Response surface approximation of Pareto optimal front in multi-objective optimization

Goel, Tushar; Vaidyanathan, Rajkumar; Haftka, Raphael T.; Shyy, Wei; Queipo, Néstor V.; Tucker, Kevin

doi:10.1016/j.cma.2006.07.010

Cited by 247 publications

(123 citation statements)

References 30 publications

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“…The surrogate models are formulated and trained using the numerical data for objective functions and design variables. The global POSs were obtained through a hybrid-MOEA (Deb, 2001;Goel et al, 2007). In this method, first, approximate POSs are obtained using the real-coded NSGA-II (Non-dominated Sorting Genetic Algorithm) (Deb, 2001) for two objective functions, viz., the mixing index and normalized friction factor.…”

Section: Multi-objective Evolutionary Algorithmmentioning

confidence: 99%

Optimization of Micromixer with Staggered Herringbone Grooves on Top and Bottom Walls

Hossain

Husain

Kim

2011

Engineering Applications of Computational Fluid Mechanics

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Multi-objective shape optimization of a micromixer with staggered herringbone grooves on the top and bottom walls has been performed through three-dimensional Navier-Stokes analysis, surrogate method and multi-objective evolutionary algorithm. Mixing index and friction factor are selected as objective functions, and four design variables, viz., number of grooves per half cycle (N), angle of groove (θ), groove depth to channel height ratio (d/h), and groove width to pitch ratio (Wd/pi) are chosen out of the various geometric parameters which affect the performance of the micromixer for the shape optimization. Numerical analysis has been performed with two working fluids, viz., water and ethanol at Reynolds number 1. The variance of the mass fraction at various nodes on a plane is used to quantify the mixing performance in the micromixer. The design space is explored through some preliminary calculations and a Latin hypercube sampling method is used as a design of experiments to exploit the design space. Response surface approximation model is constructed using numerical solutions at the designed-sites. The trade-off between the two competing objective functions has been found and discussed in the light of the distribution of Pareto-optimal solutions in the design space. It is observed that the Pareto-optimal solutions shift towards lower values of the design variables θ and wd/pi, and towards higher value of the design variable d/h whereas the design variable N remains insensitive along the Pareto-optimal front in the direction of higher mixing index.

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Section: Multi-objective Evolutionary Algorithmmentioning

confidence: 99%

Optimization of Micromixer with Staggered Herringbone Grooves on Top and Bottom Walls

Hossain

Husain

Kim

2011

Engineering Applications of Computational Fluid Mechanics

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“…Many optimal solutions within the design space are required to find the Pareto-optimal front (PoF). A hybrid MOO consists of elitist non-dominated sorting of genetic algorithm (NSGA-II) (Goel et al, 2007).…”

Section: Introductionmentioning

confidence: 99%

Shape optimization of a bidirectional impulse turbine via surrogate models

Ezhilsabareesh

Rhee

Samad

2017

Engineering Applications of Computational Fluid Mechanics

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In this work, a bidirectional impulse turbine used in a wave energy device is simulated using a CFD technique and a shape optimization performed with multiple surrogates-assisted multi-objective evolutionary algorithm. The surrogates have been generated using the validated CFD technique. The objectives for the optimization are to maximize the shaft power and to minimize the pressure drop across the turbine. The hub and the tip thickness of the rotor blade profiles are modified and considered as the design variables. The Latin hypercube sampling technique generated design points are evaluated in the CFD solver, the objective responses are used to construct multiple surrogates, and a Pareto optimal front is generated through a multi-objective optimization approach. The turbine efficiency, which is the function of pressure drop and shaft power, is relatively increased by 10.4%.

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“…A survey [22] summarizes methods published before 2003. More recent approximation methods for nonlinear MOPs are given e.g., in [3,5,15,16]. However, the uses of the PF approximations in decision making have not received the attention that they deserve.…”

mentioning

confidence: 99%

Decision Making on Pareto Front Approximations with Inherent Nondominance

Hartikainen

Miettinen

Wiecek

2011

Lecture Notes in Economics and Mathematical Systems

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Approximating the Pareto fronts of nonlinear multiobjective optimization problems is considered and a property called inherent nondominance is proposed for such approximations. It is shown that an approximation having the above property can be explored by interactively solving a multiobjective optimization problem related to it. This exploration can be performed with available interactive multiobjective optimization methods. The ideas presented are especially useful in solving computationally expensive multiobjective optimization problems with costly function value evaluations.

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Response surface approximation of Pareto optimal front in multi-objective optimization

Cited by 247 publications

References 30 publications

Optimization of Micromixer with Staggered Herringbone Grooves on Top and Bottom Walls

Optimization of Micromixer with Staggered Herringbone Grooves on Top and Bottom Walls

Shape optimization of a bidirectional impulse turbine via surrogate models

Decision Making on Pareto Front Approximations with Inherent Nondominance

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