A multi-objective robust optimization approach for engineering design under interval uncertainty

This paper presents a new approach aims to solve robust multidisciplinary design optimization MDO problem called Improved Multi-objective Robust Collaborative Optimization . This method combines the Multi-objective Robust Collaborative Optimization method, the Worst Possible Point constraint cuts and the Genetic algorithm NSGA-II type as an optimizer to solve the robust optimization problem of complex structure named Y-stiffened panel under interval uncertainty . The proposed approach hierarchically decomposes the optimization problem into a structure level considered as an upper level in the Y-stiffened panel and a second level considered as a lower level of the studied panel. A robust multi-objective optimization problem intended to optimize the eigenfrequency, the global mass and the displacement at a fixed point of the Y-stiffened panel at the first level and each structure’s robust optimization problem allows optimizing its eigenfrequency and mass limited by their local constraint functions at the second one. Tor demonstrate our method, an engineering example of Y-stiffened panel is treated. A good performance of proposed method is proved by a comparison between obtained results and Non-Distributed Multi-objective Robust Optimization .

In order to maximise the impact automotive energy-absorbing capacity considering uncertainties in the parameters of the design, it is desired to perform a robust optimum design process. Moreover, the optimum design of such absorption system is inherently a multi-objective optimisation problem. In this paper, a multi-objective optimisation approach is thus proposed to consider the robustness issue of those objective functions in the presence of parameter uncertainties. First, the axial impact crushing behaviour of the S-shaped box beams, as a highly simplified model of the front member of a vehicle body, is studied by the finite-element method using the software ABAQUS. Two polynomial meta-models based on the evolved group method of data handling (GMDH) neural networks are then obtained to simply represent both the absorbed energy (E) and the peak crushing force (F max) with respect to geometrical and material design variables using the training and testing data obtained from the finite-element study. Using such obtained polynomial neural network models and the Monte Carlo simulation, a multi-objective genetic algorithm is then used for the reliability-based robust Pareto design of the S-shaped box beams having probabilistic uncertainties in material and geometrical parameters. In this way, the statistical moments of mean and variances of the important crashworthiness criteria functions, namely the specific energy absorption (SEA) and the peak crushing force (F max), are considered as the conflicting objectives. It is shown that some useful optimal design principles involved in the performance of the S-shaped box beams can be discovered by the reliability-based robust Pareto optimisation.

Aiming at the problem of supply chain robust optimization with multiple performance responses, a robust optimization method was proposed by combining principal component analysis with double response surface method based on Kriging meta-model. Firstly, through principal component analysis, the location characteristics and divergence characteristics of multiple related performance responses were transformed into the principal component comprehensive score of supply chain performance; secondly, the Kriging metamodels of location characteristics and divergence characteristics of multiple performance responses were constructed respectively, and the principal component comprehensive score model of comprehensive performance based on Kriging meta-model was constructed. Thus the optimal operating conditions by optimizing the constructed robust optimization strategy were obtained in order to realize the robust optimization of supply chain system with correlated multiple responses. Finally, a supply chain simulation case was given to illustrate the effectiveness of our proposed optimization method, and the robustness of different methods was also discussed. The comparison results showed that our proposed was more robust.

Multi-objective target oriented robust optimization for the design of an integrated biorefinery

Isothermal forging stands as an effective technology for the production of large-scale titanium alloy multi-rib components. However, challenges have persisted, including die underfilling and strain concentration due to the complex material flow and heterogeneous deformation within the forging die cavity. While approaches centered on optimized billet designs have mitigated these challenges, uncertainties in process parameters continue to introduce unacceptable variations in forming accuracy and stability. To tackle this issue, this study introduced a multi-objective robust optimization approach for billet design, accounting for the multi-rib eigenstructure and potential uncertainties. The approach includes finite element (FE) modeling for analyzing the die-filling and strain inhomogeneity within the multi-rib eigenstructure. Furthermore, it integrated image acquisition perception and feed back technologies (IAPF) for real-time monitoring of material flow and filling sequences within die rib-grooves, validating the accuracy of the FE modeling. By incorporating dimensional parameters of the billet and uncertainty factors, including friction, draft angle, forming temperature, speed, and deviations in billet and die, quantitative analyses on the rib-groove filling and strain inhomogeneity with fluctuation were conducted. Subsequently, a dual-response surface model was developed for statistical analysis of the cavity filling and strain homogeneity. Finally, the robust optimization was processed using a non-dominated sorting genetic algorithm II (NSGA-II) and validated using the IAPF technologies. The proposed approach enables robust design enhancements for rib-groove filling and strain homogeneity in titanium alloy multi-rib components.

Pareto based multi-objective optimization of turbulent heat transfer flow in helically corrugated tubes

The main concern of this research is to control traffic flow and monitor highways by installing wireless sensors. Therefore, a new multi-objective model is proposed to find the optimal location of wireless sensors along highways. The sensors are paired and each pair of sensors communicates and interacts with each other to receive information from passing cars. The speed estimation of the vehicles passing through this pair of sensors must have the minimum deviation from the actual speed that is obtained by an accurate measurement. This deviation is called measurement error, which is minimized in the first objective function. In this research when traffic jams happens, some sensors located in proper distance with enough energy, move into the traffic area to reduce the measurement error which is caused by traffic congestion. In fact, for each traffic area a new location problem should be solved to relocate sensors so that the maximum decrease in error rate happens. The second objective maximizes the error reduction resulted from sensors movement. In this paper, movement of sensors is considered based on the amount of solar energy stored in the sensor at that moment. Finally, the third objective function maximizes the benefits resulted from detecting the bottlenecks in highways. Since some parameters of the objective functions such as error rates, error reduction resulted from movement of sensors and benefits are uncertain, this research employs a multi-objective robust optimization approach which results in a traffic control plan which is less sensitive to the realization of uncertain parameters.

In engineering design, an optimized solution often turns out to be suboptimal when errors are encountered. Although the theory of robust convex optimization has taken significant strides over the past decade, all approaches fail if the underlying cost function is not explicitly given; it is even worse if the cost function is nonconvex. In this work, we present a robust optimization method that is suited for unconstrained problems with a nonconvex cost function as well as for problems based on simulations, such as large partial differential equations (PDE) solver, response surface, and Kriging metamodels. Moreover, this technique can be employed for most real-world problems because it operates directly on the response surface and does not assume any specific structure of the problem. We present this algorithm along with the application to an actual engineering problem in electromagnetic multiple scattering of aperiodically arranged dielectrics, relevant to nanophotonic design. The corresponding objective function is highly nonconvex and resides in a 100-dimensional design space. Starting from an “optimized” design, we report a robust solution with a significantly lower worst-case cost, while maintaining optimality. We further generalize this algorithm to address a nonconvex optimization problem under both implementation errors and parameter uncertainties.

A multi-objective optimization-based computational approach to nondestructive evaluation of damage in structural components, and more generally in solid continua, is discussed and numerically evaluated. The multi-objective approach provides a substantial improvement in the capabilities to traverse the optimization search space to minimize the measurement error and produce accurate damage estimates. Through simulated test problems based on the characterization of damage in structural steel components, including internal pipe surface geometry as well as material loss within a plate structure utilizing steady-state dynamic measurements of outer surface displacement, a multi-objective genetic algorithm optimization approach is shown to provide substantial computational improvement over single-objective strategies. The multi-objective approach consistently and efficiently produces more accurate characterization results in contrast to equivalent single-objective strategies. More importantly, the multi-objective approach is shown to exhibit consistently better tolerance to test measurement noise and measurement sparsity. Moreover, the multi-objective strategy was found to provide improved diversity in the solution estimates for ill-posed problems, which is an important step leading to insight into the necessary changes to the testing or parameterization to subsequently produce more accurate and unique solutions to such inverse characterization problems.

Mechanical and hydrophobic properties of chromium carbide films via a multi-objective optimization approach

Optimization of transverse shear moduli for composite honeycomb cores

:A robust multi-objective wing design optimization procedure using CFD is presented in this work. Instead of directly applying CFD to wing design optimization, a Kriging aerodynamic model that approximates CFD result is proposed to save computational cost. By introducing 6σ robust approach as a sub-objective function, multi-objective wing design problems can be solved with aerodynamic robustness. Non-Uniform Rational B-Spline curves (NURBS) are introduced to depict the wing geometry in design optimization process. The most important parameters of the wing geometry can then be screened by design of experiment and treated as design variables due to the local variation property of NURBS. Under this formulation, a multi-objective genetic algorithm based on non-dominated sorting is employed to handle multiple flight conditions in wing design. The optimum wing geometry is selected according to trade-off among design objects on the non-dominated front. To validate the proposed approach, two robust design optimization cases are studied for ONERA-M6-Wing. It turns out that the drag coefficient is insensitive to Mach number between Ma0.8–Ma0.9 after robust optimization. The result also verifies the effectiveness of our method in boosting performance and robustness of multiple flight conditions: the lift curve slope (Ma0.3) of optimum wing and the 6σ objective function of transonic drag (Ma0.8–Ma0.9) increase by 11.9% and 25.4%, respectively. Observations in the optimization cases are concluded as follows: 1) For wing aerodynamic design problems, the multi-objective robust optimization can both improve the performance at different flight conditions and provide robustness. 2) The Kriging aerodynamic model derived from CFD result can satisfy the precision requirement of wing design. 3) Even though the optimization result is subject to the weights of the 6σ function in sub-object, the influence is not comparable to the trade-off among design objects. 4) The optimum solution obtained by proposed approach is superior to gradient based optimization method, while the computational cost is acceptable.

Smart Energy-Aware Manufacturing Plant Scheduling under Uncertainty: A Risk-Based Multi-Objective Robust Optimization Approach

In this paper, we propose a novel design-for-manufacture strategy for integrated photonics which specifically addresses the commonly encountered scenario in which probability distributions of the manufacturing variations are not available, however their bounds are known. The best design point for the device, in the presence of these uncertainties, can be found by applying robust optimization. This is performed by minimizing the maximum realizable value of the objective with respect to the uncertainty set so that an optimum is found whose performance is relatively immune to fabrication variations. Instead of applying robust optimization directly on a computationally expensive simulation model of the integrated photonic device, we construct a cheap surrogate model by uniformly sampling the simulated device at different values of the design variables and interpolating the resulting objective using a Kriging metamodel. By applying robust optimization on the constructed surrogate, the global robust optimum can be found at low computational cost. As an illustration of the method's general applicability, we apply the robust optimization approach on a 2x2 multimode interference (MMI) coupler. We robustly minimize the imbalance in the presence of uncertainties arising from variations in the fabricated design geometry. For this example device, we also study the influence of the number of sample points on the quality of the metamodel and on the robust optimization process.

Coordinated multi-stage and multi-objective optimization approach for ship collision avoidance decision-making