Da Silva; Nelson Manzanares-Filho; Ramiro G. Ramirez Camacho UNIFEI, Federal University of Itajubá, P.O. Box 50, CEP 37500 903, Pinheirinho, Itajubá – MG, Brazil. ' UNIFEI, Federal University of Itajubá, P.O. Box 50, CEP 37500 903, Pinheirinho, Itajubá – MG, Brazil. ' UNIFEI, Federal University of Itajubá, P.O. Box 50, CEP 37500 903, Pinheirinho, Itajubá – MG, Brazil metamodelling global optimisation controlled random search algorithm CRSA constrained optimisation response surfaces CORS computational fluid dynamics CFD blade cascade design radial basis functions inverse multiquadrics airfoil camber lift-to-drag ratio airfoil pitch. 2012-01-04T23:20:50-05:00 3 1/2 82 97 2012-01-04T23:20:50-05:00