Multi-objective Shape Optimization Research Articles

Multi-objective shape optimization of TESLA-like cavities: Addressing stochastic Maxwell's eigenproblem constraints

In this paper, we present a robust formulation to address nonlinear equality-constrained and inequality-constrained multi-objective optimization problems for multi-cell accelerating cavities with TESLA-like geometry under consideration of uncertain parameters. We propose to explore a robust approach that employs the polynomial chaos expansion (PCE) to model the uncertainty. For the uncertainty quantification (UQ), the resulting random-dependent eigenvalue problem is solved using the stochastic collocation method (SCM) combined with PCE. As a result, the shape optimization of the studied multi-cell cavity is defined in terms of statistical moments, which serve as the cost functionals in the multi-objective (MO) steepest descent algorithm. Two versions of this method are developed and implemented. Finally, the optimization results and their implications for the operation of a multi-cell cavity are discussed.

Multi-objective shape optimization of underwater vehicles based on an adaptive sampling algorithm

Shape optimization can effectively enhance the endurance of autonomous streamlined underwater vehicles (SUVs). This paper compares the multi-objective optimization results (volume maximization and resistance minimization) for three distinct SUV styles with appendages. The shape optimization process adopts a stochastic population-based approach called the metamodel-based design optimization (MBDO) method, which involves parametric geometric model representation, deterministic simulator design, global metamodel establishment, and multi-objective optimization. The global metamodels are established using novel sequential sampling methods that handle a large number of design variables to improve the robustness of modeling black-box functions. The multi-objective optimization problems are solved by a multi-objective particle swarm optimization–crowding distance algorithm. The SUV style having the highest number of curvature parameters achieved the best multi-objective solution set. The developed research method and framework are expected to extend the application of MBDO in computational fluid dynamics optimization and to guide the optimization design of SUV shapes.

Machine learning and genetic algorithm as tools for single and multi-objective shape optimization of micromixers with Cantor fractal structure

Machine learning and genetic algorithm as tools for single and multi-objective shape optimization of micromixers with Cantor fractal structure

Multi-objective shape optimization of autonomous underwater vehicle by coupling CFD simulation with genetic algorithm

In this paper, a new method of multi-objective optimization of the shape parameters was proposed for the Autonomous Underwater Vehicle (AUV) with both towed and self-propelled, aiming to reduce drag and enhance motion stability during navigation. In this study, the hydrodynamics calculation of AUV was conducted by CFD method covering a wide range of Reynolds number between 105 and 107, and the optimization was performed by NSGA-II multi-objective optimization algorithm. Prior to deploying the optimization process, a sample library was created using the Latin hypercube sampling method to construct the Kriging approximation model. Thereafter, the model was used as the NSGA-II multi-objective optimization function, in which the range of design variables was considered to obtain the Pareto optimal solution. Furthermore, we also introduce and discuss the Pareto optimal points with special characteristics. In addition, the objective function values of these four optimal points were compared with the results of the initial model. The results showed that the drag at the four optimal points were reduced by 12.07%, 11.59%, 10.98% and 7.94%, respectively, and the overturning moments were reduced by 1.96%, 7.38%, 12.73% and 14.08%, respectively. The proposed multi-objective optimization method optimizes the shape of AUV effectively and provides valuable guidance for the design of AUV.

Multi-objective Shape and Flow Optimization of Finned Double-Tube Heat Exchanger Filled with Nanofluid: A CFD and RSM Study

Multi-objective Shape and Flow Optimization of Finned Double-Tube Heat Exchanger Filled with Nanofluid: A CFD and RSM Study

Multi-objective shape optimization of doubly offset serpentine diffuser using Adjoint method

Doubly offset serpentine diffusers are needed in the compact designs of modern stealth fighters with highly integrated propulsion systems. In addition, these doubly offset serpentine diffusers are also essential to provide reduced radar cross-section (RCS) due to the blockage of a complete line of sight. In this research, shape optimization of the doubly offset serpentine diffuser is achieved using a multi-objective approach to maximize the pressure recovery (PR) and minimize the flow swirl angle (α) and distortion coefficient (DC) at the aerodynamic interface plane (AIP). A computationally efficient Adjoint-based method was implemented for the optimization. For baseline geometry, an additional offset is added to NASA’s M2129 single serpentine duct to make it doubly offset serpentine diffusers. The freeform deformation technique was used to parametrize the baseline shape using 180 control points. A steady-state flow solution through the diffuser was achieved by solving Reynolds-Averaged Navier-Stokes (RANS) equations using a general-purpose computational analysis tool, i.e., ANSYS Fluent. The sensitivity of objective functions from the Adjoint solver was used to compute the required design change in the direction of minima or maxima of the objective functions using the steepest descent optimization technique. Subsequently, the calculated design changes were implemented through mesh Morpher. The Adjoint-based approach and freeform deformation resulted in a powerful and efficient optimization framework. The optimized shape showed a significant reduction in distortion coefficient and flow swirl angle, along with a slight increase in pressure recovery.

Multi-objective shape optimization of developable Bézier-like surfaces using non-dominated sorting genetic algorithm

The shape optimization design of the developable surface is an important research topic in CAD/CAM, and it is widely used in engineering manufacturing. In this paper, NSGA-II (the elitist non-dominated sorting genetic algorithm) is used to study the multi-objective shape optimization problem of generalized cubic developable Bézier-like surfaces (GCDBLS, for short) to promote the application of GCDBLS in industrial software and engineering design. Firstly, the shape optimization of developable surfaces is transformed into the shape optimization of dyadic curves based on the point-to-plane duality theory. Secondly, a multi-objective shape parameter optimization model is developed based on three surface optimality criteria (the shortest arc length, the smallest energy, and the smallest curvature change rate of the dual curve). Finally, the results of shape parameter optimization of GCDBLS obtained by NSGA-II are compared with MSSA and MOGOA to verify the feasibility and superiority of NSGA-II in solving multi-objective shape optimization problems for developable surfaces and the flexibility of GCDBLS in the construction of developable surfaces.

Design optimization of prismatic rib turbulators in a rectangular channel based on multi-objective criterion

A multi-objective shape optimization of truncated prismatic ribs in a rectangular channel has been performed to optimize simultaneously, heat transfer and pressure loss. The numerical analysis was performed using Reynolds-averaged Navier-Stokes equations with eddy viscosity-based models for turbulence closure. The optimization was performed using multi-objective genetic algorithm technique, and the fitness functions for the objectives were obtained using surrogate modeling. Using literature survey and preliminary parametric analysis, three design variables related to prismatic ribs viz. ratio of rib-height (e) to hydraulic-diameter (Dh) of a rectangular channel, ratio of rib-pitch (p) to rib-height (e), and ratio of rib-height at end (ep) to rib-height at center (e) were selected. The augmentation Nusselt number (FNu) and friction factor (Ff) ratios were chosen as the multi-objective functions for heat transfer and pressure drop, respectively in the rectangular channel. Numerical analysis and multi-objective optimization have been done at fixed Reynolds number, Re = 42,500. Using the proposed optimization framework, Pareto-optimal front design (POD) signifies the trade-off between the obtained objective functions, and among them, five PODs have been chosen using K-means clustering technique. In the paper, results indicated that the POD which offer high blockage effect to the incoming flow lead to high heat transfer performance, but accompanied by greater pressure losses. The blockage effect is discussed using spatial flow and thermal patterns. An optimum design with a relative thermal performance enhancement of 168.60% compared with the reference design is reported.

Shape Optimization of the Streamlined Train Head for Reducing Aerodynamic Resistance and Noise

Aiming to improve the comprehensive aerodynamic performance of a high-speed train, a multi-objective shape optimization method for a streamlined train head is proposed in this work. The shape of the streamlined train head is parameterized with some spline curves. The optimization design variables are uniformly sampled using the optimal Latin hypercube design method. The aerodynamic resistance and dipole noise sources are chosen as the optimization objectives, which can be obtained through the computational fluid dynamics (CFD) method. An approximate calculation model is established by the radial basis function neural network so as to effectively predict the values of optimization objectives. The error between the predicted values and actual values of the aerodynamic resistance is less than 1%, and that of the dipole noise source is less than 3 dB, which demonstrate the validity of the approximate calculation model. In the optimization process, the algorithm NSGA-II is adopted to update the values of the optimization design variables, and the approximate calculation model is used to calculate the optimization objectives, which greatly reduces the optimization computation time of the streamlined head shape. Through iterative computation of the optimization algorithm in the design space, each optimized design variable shows a trend of convergence, and the aerodynamic resistance and dipole noise source generally show a decreasing trend. The Pareto front is corrected by the CFD method after optimization. The aerodynamic resistance can be reduced by up to 4.5%, and the dipole noise source can be reduced by up to 3.9 dB.

A pareto optimal front of fluidic diode for a wave energy harnessing device

A twin-turbine or turbine duo (TUD) is constructed from a pair of unidirectional turbines. Flow reversal hampers the performance of these units. A Fluidic diode (FD) that offers a variable resistance to the flow can be used with TUD to prevent flow reversal, and its performance is governed by diodicity. With the increase in diodicity, flow blockage improves, but the resistance across the turbines increases too. As these turbines operate under a smaller pressure drop, the FD used with them should have higher diodicity with lesser fluid resistance across them. This study presents a multi-objective shape optimization of an FD to maximize diodicity and minimize pressure drop. The shape optimization is performed by simultaneously varying six design parameters. The performance of FD was evaluated by solving the 3D Reynolds Averaged Navier-Stokes equations. The popular evolutionary search algorithm (NSGA-II) with an artificial neural network produced a set of non-dominated optimal solutions (Pareto optimal set). Compared to the base model, the optimal design set shows improved diodicity from 17.2 to 21.57% and pressure drop from −2.535% to 78.67%, respectively. Further, the flow analyses of optimal designs show that the nozzle angle and the toroidal cup radius affect more than the other variables.

Multi-objective Shape Optimization of Airfoils for Mars Exploration Aircraft Propellers

Multi-objective Shape Optimization of Airfoils for Mars Exploration Aircraft Propellers

Multi-objective shape optimization of siphon outlet in pumping station considering two-phase flow

The siphon outlet is widely used in pumping stations due to its reliable and convenient cut-off performance. Long siphoning time or high hydraulic loss caused by the inappropriate design of the siphon outlet can significantly affect the safety of stations. The air compressibility volume-of-fluid (VOF) method is conducted to simulate the two-phase flow in the siphoning formation process at the design points selected by the optimal Latin hypercube design (OLHD), the results of which show good agreement with the experimental data. In this work, the siphoning time and hydraulic loss coefficient are selected as the objective functions, and a multi-objective shape optimization strategy is proposed for the siphon outlet in conjunction with the response surface method (RSM). This optimization strategy can not only reconcile conflicting objective functions but also obtain the effect and interaction of design variables. Sensitivity analysis on the constructed response surface models indicates that among three design variables, the aspect ratio has the greatest effect on the objective functions, the descending angle has the second greatest effect, and the ascending angle has almost no effect. Compared with the original design, the hydraulic loss coefficient and siphoning time of the optimized design are reduced by 2.95% and 26.76%, respectively. A higher vorticity magnitude and more uniform outflow are created in the optimized design, which results in the improvement of hydraulic performance.

Multi-objective Shape Optimization of Bone Scaffolds: Enhancement of Mechanical Properties and Permeability

Porous scaffolds have recently attracted attention in bone tissue engineering. The implanted scaffolds are supposed to satisfy the mechanical and biological requirements. In this study, two porous structures named MFCC-1 (modified face centered cubic-1) and MFCC-2 (modified face centered cubic-2) are introduced. The proposed porous architectures are evaluated, optimized, and tested to enhance mechanical and biological properties. The geometric parameters of the scaffolds with porosities ranging from 70% to 90% are optimized to find a compromise between the effective Young's modulus and permeability, as well as satisfying the pore size and specific surface area requirements. To optimize the effective Young's modulus and permeability, we integrated a mathematical formulation, finite element analysis, and computational fluid dynamics simulations. For validation, the optimized scaffolds were 3D-printed, tested, and compared with two different orthogonal cylindrical struts (OCS) scaffold architectures. The MFCC designs are preferred to the generic OCS scaffolds from various perspectives: a) the MFCC architecture allows scaffold designs with porosities up to 96%; b) the very porous architecture of MFCC scaffolds allows achieving high permeabilities, which could potentially improve the cell diffusion; c) despite having a higher porosity compared to the OCS scaffolds, MFCC scaffolds improve mechanical performance regarding Young's modulus, stress concentration, and apparent yield strength; d) the proposed structures with different porosities are able to cover all the range of permeability for the human trabecular bones. The optimized MFCC designs have simple architectures and can be easily fabricated and used to improve the quality of load-bearing orthopedic scaffolds. Statement of significancePorous scaffolds are increasingly being studied to repair large bone defects. A scaffold is supposed to withstand mechanical loads and provide an appropriate environment for bone cell growth after implantation. These mechanical and biological requirements are usually contradicting; improving the mechanical performance would require a reduction in porosity and a lower porosity is likely to reduce the biological performance of the scaffold. Various studies have shown that the mechanical and biological performance of bone scaffolds can be improved by internal architecture modification. In this study, we propose two scaffold architectures named MFCC-1 and MFCC-2 and provide an optimization framework to simultaneously optimize their stiffness and permeability to improve their mechanical and biological performances.

Multi-objective shape optimization of transonic compressor cascade at the same inlet Mach number

ABSTRACT In this paper, a two-dimensional transonic cascade of German Aerospace Center (DLR) was redesigned with multi-objective optimization. The aerodynamic performance of the cascade was optimized with inlet Mach number of 1.1 by using the blade design method with thickness distribution superposed on the camber line. The non-dominated sorting genetic algorithm, (NSGA) II multi-objective optimization algorithm, was used to determine higher performance cascades. Cascade optimization was carried out within a unique inlet Mach number by varying the shapes of both the camber line and the thickness distribution curve. To enable the cascade to operate under specific conditions, we used an inlet Mach number control loop (IMCL) to regulate the outlet boundary conditions. Optimization was conducted to minimize the cascade total pressure loss coefficient under the three inlet conditions. The optimization results indicated that the total pressure loss coefficient can be reduced by 22% under the design condition, and the range of working conditions was widened.

Large yacht resistance reduction by hydrodynamic multi-objective shape optimization

ABSTRACT This paper presents the results of the hydrodynamic optimization of a large yacht concept design that is meant to be used as a reference for future buildings. The optimization framework is used to improve the calm water resistance performance of a generic baseline design while satisfying a set of geometrical constraints. The shape of the hull is modified according to a geometrical interpolation approach where two shapes are combined to obtain a third design. The search towards the optimum is driven by a global convergence, multi-objective, genetic algorithm where the resistance of each candidate is evaluated by a Boundary Element Method. The final optimal design is then verified by means of a high-fidelity Reynolds Averaged Navier–Stokes technique, preliminary validated against available experimental data. The obtained results show the strong influence of the stern shape of the hull on the final resistance performance, highlighting the effects of the pressure recovery due to a so-called S-shape bottom. The bow shape is modified consistently to fulfil the geometric constraints and to further improve the resistance performance by inducing a positive interference effect on the generated wave pattern.

Multi-objective shape optimization of large strain 3D helical structures for mechanical metamaterials

The need for mechanical metamaterials with large strain range and lightweight properties are evidenced to engineering applications. In this regard, novel helical structures are proposed as suitable unit cell’s components of mechanical metamaterials. Three-dimensional helical structures composed of varying coil numbers, defined in a cylindrical spatial domain are shape optimized through genetic algorithm in a finite element script for conflicting objectives of minimum mass and maximum tensile range. The superior performance of the shape optimized helical structure is highlighted in terms of structural rigidity, large deformation capability, buckling and vibrational modal analysis in compare to equivalent coil springs of identical weight and comparable domain. Deformation mechanism is analyzed carefully to justify the improved performances of proposed structure. Tensile and compressive experimental analysis are undertaken to validate the enhanced strain ranges. One dimensional metamaterials implementations with various tessellation arrangements are simulated. Results show that the proposed design can effectively generate lightweight substitutes of metamaterials unit cells ligaments to improve the strain range performance. Planar and lattice metamaterial concepts employing shape optimized helical structure are illustrated to demonstrate the possibilities of promoting lightweight structural integrities in the design of mechanical metamaterials.

Multiobjective design optimization of a quadrupole resonator under uncertainties

For a precise determination of the rf properties of superconducting materials, a calorimetric measurement is carried out with the aid of a so-called quadrupole resonator (QPR). This procedure is affected by certain systematic measurement errors with various sources of uncertainties. In this paper, to reduce the impact of geometrical uncertainties on the measurement bias, the modified steepest descent method is used for the multiobjective shape optimization of a QPR in terms of an expectation measure. Thereby, variations of geometrical parameters are modeled by the polynomial chaos expansion technique. Then, the resulting Maxwell's eigenvalue problem with random input data is solved using the polynomial chaos-based stochastic collocation method. Furthermore, to assess the contribution of the particular geometrical parameters, the variance-based sensitivity analysis is proposed. This allows for modifying the steepest descent algorithm, which results in reducing the computational load needed to find optimal solutions. Finally, optimization results in the form of an efficient approximation of the Pareto front for a three-dimensional model of the QPR are shown.

Multi-Objective Shape Optimization of Two-Phase Microchannels

Multi-Objective Shape Optimization of Two-Phase Microchannels

Hybrid Meta-heuristic Adaptive Fuzzy Inference Systems in Rockfill Dam Multi-objective Shape Optimization

This study aims to approach the optimal design of the Sardasht rockfill dam, while two classic and three hybrid meta-heuristic adaptive nero-fuzzy inference systems (ANFIS) are utilized to estimate the seepage and factor of safety (FOS) according to the simulated values within SEEP/W and SLOP/W. The ANFIS is trained with classic gradient distance (CGD), hybrid back propagation and least square algorithm (BP&LS), particle swarm optimization (PSO), genetic algorithm (GA), and firefly optimization algorithm (FA). The non-dominated sorting genetic algorithm-III (NSGA-III) is employed to handle the multi-objective problem when the dam's construction cost, seepage, and FOS are considered as objective functions. Thus, besides an extensive comparison among classic and hybrid meta-heuristic ANFISs, their influences on optimization results are investigated. Comparing the outcomes of ANFISs based on several statistical criteria and the Mann-Whitney test reveals that all ANFISs can estimate the seepage and FOS, and there is no significant difference between estimated and simulated values at 99% confidence level for all ANFISs. Nonetheless, hybrid meta-heuristic ANFISs report higher confidence than ANFIS-CGD and ANFIS-BP&LS, while the PSO improved the confidence of ANFIS more than other algorithms. The NSGA-III is executed 100 times, and optimization results are investigated in terms of the Hypervolume metric. It is found that utilizing meta-heuristic ANFISs, increases the convergence corresponding to the optimal Pareto front by 22.5%. Eventually, the NSGA-III provides two hundred optimal designs, all of which dominate the original design of the Sardasht dam.

CFD-based optimization of a displacement trimaran hull for improving its calm water and wavy condition resistance

This paper presents a multi-objective shape optimization approach for improving the bow region of a trimaran ship hull. A CFD-based design study is conducted to reduce the total resistance of trimaran ship hull in calm water and wavy condition. Accordingly, a practical multi-objective optimization platform is established and developed for ship hull modification. In addition, the hullform of a displacement trimaran ship with inverted bow is modified as a case study. Six objective functions are utilized in the present study by considering the weighted sum optimization method. Reduction of total resistance at two cruise and sprint speeds in calm water, reduction of resistance in two different wave conditions, and two cruise and sprint speeds are the six objectives of the study. Two aspects of ship hydrodynamics, resistance, and seakeeping are the disciplines that are considered through the proposed optimization process. Ship hull parametrization is performed by Arbitrary Shape Deformation (ASD) technique that defines the input variables for optimization process. The geometry reconstruction step connects to CFD solver in order to calculate the response of the optimization cycle. An innovative Simcenter SHERPA algorithm is employed to optimize the design objectives. The optimization results show a 3.14% reduction in the aggregated objective function. Generated waves around the hulls of the optimized trimaran have constructive interaction and diminish each other in calm water. A forefoot angle and sharper nose are created at bow region of the optimized hullform. Moreover, the comparison between baseline and optimized trimaran hull confirms the validity of the proposed optimization design strategy.