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This paper aims to propose a gradient-based shape optimization framework in which traditional time-consuming conversions between computer-aided design and computer-aided engineering and the mesh update procedure are avoided/eliminated. The scheme is general so that it can be used in all cases as a black box, no matter what the objective and/or design variables are, whilst the efficiency and accuracy are guaranteed.

The authors integrated CAD and CAE by using isogeometric analysis (IGA), enabling the present methodology to be robust and accurate. To overcome the difficulty in evaluating the sensitivities of objective and/or constraint functions by analytic method in some cases, the authors adopt the finite difference method to calculate these sensitivities, thereby providing a universal approach. Moreover, to further eliminate the inefficiency caused by the finite difference method, the authors advance the exact reanalysis method, the indirect factorization updating (IFU), to exactly and efficiently calculate functions and their sensitivities, which guarantees its generality and efficiency at the same time.

The proposed isogeometric gradient-based shape optimization using our IFU approach is reliable and accurate, as well as general and efficient.

The authors proposed a gradient-based shape optimization framework in which they first integrate IGA and the proposed exact reanalysis method for applicability to structural response and sensitivity analysis.

A collaborative design environment is needed for multidisciplinary design optimization (MDO) process, based on all the modules those for different design/analysis disciplines, and a systematic coupling should be made to carry out aerodynamic shape optimization (ASO), which is an important part of MDO.

Computerized environment for aircraft synthesis and integrated optimization methods (CEASIOM)-ASO is developed based on loosely coupling all the existing modules of CEASIOM by MATLAB scripts. The optimization problem is broken down into small sub-problems, which is called “sequential design approach”, allowing the engineer in the loop.

CEASIOM-ASO shows excellent design abilities on the test case of designing a blended wing body flying in transonic speed, with around 45 per cent drag reduction and all the constraints fulfilled.

Authors built a complete and systematic technique for aerodynamic wing shape optimization based on the existing computational design framework CEASIOM, from geometry parametrization, meshing to optimization.

CEASIOM-ASO provides an optimization technique with loosely coupled modules in CEASIOM design framework, allowing engineer in the loop to follow the “sequential approach” of the design, which is less “myopic” than sticking to gradient-based optimization for the whole process. Meanwhile, it is easily to be parallelized.

Environmental and operational restrictions increasingly drive modern aircraft design due to the growing impact of global warming on the ecology. Regulations and industrial measures are being introduced to make air traffic greener, including restrictions and environmental targets for aircraft design that increase aerodynamic efficiency. This study aims to maximize aerodynamic efficiency by identifying optimal values for sweep angle, taper ratio, twist angle and wing incidence angle parameters in wing design while keeping wing area and span constant.

Finding optimal wing values by using gradient-based and evolutionary algorithm methods is very time-consuming. Therefore, an artificial neural network-based surrogate model was developed. Computational fluid dynamics (CFD) analyses were carried out by using Reynolds-averaged Navier–Stokes equations to create a properly trained data set using a feedforward neural network.

The results showed how a wing could be optimized by using a CFD-based surrogate model. The two optimum results obtained resulted in increases of 10.7397% and 10.65% in the aerodynamic efficiency of the baseline design ONERA M6 wing.

The originality of this study lies in the combination of sweep angle, taper ratio, twist angle and wing incidence angle within the scope of wing optimization calculations.

Topology optimization is a method used for developing optimized geometric designs by distributing material pixels in a given design space that maximizes a chosen quantity of interest (QoI) subject to constraints. The purpose of this study is to develop a problem-agnostic automatic differentiation (AD) framework to compute sensitivities of the QoI required for density distribution-based topology optimization in an unstructured co-located cell-centered finite volume framework. Using this AD framework, the authors develop and demonstrate the topology optimization procedure for multi-dimensional steady-state heat conduction problems.

Topology optimization is performed using the well-established solid isotropic material with penalization approach. The method of moving asymptotes, a gradient-based optimization algorithm, is used to perform the optimization. The sensitivities of the QoI with respect to design variables, required for optimization algorithm, are computed using a discrete adjoint method with a novel AD library named residual automatic partial differentiator (Rapid).

Topologies that maximize or minimize relevant quantities of interest in heat conduction applications are presented. The efficacy of the technique is demonstrated using a variety of realistic heat transfer applications in both two and three dimensions, in conjugate heat transfer problems with finite conductivity ratios and in non-rectangular/non-cuboidal domains.

In contrast to most published work which has either used finite element methods or Cartesian finite volume methods for transport applications, the topology optimization procedure is developed in a general unstructured finite volume framework. This permits topology optimization for flow and heat transfer applications in complex design domains such as those encountered in industry. In addition, the Rapid library is designed to provide a problem-agnostic pathway to automatically compute all required derivatives to machine accuracy. This obviates the necessity to write new code for finding sensitivities when new physics are added or new cost functions are considered and permits general-purpose implementations of topology optimization for complex industrial applications.

In magnetostatics, topology optimization (TO) addresses the problem of finding the distributions of both current densities and ferromagnetic materials to comply with fixed magnetic specifications. The purpose of this paper is to develop TO in order to design Hall-effect Thrusters (HETs).

In fact, TO problems are known to be large-scale optimization problems. The authors therefore adopt the adjoint method to reduce the computation time required to obtain the gradient information. In this paper, they illustrate the continuous variant of the adjoint method in the context of magnetostatics TO. Herein, the authors propose an implementation of the adjoint method then use it within a gradient-based optimization solver fmincon-MATLAB to solve a HET TO design problem.

By comparison with finite difference method, the authors validate the accuracy of the suggested implementation of the adjoint method. Then, they solve a large-scale HET TO design problem. The resultant design of TO is distinctly original and not intuitive.

In this paper, the authors introduce TO as a tool that has allowed them to explore new and innovative design of a HET. However, although the design presented is original, its manufacture is not feasible. Thus, a discussion section has been included at the end of paper to suggest a possible way to concretize topological solutions.

TO helps to explore more original design possibilities. In this paper, the authors present an implementation of the adjoint method that makes it possible to solve efficiently and in less central processing unit time large-scale TO design problem.

An easy implementation of the adjoint method is presented in magnetostatics TO. This implementation was first validated by comparison with the finite difference method and then used to solve a large-scale design problem. The result of the TO design problem is distinctly original and non-intuitive.

This paper aims to deal with the design optimization of a synchronous reluctance machine to be used in an X-ray tube, where the goal is to maximize the torque while keeping low the amount of material used, by means of gradient-based free-form shape optimization.

The presented approach is based on the mathematical concept of shape derivatives and allows to obtain new motor designs without the need to introduce a geometric parametrization. This paper presents an extension of a standard gradient-based free-form shape optimization algorithm to the case of multiple objective functions by determining updates, which represent a descent of all involved criteria. Moreover, this paper illustrates a way to obtain an approximate Pareto front.

The presented method allows to obtain optimal designs of arbitrary, non-parametric shape with very low computational cost. This paper validates the results by comparing them to a parametric geometry optimization in JMAG by means of a stochastic optimization algorithm. While the obtained designs are of similar shape, the computational time used by the gradient-based algorithm is in the order of minutes, compared to several hours taken by the stochastic optimization algorithm.

This paper applies the presented gradient-based multi-objective optimization algorithm in the context of free-form shape optimization using the mathematical concept of shape derivatives. The authors obtain a set of Pareto-optimal designs, each of which is a shape that is not represented by a fixed set of parameters. To the best of the authors’ knowledge, this approach to multi-objective free-form shape optimization is novel in the context of electric machines.

This paper's purpose is to deal with single point and multipoint optimization of an airfoil. The aim of the paper is to discuss optimization in several design points (multipoint optimization) and compare the results with those of optimization at a specified design point.

A gradient‐based method is adopted for optimization and the flow is governed by two dimensional, compressible Euler equations. A finite volume code based on unstructured grid is developed to solve the equations.

Two test cases are studied for an airfoil with initial profile of NACA0012, with two types of design variables. And at the end a multi‐point case is presented.

The advantage of this technique over the other gradient‐based methods is its high‐convergence rate.

The overall pressure drop in an axisymmetric contraction is minimised using two different grid sizes. The transition region was parameterised with only two design variables to make it possible to create surface plots of the objective function in the design space, which were based on 121 CFD calculations for each grid. The coarse grid showed to have significant numerical noise in the objective function while the finer grid had less numerical noise. The optimisation was performed with two methods, a Response Surface Model (RSM) and a gradient‐based method (the Method of Feasible Directions) to study the influence from numerical noise. Both optimisation methods were able to find the global optimum with the two different grid sizes (the search path for the gradient‐based method on the coarse grid was able to avoid the region in the design space containing local minima). However, the RSM needed fewer iterations in reaching the optimum. From a grid convergence study at two points in the design space the level of noise appeared to be sufficiently low, when the relative step size is 10^–4 for the finite difference calculations, to not influence the convergence if the errors are below 5 per cent for this contraction geometry.

Reliability-based design optimizations (RBDOs) of engineering structures involve complex non-linear/non-differentiable performance functions, including both continuous and discrete variables. The gradient-based RBDO algorithms are less than satisfactory for these cases. The simulation-based approaches could also be computationally inefficient, especially when the double-loop strategy is used. This paper aims to present a pseudo-double loop flexible RBDO, which is efficient for solving problems, including both discrete/continuous variables.

The method is based on the hybrid improved binary bat algorithm (BBA) and weighed simulation method (WSM). According to this method, each BBA’s movement generates proper candidate solutions, and subsequently, WSM evaluates the reliability levels for design candidates to conduct swarm in a low-cost safe-region.

The accuracy of the proposed enhanced BBA and also the hybrid WSM-BBA are examined for ten benchmark deterministic optimizations and also four RBDO problems of truss structures, respectively. The solved examples reveal computational efficiency and superiority of the method to conventional RBDO approaches for solving complex problems including discrete variables.

Unlike other RBDO approaches, the proposed method is such organized that only one simulation run suffices during the optimization process. The flexibility future of the proposed RBDO framework enables a designer to present multi-level design solutions for different arrangements of the problem by using the results of the only one simulation for WSM, which is very helpful to decrease computational burden of the RBDO. In addition, a new suitable transfer function that enhanced convergence rate and search ability of the original BBA is introduced.

The purpose of this paper is to develop a mathematical framework to address some algorithmic features of approximate dynamic programming (ADP) by using an average cost formulation based on the concepts of differential costs and performance gradients. Under such a framework, a modified value iteration algorithm is developed that is easy to implement, in the mean time it can address a class of partially observable Markov decision processes (POMDP).

Gradient‐based policy iteration (GBPI) is a top‐down, system‐theoretic approach to dynamic optimization with performance guarantees. In this paper, a bottom‐up, algorithmic view is provided to complement the original high‐level development of GBPI. A modified value iteration is introduced, which can provide solutions to the same type of POMDP problems dealt with by GBPI. Numerical simulations are conducted to include a queuing problem and a maze problem to illustrate and verify features of the proposed algorithms as compared to GBPI.

The direct connection between GBPI and policy iteration is shown under a Markov decision process formulation. As such, additional analytical insights were gained on GBPI. Furthermore, motivated by this analytical framework, the authors propose a modified value iteration as an alternative to addressing the same POMDP problem handled by GBPI.

Several important insights are gained from the analytical framework, which motivate the development of both algorithms. Built on this paradigm, new ADP learning algorithms can be developed, in this case, the modified value iteration, to address a broader class of problems, the POMDP. In addition, it is now possible to provide ADP algorithms with a gradient perspective. Inspired by the fundamental understanding of learning and optimization problems under the gradient‐based framework, additional new insight may be developed for bottom‐up type of algorithms with performance guarantees.