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:10.2514/6.2004-4501

Cited by 35 publications

(30 citation statements)

References 1 publication

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“…Goel et al [13] noted that in MOEA, the genetic operators may destroy some of the solutions to explore the design space. Introducing elitism in MOEAs alleviates this problem to some extent, but when the number of nondominated solutions in the combined population exceeds the population size, as happens commonly in elitist MOEAs, some of the non-dominated solutions have to be dropped.…”

Section: Mogamentioning

confidence: 99%

“…Therefore, an archiving strategy is suggested to augment NSGA-II, and is referred to as archiving NSGA-II (NSGAIIa) [13]. The strategy of NSGA-IIa is to keep all the potential non-dominated solutions in one group during the whole evolution process.…”

Section: Mogamentioning

confidence: 99%

“…The load path is therefore optimized by minimizing each of these formability objectives (Eqs. [10][11][12][13][14], and the problem can be summarized by the following formulation which places constraints on each objective:…”

Section: Objective Functions and Constraintsmentioning

confidence: 99%

“…As pointed out by Hughes [12], one concern with the methods described so far is that fitness assignments based on dominance rank (like NSGA-II) often performs poorly when the number of objectives is greater than three or four. Although the accuracy can be improved by adding more sampling points, the prediction error may still affect the constraint handling and the poor results may be amplified through the effect of Pareto drift [13].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming

Hong-gang

Green

Johrendt

2011

Int J Adv Manuf Technol

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The production of a tubular hydroformed part often requires a combination of internal pressure and axial force at the tube ends to fully form the tube to its specified geometry. A successful hydroforming process requires not only achieving a part that conforms to the design specifications, but also ensures that the part has a reasonably uniform thickness distribution and is free of defects, such as wrinkles, severe thinning, or fractures. The load path design (pressure vs. end feed history) largely determines the robustness of the process and the quality of the finished parts. In this paper, a hybrid constrained optimization method was proposed to solve this type of multi-objective problem by coupling a multi-objective genetic algorithm and a local search. The load path design procedure was developed by considering five objectives: four formability objectives (i.e., to minimize the risk of wrinkling, global and local thinning, and fracture) and a geometric objective (to minimize the corner radius). A Kriging predictor was used to accelerate the computation of genetic operations and generate new feasible solutions. Finite element simulations of the hydroforming process were also used after each generation to accurately evaluate the objectives of the offspring, and solutions with rank 1 were retained throughout all generations. Once the Pareto solutions were obtained by multi-objective genetic algorithm, a local search was carried out in the regions of interest with the assistance of visualization. This optimization method was applied to the hydroforming of a straight tube to create a part with an expanded region with a square cross section; the optimum load path produced a very safe part with a corner radius of only 9.115 mm and a maximum thinning of only 23.9%.

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Section: Mogamentioning

confidence: 99%

Section: Mogamentioning

confidence: 99%

Section: Objective Functions and Constraintsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming

Hong-gang

Green

Johrendt

2011

Int J Adv Manuf Technol

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“…Other options are, for example, neural networks (Beyer et al 2006), lolimot models (Pedram et al 2006), multivariate splines (Chui 1988), Kriging (Sacks et al 1989;Queipo et al 2005) and radial basis functions (Buhmann 2000(Buhmann , 2003Wendland 2005). In Goel et al (2007) and Queipo et al (2005) the authors apply surrogate models to optimization and multiobjective optimization, respectively. All these approximations can be combined with transformations of both the parameter space and the objective functions themselves to yield more accurate approximations.…”

Section: Introductionmentioning

confidence: 97%

Combustion engine optimization: a multiobjective approach

et al. 2009

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To simulate the physical and chemical processes inside combustion engines is possible by appropriate software and high performance computers. For combustion engines a good design is such that it combines a low fuel consumption with low emissions of soot and nitrogen oxides. These are however partly conflicting requirements. In this paper we approach this problem in a multi-criteria setting which has the advantage that it is possible to estimate the trade off between the different objectives and the decision of the optimal solution is postponed until all possibilities and limitations are known. The optimization algorithm is based on surrogate models and is here applied to optimize the design of a diesel combustion engine.

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Multi‐objective optimization of a rotating cooling channel with staggered pin‐fins for heat transfer augmentation

Moon

Husain

Kim

2011

Numerical Methods in Fluids

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SUMMARYA rotating channel with staggered pin-fins is formulated numerically and optimized for performance (heat transfer/required pumping power) using a Kriging meta-model and hybrid multi-objective evolutionary algorithm. Two design variables related to cooling channel height, pin diameter, and spacing between the pins are selected for optimization, and two-objective functions related to the heat transfer and friction loss are employed. A design of experiment is performed, and 20 designs are generated by Latin hypercube sampling. The objective function values are evaluated using a Reynolds-averaged Navier-Stokes solver, and a Kriging model is constructed to obtain a Pareto-optimal front through a multi-objective evolutionary algorithm. Rotation in a cooling channel with staggered pin-fins induces Coriolis force that causes a heat transfer discrepancy between the trailing (pressure) and leading (suction) surfaces, with a higher Nusselt number on the trailing surface. The tradeoff between the two competing objective functions is determined, and the distribution of the Pareto-optimal solutions in the design space is discussed through k-means clustering. In the optimal designs, with a decrease in spacing between the pins, heat transfer is enhanced whereas friction loss is increased.

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Response Surface Approximation of Pareto Optimal Front in Multi-objective Optimization

Cited by 35 publications

References 1 publication

A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming

A hybrid-constrained MOGA and local search method to optimize the load path for tube hydroforming

Combustion engine optimization: a multiobjective approach

Multi‐objective optimization of a rotating cooling channel with staggered pin‐fins for heat transfer augmentation

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