Multi-objective Robust Optimization Approach Research Articles

Enhancing the Robustness of Rib-Groove Filling and Strain Homogeneity in the Isothermal Forging of Titanium Alloy Multi-Rib Components

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.

Multi-objective robust optimization of foam-filled double-hexagonal crash box using Taguchi-grey relational analysis

In this paper, a novel thin-walled double-hexagonal crash box is first proposed and then multi-objective robust optimized for better overall crashworthiness under multi-angle impact loading, using a proposed hybrid method combining aluminum foam-filling and Taguchi-grey relational analysis (GRA). Specifically, the finite element (FE) models of the regularly-shaped double-hexagonal column (DHC) extracted from original irregularly-shaped crash box under multi-angle impact loading, including hollow (H-DHC) and foam-filled (F-DHC), are first built and validated by experiments. On this basis, a comprehensive crashworthiness comparison is conducted to explore relative merits of F-DHC over original H-DHC under multi-angle impact loading. After that, the F-DHC is multi-objective robust optimized for maximizing overall specific energy absorption (SEAθ) and minimizing overall initial peak crushing force (IPCF0) simultaneously under multi-angle impact loading, using a hybrid method of Taguchi-GRA. At last, a bumper-crash box integrated crashworthiness analysis under multi-angle impact loading is executed to further verify the optimization. The optimal F-DHC and the optimized crash box within the optimal F-DHC demonstrate evident improvement of crashworthiness compared to their respective initial designs, indicating aluminum foam-filling combined with Taguchi-GRA could be an effective approach for multi-objective robust optimization of the novel crash box and other similar vehicle structures.

Impacts of GCM credibility on hydropower production robustness under climate change: CMIP5 vs CMIP6

Climate change has emerged as a vital issue for hydropower management in the future. General circulation model (GCM)-informed climate is commonly applied to assess the impact of climate change on hydropower. However, the effect of GCM credibility on hydropower robustness has been rarely explored. One objective of this study is to seek valuable and robust policies, and the other is to evaluate the effects of GCM credibility on hydropower robustness based on the pre-optimized operating policies. A multi-objective robust optimization approach is first proposed to design operating policies by coupling stochastic simulation, heuristic parameterized policy search, and robust optimization. The GCM credibility is then evaluated based on multi-criteria ranking scores, and the hydropower robustness is illustrated by stepwise culling the lowest credible GCMs. The climate-induced impacts on hydropower robustness rely on an ensemble of 18 GCMs under three representative concentration pathways in Coupled Model Intercomparison Project 5 (CMIP5) and 17 GCMs under three shared socioeconomic pathways in CMIP6. The Longyangxia and Liujiaxia reservoirs in Upper Yellow River Basin are selected as a case study. The results show that (1) the proposed stochastic approach outperforms the deterministic approach regarding hydropower generation and firm output where the mean annual hydropower generation of stochastic operation is improved by -0.50- 19.53% compared to deterministic operation, indicating that the operating rules derived using historical stochastic inflows can adapt flexibly to future inflow changes than that using deterministic inflow. (2) CMIP6 maintains a more robust performance than CMIP5 with higher satisficing measures and lower regret measures. (3) Hydropower robustness tends to be higher when considering credibility and will be lower with time due to increasing uncertainty. Ignorance of GCM credibility may lead to biased climate change adaptation decisions.

Nondeterministic multiobjective optimization of 3D printed ceramic tissue scaffolds

Despite significant advances in the design optimization of bone scaffolds for enhancing their biomechanical properties, the functionality of these synthetic constructs remains suboptimal. One of the main challenges in the structural optimization of bone scaffolds is associated with the large uncertainties caused by the manufacturing process, such as variations in scaffolds’ geometric features and constitutive material properties after fabrication. Unfortunately, such non-deterministic issues have not been considered in the existing optimization frameworks, thereby limiting their reliability. To address this challenge, a novel multiobjective robust optimization approach is proposed here such that the effects of uncertainties on the optimized design can be minimized. This study first conducted computational analyses of a parameterized ceramic scaffold model to determine its effective modulus, structural strength, and permeability. Then, surrogate models were constructed to formulate explicit mathematical relationships between the geometrical parameters (design variables) and mechanical and fluidic properties. The Non-Dominated Sorting Genetic Algorithm II (NSGA-II) was adopted to generate the robust Pareto solutions for an optimal set of trade-offs between the competing objective functions while ensuring the effects of the noise parameters to be minimal. Note that the nondeterministic optimization of tissue scaffold presented here is the first of its kind in open literature, which is expected to shed some light on this significant topic of scaffold design and additive manufacturing in a more realistic way.

Multi-Objective Robust Optimization for the Traffic Sensors Location Problem

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.

A multi-objective robust optimization approach for green location-routing planning of multi-modal transportation systems under uncertainty

Carbon emission has been widely studied in transportation research in general, yet research on carbon emission specifically in hazardous material transportation remains surprisingly limited. This study presents a multi-objective model for locating transfer points and routing in a multi-modal network of hazardous materials, accounting for multiple different uncertainties, while minimizing carbon emission alongside risk and cost of transportation. This study models uncertainties in accident probabilities, emission factors, and costs of establishing transfer points with polyhedral uncertainty sets, and utilizes robust counterpart optimization to tackle these uncertainties. The application of the proposed approach is examined in a case study of petroleum product transportation. The results of our analyses confirm the effectiveness and robustness of the developed model. Specifically, it is found that the proposed model can reduce carbon emissions by 873 g, and individuals at risk by 0.28, for every additional dollar spent.

Multi-objective robust design optimization (MORDO) of an aeroelastic high-aspect-ratio wing

In this paper, a new approach for multi-objective robust optimization of flutter velocity and maximum displacement of the wing tip are investigated. The wing is under the influence of bending–torsion coupling and its design variables have different levels of uncertainty. In designing and optimizing wings with a high aspect ratio, the optimization process can be done in such a way to increase the flutter velocity, but this can increase the amplitude of the wing tip displacement to a point that leads to the wings damage and structural failure. Therefore, single-objective design optimization may lead to infeasible designs. Thus, for multi-objective optimization, modeling is based on the Euler–Bernoulli cantilever beam model in quasi-steady aerodynamic condition. Using the Galerkin’s techniques, the aeroelastic equations are converted to ODE equations. After validating the results, the system time response is obtained by the numerical solution of the governing equations using 4th Runge–Kutta method and the flutter velocity of the wing is obtained using the theory of eigenvalues. Subsequently, by choosing bending and torsional rigidity and mass per unit wing length as the optimization variables, using Monte Carlo–Latin hypercube (MC-LH) simulation and 4th polynomial chaos expansion (PCE), the effect of uncertainty on these variables is modeled in modeFRONTIER™ software coupled with MATLAB™ and optimization is performed by genetic algorithm. Finally, by plotting the Pareto front, it is observed that with an acceptable increase in flutter velocity, the maximum wing displacement amplitude is reduced as much as possible. The results of the multi-objective robust optimization show more feasible results compared with deterministic optimization.

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

Considering economic and environmental concerns as well as thermal and visual comfort requirements, this paper introduces the idea of Smart Energy-Aware Manufacturing Plant Scheduling for general manufacturing processes, especially high-value-added ones. The integrated system benefits from the use of a grid-connected Microgrid, a combined cooling, heat, and power system, and renewable power. Employing the Conditional Value-at-Risk and guaranteeing both solution and model robustness through an original multi-objective risk-based robust mixed-integer linear programming to optimally support the system make the contribution of the paper novel and unique. The main objective is to schedule manufacturing (non-shiftable) and non-manufacturing (shiftable and interruptible) loads, and distributed energy resources based on the real-time-pricing policy in an interactive decentralized operation of a capacitated multi-carrier energy production-consumption system. Compared to the conventional system, the results outline 64.63%, 1.62%, 100%, and 65.23% less Carbon dioxide emissions, net production, power exchange, and total costs, on average. The proposed framework is preferable to the framework that is based on the use of combined heat and power systems, at least in terms of a reduction in production costs. Considering both the supply- and demand-side uncertainties, the framework performs good trade-offs between solution robustness and model robustness, and environmental and economic concerns.

Green and Resilient Design of Electricity Supply Chain Networks: A Multiobjective Robust Optimization Approach

Smart grids provide great opportunities for design and implementation of sustainable and efficient electricity supply chains that are more resilient to disruptions. The problem with electricity supply chain network design (ESCND) using smart grid has not been broadly explored by researchers. This paper aims to approach this problem using a multiobjective robust optimization method. The three objectives are economic (profit maximization), environmental (greenhouse gas emissions minimization), and resilience (network resilience maximization). Efficiency maximization—power loss minimization—has also been taken into account using its corresponding cost element in the economic objective function. The proposed approach accounts for different unique smart grid components such as demand side management programs, microgrid structure, two-way distribution lines, and supplier–consumer nodes, while incorporating different interrelated decisions including facility location, capacity expansion, load allocation, and pricing. To solve the resultant model, a hybrid multiobjective robust optimization technique is proposed based on cutting plane and AUGMECON2 algorithms. The proposed model and solution approach are then applied to an actual case study and the produced results are thoroughly analyzed. We find that while economic and environmental objectives can be strictly conflicting, the implementation of smart grids can result in concurrent boost in both environmental performance and network resilience.

Advanced Multi-Objective Robust Optimization Under Interval Uncertainty Using Kriging Model and Support Vector Machine

There are a large number of real-world engineering design problems that are multi-objective and multiconstrained, having uncertainty in their inputs. Robust optimization is developed to obtain solutions that are optimal and less sensitive to uncertainty. Since most of complex engineering design problems rely on time-consuming simulations, the robust optimization approaches may become computationally intractable. To address this issue, an advanced multi-objective robust optimization approach based on Kriging model and support vector machine (MORO-KS) is proposed in this work. First, the main problem in MORO-KS is iteratively restricted by constraint cuts formed in the subproblem. Second, each objective function is approximated by a Kriging model to predict the response value. Third, a support vector machine (SVM) classifier is constructed to replace all constraint functions classifying design alternatives into two categories: feasible and infeasible. The proposed MORO-KS approach is tested on two numerical examples and the design optimization of a micro-aerial vehicle (MAV) fuselage. Compared with the results obtained from other MORO approaches, the effectiveness and efficiency of the proposed MORO-KS approach are illustrated.

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

PurposeEngineering system design and optimization problems are usually multi-objective and constrained and have uncertainties in the inputs. These uncertainties might significantly degrade the overall performance of engineering systems and change the feasibility of the obtained solutions. This paper aims to propose a multi-objective robust optimization approach based on Kriging metamodel (K-MORO) to obtain the robust Pareto set under the interval uncertainty.Design/methodology/approachIn K-MORO, the nested optimization structure is reduced into a single loop optimization structure to ease the computational burden. Considering the interpolation uncertainty from the Kriging metamodel may affect the robustness of the Pareto optima, an objective switching and sequential updating strategy is introduced in K-MORO to determine (1) whether the robust analysis or the Kriging metamodel should be used to evaluate the robustness of design alternatives, and (2) which design alternatives are selected to improve the prediction accuracy of the Kriging metamodel during the robust optimization process.FindingsFive numerical and engineering cases are used to demonstrate the applicability of the proposed approach. The results illustrate that K-MORO is able to obtain robust Pareto frontier, while significantly reducing computational cost.Practical implicationsThe proposed approach exhibits great capability for practical engineering design optimization problems that are multi-objective and constrained and have uncertainties.Originality/valueA K-MORO approach is proposed, which can obtain the robust Pareto set under the interval uncertainty and ease the computational burden of the robust optimization process.

A multi-objective robust optimization approach based on Gaussian process model

The design and optimization of engineering products is usually multi-objective, constrained and has uncertainties in the inputs. It is of great importance for taking these uncertainties into consid...

Kriging-Model-Based Multi-Objective Robust Optimization and Trade-Off Rule Mining of a Centrifugal Fan with Dimensional Uncertainty

We propose a new method of design called MORDE (multi-objective robust design exploration) that combines a multi-objective robust optimization approach and data-mining techniques for analyzing trade-offs. The probabilistic representation of design parameters, which is compatible with the Taguchi method, is incorporated into the optimization system we previously developed that uses a multi-objective genetic algorithm. The means and standard deviations of responses of evaluation functions against uncertainties in design variables are evaluated by descriptive Latin hypercube sampling using Kriging surrogate models. Design space is visualized by Self-organizing map (SOM). To extract design rules further, a new approach that adopts the association rule with an aspiration vector is proposed. MORDE is then applied to an industrial design problem with a centrifugal fan for a washer-dryer. Taking dimensional uncertainty into account, we optimize the means and standard deviations of the resulting distributions of the fan efficiency and turbulent noise level. Steady Reynolds-averaged Navier Stokes simulations are carried out to collect the necessary dataset for Kriging models. We demonstrate the advantages of the proposed method of multi-objective robust optimization over traditional non-robust ones in that the solutions are diverse. We clarify that the association rule can extract both sufficient and necessary conditions as design rules to achieve trade-off balances. The association rule is also more beneficial than SOM in finding quantitative relations, particularly those that are concerned with more than three design parameters.