Multi-objective Design Optimization Problem Research Articles

Robust design optimization of a multi-body system with aleatory and epistemic uncertainty

There are several issues in robust design optimization of the multi-body system with aleatory and epistemic uncertainty, such as the difficulty in the multi-source uncertainty characterization and low efficiency in dynamic modeling, analysis and the corresponding solving strategy for its robust design optimization. To address these problems, this paper firstly constructs a unified analysis framework for aleatory and epistemic uncertainty for the multi-body system based on probability theory and evidence theory. Taking a multi-body system of a shipborne artillery model as an example, the transfer matrix method is next employed to rapidly calculate the dynamic response of the muzzle. The results are compared with those by the finite element method to verify the accuracy and efficiency of the transfer matrix method. A decision model of the robust design optimization with both aleatory and epistemic uncertainty is proposed. Based on the polynomial chaos expansion-Kriging model, subset simulation optimization method and a weighted single-objective solving strategy, the multi-objective robust design optimization problem involving aleatory and epistemic uncertainty is then transformed into a single-objective optimization one. Finally, results of both the multi-objective and weighted single-objective robust design optimization methods for the shipborne artillery model are compared to demonstrate the performance of the proposed method.

Reliability based design optimization of a two-stage wind turbine gearbox

This paper describes a multi-objective reliability-based design optimization (MORBDO) of a two-stage wind turbine gearbox. The optimization process incorporates the gear's reliability of accounting for the uncertainty of its internal geometric parameters. It also ensures that constraints relating to the gear's reliability index and efficiency are respected. The objective functions are to minimize both the total volume and the center distance. A specific reliability target is established, and to address the multi-objective reliability-based design optimization (MORBDO), the hybrid method (HM) in conjunction with the constrained non-dominated sorting genetic algorithm (C-NSGA-II) is employed. The outcomes demonstrate that applying C-NSGA-II to solve the multi-objective reliability-based design optimization problem yields dependable Pareto solutions that are well-distributed in relation to the desired reliability level. The optimization using C-NSGA-II with a population size of 300 particles and 1000 generations produced the most favorable outcomes. This research significantly contributes to the multi-objective design optimization of wind turbine gear while simultaneously considering their reliability.

Optimal design of forced-draft counter-flow evaporative-cooling towers through single and multi-objective optimizations using oppositional chaotic artificial hummingbird algorithm

In this study, single-objective (SOP) and multi-objective (MOP) design optimization problems have been solved for mechanical forced-draft counter-flow wet-cooling towers using an enhanced-search variant of a recently proposed swarm-intelligence based metaheuristic, artificial hummingbird algorithm (AHA). Incorporating the oppositional rule to ensure a faster convergence by avoiding unnecessary search of the space, and with chaos-embedded sequences to obtain more diversifying search-population towards more accuracy in the obtained solutions, the proposed oppositional chaotic artificial hummingbird algorithm (OCAHA) has been implemented for effective design optimizations of cooling towers. In SOP, six number cases of literature have been algorithmically experimented for minimizing the total annual cost TAC as the single-objective function with mass flow rate of cooling air and cross-sectional area of tower fill as the two decision variables and with fourteen number of design inequality constraints based on the process temperatures and enthalpies. Merkel’s method has been used for deriving the tower geometrical dimensions from empirical correlations of overall mass transfer-coefficient and loss-coefficient for the specified type of tower fill-packing. In MOP, range, tower characteristic ratio, effectiveness are the three objective functions, which have been maximized simultaneously with minimizing the water evaporation rate as the fourth objective for the problem. Mass flow rates of cooling air and circulating water are the two decision variables with the required input parameters of recent literature have been considered for multi-objective problem. The obtained designs through SOP and MOP have been analyzed with the competing designs, and a superior performance of OCAHA in both the optimizations have been validated.

A near-optimum multi-objective optimization approach for structural design

Multi-objective design optimization problems offer a set of solution alternatives within a Pareto-front. In structural design, the design variables are typically the section properties. The outcomes of these design variables are usually used in selecting standard sections. However, the properties of the selected standard sections normally have different values from the determined design variables. Accordingly, the values of the objective functions for these solutions will change after selecting standard sections. This change may be different among these solutions. Thus far, only Pareto-optimal solutions have been standardized in the literature. The effects of the inclusion of non-Pareto solutions in the standardization process have never been examined. In this paper, the differences between including the near-optimal solutions and not including them in the final structural design optimization set are explored. The paper investigates the impact of selecting standard sections on both Pareto-front solutions and near-optimal solutions, and it studies the importance of keeping track of the near-optimal solutions. A modified version of a multiple-objective particle swarm optimization method, enhanced with a proposed computationally efficient section standardization algorithm, is used to solve multi-objective system-reliability design optimization problems. The concepts of the paper are applied to examples of bridge structures. The results demonstrate the efficiency of the proposed technique in capturing final design solutions that would have been otherwise missed due to standardization.

Multi-Objective Reliability-Based Partial Topology Optimization of a Composite Aircraft Wing

Reliability-based partial topology optimization (RBPTO) is a new approach for aircraft structural design; however, it brings computational complexity and makes aeroelasticity analysis quite challenging. Therefore, the present study proposed the multi-objective reliability-based partial topology optimization of a composite aircraft wing using a fuzzy-based metaheuristic (MRBPTOFBMH) approach. The objective is to obtain an optimal layout including partial topology and sizing of the aircraft wing structure. Here, an optimal aeroelastic structure is designed by taking into account the uncertain nature of material properties and the permitted transverse displacement. To increase computational efficiency in the design process, a non-probabilistic approach called a possibilistic safety index-based design optimization (PSIBDO) with fuzzy uncertainties is proposed to quantify the uncertainties due to aeroelastic and structural constraints. Various optimum partial topological shapes and sizing of aircraft wing structures with various PSI values in the range of [0.001, 1.0] have been obtained in a single optimization run. These outcomes, including deterministic and reliable optimal aircraft wing structures, demonstrate the high effectiveness of the proposed MRBPTOFBMH technique to alleviate the complexity of unconventional aircraft wing structure design. The findings also reveal the ease in cooperation of the suggested technique with a high-performance multi-objective evolutionary algorithm (MOEA) and its application in real-world multi-objective design optimization (MODO) problems with the least computational requirements against the traditional method’s multiple runs. Furthermore, the proposed methodology can generate potential aircraft wing structures in a range of m = [89.38–127.84] kg, and flutter speed = [285.61–632.78] m/s, that adhere to all the constraints requirements.

Forecasting compressive strength and electrical resistivity of graphite based nano-composites using novel artificial intelligence techniques

To produce highly effective electrically conductive cementitious composites and advance non-destructive structural-health monitoring techniques, graphite-based nanomaterials (GrNs) are viable conductive fillers. A comprehensive database was created for CS and ER pertinent to GrNCC’s experimental studies from open sources. It is a challenging multi objective optimization problem (MOOP) due to the requirement of both mechanical strength and electrical resistivity for the design of Graphene nanoparticles-reinforced cementitious composites (GrNCC). The current study provides an ample data-driven approach employing machine learning (ML) techniques and a non-dominated sorting genetic algorithm (NSGA-II) to address this multi objective design optimization (MODO) problem for GrNCC. ML theories quantify how important parameters affect GrNCC’s qualities. First, using processed experimental datasets, gene expression programming (GEP) is used to develop prediction models for GrNCC’s uniaxial compressive strength (CS) and electrical resistivity (ER). The findings demonstrate its superior predictive accuracy, as evidenced by high R2 of 0.92 and 0.91 and low mean absolute error (MAE) scores of 1.57 MPa, and 60.46 kΩ.cm for CS and ER, respectively. For the MODO technique, parameter analysis was performed, which aids in identifying the parameters that need to be optimized and defining their constraints. Finally, NSGA-II is used as the foundation for the MODO technique. With the proposed prediction models as objective functions, it simultaneously optimizes the CS and ER of the GrNCC. It successfully produces a collection of Pareto solutions that make it easier to choose the right parameters for the GrNCC design. The proposed MODO technique can be efficiently applied to multiobjective design and optimization of electrical and mechanical properties of GrNCC.

Multi-objective optimization of nonlinear inelastic steel trusses with continuous design variables using NSGA-II

Thank to the rapid development of computer technology, optimization design has been increasingly widely applied in all areas of life. In structural optimization, due to the variety and even contradiction between the desired goals of design engineers, multi-objective optimization attracts more and more attention from scientists. In this paper, the author presents the multi-objective optimization design problem for steel truss with two basic objectives: the truss mass and the horizontal displacement of the top of the truss is minimized. The design variables are the cross-sectional areas of the structure that are in the defined ranges. Direct analysis is used to capture the nonlinear behavior as well as calculate the maximum load-carrying capacity of the structure. The optimization problem set up above is solved by NSGA-II (Non-dominated sorting GA-II) algorithm. A 47-bar planar truss is studied to illustrate the optimal design problem. The results show that the NSGA-II algorithm is very effective in solving the given optimization problem.

Robust method for the identification of dynamical anisotropic flexible bearing parameters using multi-objective optimization and structural modification technique

In this paper, a deterministic multi-objective design optimization problem is addressed in order to identify the dynamical joint parameters such as mass, stiffness, damping and cross-coupling parameters. The proposed formulation uses directly the measured frequency transfer functions of the constrained system (with supports) and the mode of the unconstrained system (without supports) to predict the joint dynamic parameters. Since measurement noise often leads to erroneous identifications, the deterministic multi-objective optimization (DMOO) is used to eliminate the redistribution and amplification of noise due to the inversion of the frequency transfer function matrices. The proposed optimization design gives satisfactory results when using noise-free data as well as under realistic noise levels. A parametric study was also performed in order to assert the sensitivity of dynamical joints parameters against the level of noise. The results show also that the constrained non-dominated sorting genetic algorithm (C-NSGA-II) was capable to generate well-distributed reliable Pareto solutions.

Dynamic Analysis and Design of Metamaterial Plates With Crossed Acoustic Black Holes for Vibration Control

Abstract Acoustic black holes (ABHs) have shown great potential in vibration and noise control. Merging the ABH effect and the metamaterial can be a more efficient approach for vibration control. The aim of this article is to study the dynamics of a metamaterial plate with crossed acoustic black holes. The band gap properties of the infinite structure and the influence of the design variables are investigated by using the finite element method and the Floquet–Bloch theorem. The vibration transmission and frequency response functions of the finite structure are presented to reveal the vibration attenuation mechanism. The effect of elastic boundary conditions on the vibration properties of the metamaterial plate is also studied. Numerical results demonstrate that the vibration is remarkably weakened due to the band gap and local modes induced by the ABH effect. Then, experimental validation is given by using 3D printing techniques. Finally, we study the multi-objective optimal design problem of the ABH plate to reduce the vibration amplitude and the structural mass simultaneously. Optimization results provide more options for the trade-off design of metamaterial plates between the lightweight design and vibration suppression capability.

Inverse design of direction independent metamaterials to control longitudinal and transverse waves

Direction-independent elastic metamaterials that can control longitudinal and transverse elastic waves independently for nonlinear ultrasonic testing are designed using an inverse design approach by defining the time-dependent inverse problem. Forward finite element wave propagation models are solved inversely as multiple multi-objective design optimization problems using gradient-free algorithms. Suppressing the 2nd harmonics (2f) generated due to instrumentation during nonlinear ultrasonic testing is obtained by keeping the first objective as reducing only second harmonics without concentrating on the amplitude of the 1st harmonics, which is a necessary condition for ultrasonic testing, whereas almost all the inversely designed metamaterials take care of this condition due to intelligent selection of material combinations. The second objective is defined as reducing error due to the difference between a pulse with 1st (f) and 2nd (2f) harmonics and a delayed pulse with 1st harmonics (f), as well as maximizing the power of the output pulse by defining min-max multi-objective optimization problems.

Grid Feature-Based Weighted Simulation Method for Multi-Objective Reliability-Based Design Optimization

Reliability analysis and reliability-based design have attracted huge attention since their origin, especially in the engineering design optimization field. Integrating a novel grid feature (GF) mechanism into the weighted simulation method (WSM), a grid feature-based weighted simulation method (GFWSM) is proposed in this paper. By sorting the samples in the random variable space, the GF mechanism serializes the failure probability calculation process, which can reduce the number of performance function evaluations required by the WSM. The proposed GFWSM is integrated into an efficient evolutionary multi-objective optimizer, disruption-based multi-objective equilibrium optimization algorithm (DMOEOA), for solving multi-objective reliability-based design optimization (MORBDO) problems. Different reliability analysis examples are employed to verify the advantages of the proposed GFWSM. Various constrained multi-objective reliability-based design optimization problems have been selected to test the effectiveness of the GFWSM-DMOEOA algorithm. The simulation results indicate that GFWSM and GFWSM-DMOEOA algorithm have achieved a good balance between accuracy and efficiency.

High Degree of Freedom Aerodynamic Shape Optimization with Design-Space Dimensionality Reduction

In aerodynamic multi-objective optimization for object geometry, design variables are often multidimensional and weakly independent, which reduces the efficiency of optimization. In this study, a design space reduction method using ANOVA and AIC was proposed and implemented, then evaluated by applying it to a multi-objective aerodynamic optimal design problem. The results show that the proposed design space reduction method can extract important variables appropriately and enables fast, efficient, and accurate solution search.

Planar Transformer With Asymmetric Integrated Leakage Inductance Using Horizontal Air Gap

This article presents a novel planar-based transformer winding and core structure with controllable leakage inductance generation for integrated magnetics applications. As a result of limitations in integrated magnetics from the literature, a new approach is proposed utilizing semi-interleaved windings and controllable leakage via a leakage flux core leg featuring a horizontal air gap. The proposed transformer design is analyzed via detailed reluctance modeling to determine closed-form equations for the magnetizing and asymmetrically distributed leakage inductances. Next, a genetic-algorithm-based multiobjective design optimization problem is developed, seeking to minimize the core and winding losses of the proposed transformer subject to a set of parametric and geometric constraints in a dc-ac dual-active-bridge topology for microinverter applications. The optimization was extended to include other integrated magnetic structures from the literature, where it is determined that the proposed transformer is superior from the perspectives of efficiency, footprint area, and parasitic capacitance. Based on the results of the optimization analysis, two designs with theoretical transformer California Energy Commission (CEC) efficiency drops (i.e., CEC efficiency reduction specifically due to the transformer loss mechanisms) of 1.19% and 0.83% were fabricated and evaluated for electrical and thermal performance in the proposed 40 V, 400 W microinverter.

Design optimization of hybrid steel/timber structures for minimal environmental impact and financial cost: A case study

In the overall aim to build more sustainably, the energy performance of buildings has received a lot of attention in the past decade. In consequence, the embodied impact of buildings has become relatively more important. As the load-bearing structure is responsible for a large share of this embodied impact, it is important to design it in such a way that its environmental impact is as low as possible. Unfortunately, the best construction materials in terms of environmental impact are not necessarily the cheapest. Reducing the environmental impact of the design may therefore lead to a higher financial cost, which may exceed the available budget. In such cases, hybrid structures, consisting of two (or more) different materials, might offer a solution, as they allow the designer to finetune the trade-off between environmental impact and financial cost. In this paper, we present a method to determine the best design of hybrid steel/timber structures in terms of environmental impact within the limits of the available budget. The method is based on the solution of a multi-objective structural design optimization problem involving environmental life cycle assessment and life cycle costing. It is applied to two test cases: a statically determinate and a statically indeterminate truss structure. The structures are optimized for three different design scenarios and typical load cases. This results in a Pareto front in the environmental and financial life cycle cost spectrum, allowing the designer to select the most appropriate solution, given the available budget. The results show that, depending on the design conditions, hybrid steel/timber structures are in some cases Pareto-optimal.

Bayesian optimization for robust design of steel frames with joint and individual probabilistic constraints

This work proposes a Bayesian optimization (BO) method for solving multi-objective robust design optimization (RDO) problems of steel frames under aleatory uncertainty in external loads and material properties. Joint and individual probabilistic constrained RDO problems are formulated to consider two different ways the frame reaches its collapse state. Each problem involves three conflicting objective functions, namely, the total mass of the frame, the mean and variance of the maximum inter-story drift. Since the uncertain objective and probabilistic constraint functions of both problems are implicit within a finite element analysis program and the computation of the probabilistic constraints is an NP-hard problem, BO is used to guide the optimization process toward better solutions after it completes an iteration and offers a set of near Pareto-optimal solutions when it terminates. Specifically, Bayesian regression models called Gaussian processes (GPs) serve as surrogates for the structural responses. Two acquisition functions are then developed for the two RDO problems and a maximization problem of these functions is formulated as a mixed-integer nonlinear programming (MINLP) problem. A new random search coupled with simulated annealing is devised to solve the MINLP problem, thereby locating the most promising point in the input variable space at which the current solutions maximize their chance to be improved and the GP models are refined before the BO starts a new iteration. A test problem and two design examples show that exact or good Pareto-optimal solutions to the RDO problems can be found by the proposed method with 20 iterations.

Optimal design of dual isolated structure with supplemental tuned inerter damper based on performance requirements

This paper investigated the use of tuned inerter damper (TID) to enhance the seismic performance of dual isolated structure (DIS). An optimization design strategy was developed based on the performance requirements and expressed as a constrained multi-objective optimization design problem, where by the displacement response ratios of isolation layers were adopted as the constraints, and the acceleration response ratio of the superstructure was selected as the objective function. Meanwhile, the time history analysis was conducted to verify the effectiveness of the optimization strategy. The results indicated that the proposed dual isolated structure could effectively decrease the displacement of the superstructure relative to the ground; furthermore, it reduces the isolation layers' deformations compared with the DIS and the base isolated structure (BIS).

Kinetostatic design and development of a non-fully symmetric parallel Delta robot with one structural simplified kinematic linkage

In this work, the structural design of a structure-simplified parallel Delta robot is presented, by considering the kinetostatics, kinematic dexterity and workspace. An approach to normalize the dimensionally inhomogeneous Cartesian stiffness matrix is introduced, and a stiffness evaluation index is defined by means of the singular value decomposition of homogenized stiffness matrix, which is used in the design optimization in turn. A multi-objective design optimization problem is formulated to provide the optimal solutions of different sets of geometric parameters. A set of parameters is selected to lay out the robot, and the tested specifications show the good performances, although the speed is not so high as the commercial FlexPicker and Quattro. A comparative study is carried out between the proposed and original Delta robots by observing joint dynamics, showing that the modified robot structure can improve the robot dynamics. The presented work turns out that the proposed robot is applicable to the pick-and-place operations without high-precision requirement in most industrial sectors.

Multi-Objective Multidisciplinary Design Optimization of a Robotic Fish System

Biomimetic robotic fish systems have attracted huge attention due to the advantages of flexibility and adaptability. They are typically complex systems that involve many disciplines. The design of robotic fish is a multi-objective multidisciplinary design optimization problem. However, the research on the design optimization of robotic fish is rare. In this paper, by combining an efficient multidisciplinary design optimization approach and a novel multi-objective optimization algorithm, a multi-objective multidisciplinary design optimization (MMDO) strategy named IDF-DMOEOA is proposed for the conceptual design of a three-joint robotic fish system. In the proposed IDF-DMOEOA strategy, the individual discipline feasible (IDF) approach is adopted. A novel multi-objective optimization algorithm, disruption-based multi-objective equilibrium optimization algorithm (DMOEOA), is utilized as the optimizer. The proposed MMDO strategy is first applied to the design optimization of the robotic fish system, and the robotic fish system is decomposed into four disciplines: hydrodynamics, propulsion, weight and equilibrium, and energy. The computational fluid dynamics (CFD) method is employed to predict the robotic fish’s hydrodynamics characteristics, and the backpropagation neural network is adopted as the surrogate model to reduce the CFD method’s computational expense. The optimization results indicate that the optimized robotic fish shows better performance than the initial design, proving the proposed IDF-DMOEOA strategy’s effectiveness.

Solving multi-objective structural optimization problems using GDE3 and NSGA-II with reference points

Structural optimization problems can be described as multi-objective optimization problems (MOOPs) due to the presence of multiple conflicting objectives. Recently, procedures based on the decision-maker’s preferences have attracted the interest of researchers. This type of information allows for the search technique to focus only on regions of interest instead of all possible solutions. Despite its advantage, incorporating these preferences into the search engine remains scarcely explored in multi-objective structural optimization design problems (MOSOPs). We propose here solving MOSOPs using multi-objective meta-heuristics guided by reference points. Particularly, variants where the decision-maker’s preferences drive the search of the Non-dominated Sorting Genetic Algorithm II (NSGA-II), the third evolution step of Generalized Differential Evolution (GDE3), and GDE3 + APM, which is GDE3 equipped with a constraint handling technique called Adaptive Penalty Method (APM), are considered. These approaches are labelled respectively as R-NSGA-II, R-GDE3, and R-GDE3 + APM. It is relevant to highlight that the R-GDE3 and R-GDE3 + APM are proposed in this paper. The results indicate that all were competitive and generated good solutions when solving the MOSOPs considered here. In addition, R-NSGA-II outperformed the remaining techniques in the computational experiments.

Data-based approach for wing shape design optimization

Aircraft design is a trade-off among different objectives and constraints, so multiple design rounds are usually required. Aerodynamic shape optimization based on high-fidelity computational fluid dynamics is consequently expensive, especially for wing design in the transonic regime. To address the interactive demand in aircraft design, we present a data-based approach to real-time high-fidelity wing shape optimization. Accurate and fast data-based models are constructed to perform aerodynamic analyses in lieu of costly computational fluid dynamic simulations. For the versatility of the data-based models, 135,108 training data that cover wing samples of different aerodynamic shapes, flight speeds, and flight altitudes are used. The verification on 47,967 wings shows that mean relative errors of CL, CD, and CM compared to computational fluid dynamic simulations are all within 0.4%. The models are further verified in multiple single-point, multi-point, and multi-objective wing design optimization problems. The optimized wings have similar shapes to those obtained by computational-fluid-dynamics-based optimization, and the differences in CD are merely one∼two counts. These results demonstrate the effectiveness of the data-based approach to fast and high-fidelity wing design. This work showcases a real-time high-fidelity optimization approach to high-dimensional nonlinear engineering problems using data-based models.