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

Abstract

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%.

The multi-objective optimization of the loading paths for T-shape tube hydroforming using adaptive support vector regression

“…The authors experienced the application of dual RBF for multi-objective robust optimization and the use of adaptive RBF to optimize the loading path for T-shape THF process [32,33]. An [34,35] used KRG to accelerate calculation speed in multi-objective optimization in THF process. Ingarao et al [36] provided a comparison between three surrogate models, namely RSM, moving least squares approximation, and KRG model, to design a THF process.…”

Multi-objective optimization design of a multi-layer honeycomb sandwich structure under blast loading

“…In comparison with the single-objective optimization problem, the fundamental difference from the multi-objective genetic algorithm (MOGA) is that its result is a set of optimum solutions rather than simply a unique solution; we call this set of optimal solutions the Pareto optimal sets, 20 and any solution within the Pareto optimal sets is a feasible design…”

The multi-objective robust optimization of the loading path in the T-shape tube hydroforming based on dual response surface model

“…Ben and EI [15] provided a deep comparison between the quadratic polynomial response surface (RS) model and radial basis function (RBF) as surrogate techniques to construct surrogate models for global sensitivities and multi-objective optimization of the THF process, and they found that the RBF showed its superiority over the quadratic polynomial RS model to deal with nonlinearities proved through analytical test function and practical THF process. An et al [16][17][18] used a multi-objective optimization algorithm combined with design of experiment (DOE) and FEM to determine the optimal loading path in the THF process. Kadkhodayan and Moghadam [19,20] established a new method to optimize the loading parameters in the T-, X-, Y-shape THF process based on Taguchi method and the RS model.…”