Topology optimization of fluid problems using genetic algorithm assisted by the Kriging model

A non‐gradient‐based approach for topology optimization using a genetic algorithm is proposed in this paper. The genetic algorithm used in this paper is assisted by the Kriging surrogate model to reduce computational cost required for function evaluation. To validate the non‐gradient‐based topology optimization method in flow problems, this research focuses on two single‐objective optimization problems, where the objective functions are to minimize pressure loss and to maximize heat transfer of flow channels, and one multi‐objective optimization problem, which combines earlier two single‐objective optimization problems. The shape of flow channels is represented by the level set function. The pressure loss and the heat transfer performance of the channels are evaluated by the Building‐Cube Method code, which is a Cartesian‐mesh CFD solver. The proposed method resulted in an agreement with previous study in the single‐objective problems in its topology and achieved global exploration of non‐dominated solutions in the multi‐objective problems. © 2016 The Authors International Journal for Numerical Methods in Engineering Published by John Wiley & Sons Ltd     

Simulation response optimization via an alternating variable methodsimulation response optimization

Simulation response optimization has wide applications for management of systems that are so complicated that the performance can only be evaluated by using simulation. This paper modifies the Hooke-Jeeves alternating variable method used in deterministic optimization to suit the stochastic environment in simulation response optimization. The basic idea underlying the proposed method is to conduct several different replications at each trial point to obtain a reliable estimate of the theoretical response. To avoid misjudging the real difference between two points due to the stochastic nature, a t-test instead of a simple comparison of the mean responses is performed. Empirical results from a stochastic Watson function with nine variables, a queueing problem with two variables, and an inventory problem with two variables indicate that the alternating variable method modified in this paper is superior to the Nelder-Mead simplex method, two stochastic approximation methods, and Fu and Healy's hybrid method. It is also robust with respect to the parameter for deciding the number of replications conducted at each trial point.     

A comparative study of controlled random search algorithms with application to inverse aerofoil design

This article presents a comparative study of some versions of the controlled random search algorithm (CRSA) in global optimization problems. The basic CRSA, originally proposed by Price in 1977 and improved by Ali et al. in 1997, is taken as a starting point. Then, some new modifications are proposed to improve the efficiency and reliability of this global optimization technique. The performance of the algorithms is assessed using traditional benchmark test problems commonly invoked in the literature. This comparative study points out the key features of the modified algorithm. Finally, a comparison is also made in a practical engineering application, namely the inverse aerofoil shape design.     

A smart repair embedded memetic algorithm for 2D shape matching problems

Shape representation plays a major role in any shape optimization exercise. The ability to identify a shape with good performance is dependent on both the flexibility of the shape representation scheme and the efficiency of the optimization algorithm. In this article, a memetic algorithm is presented for 2D shape matching problems. The shape is represented using B-splines, in which the control points representing the shape are repaired and subsequently evolved within the optimization framework. The underlying memetic algorithm is a multi-feature hybrid that combines the strength of a real coded genetic algorithm, differential evolution and a local search. The efficiency of the proposed algorithm is illustrated using three test problems, wherein the shapes were identified using a mere 5000 function evaluations. Extension of the approach to deal with problems of unknown shape complexity is also presented in the article.     

Parallel implementations of the Complex-RF algorithm

Low-dimension derivative-free optimization problems are common in many engineering applications. Usefulness is often limited by long evaluation times due to large simulation models. For such problems, direct-search algorithms often outperform the naturally parallel population-based methods. While direct-search algorithms are more difficult to parallelize, there are many unexploited opportunities. Three methods for parallelizing the Complex-RF algorithm have been implemented and evaluated. Numerical analysis of the algorithm has been performed. This provides a basis for parametrization of the parallel methods. The methods are tested on two standard test functions with five variables and one real simulation model with eight variables. An entropy rate based performance index is used to compare the methods. Experiments show performance increases ranging from 3.9 to 6.4 depending on the model. The suggested methods outperform both a particle swarm and a differential evolution algorithm with up to 32 threads. When more threads are added, parallelization efficiency decreases.     

Bio‐inspired algorithms for the optimization of offshore oil production systems

This work describes the development, implementation, and assessment of enhanced variants of three different groups of bio‐inspired methodologies: genetic algorithms, particle swarm optimization, and artificial immune system. The algorithms are implemented on a computational tool for the synthesis and optimization of offshore oil production risers that connect a floating platform at the sea surface to the wellheads at the sea bottom. Optimization procedures using bio‐inspired algorithms for such real‐world engineering problems require the calculation of the objective function through a large number of time‐consuming finite element nonlinear dynamic analyses, for the evaluation of the structural behavior of each candidate configuration. Therefore, the performance of the algorithms may be measured by the smaller number of objective function evaluations associated to a given target fitness value. The results indicate that the artificial immune system approach, incorporating some enhancements presented in this work, is more effective than the genetic algorithms and particle swarm optimization methods, requiring a smaller number of evaluations to obtain better solutions. Copyright © 2012 John Wiley & Sons, Ltd.     

Adaptive accuracy trust region: using cross-validation in the optimization process

This article presents an adaptive accuracy trust region (AATR) optimization strategy where cross-validation is used by the trust region to reduce the number of sample points needed to construct metamodels for each step of the optimization process. Lower accuracy metamodels are initially used for the larger trust regions, and higher accuracy metamodels are used for the smaller trust regions towards the end of optimization. Various metamodelling strategies are used in the AATR algorithm: optimal and inherited Latin hypercube sampling to generate experimental designs; quasi-Newton, kriging and polynomial regression metamodels to approximate the objective function; and the leave-k-out method for validation. The algorithm is tested with two-dimensional single-discipline problems. Results show that the AATR algorithm is a promising method when compared to a traditional trust region method. Polynomial regression in conjunction with a new hybrid inherited-optimal Latin hypercube sampling performed the best.     

A sweeping window method for detection of flaws using an explicit dynamic XFEM and absorbing boundary layers

We present a sweeping window method in elastodynamics for detection of multiple flaws embedded in a large structure. The key idea is to measure the elastic wave propagation generated by a dynamic load within a smaller substructural detecting window domain, given a sufficient number of sensors. Hence, rather than solving the full structure, one solves a set of smaller dynamic problems quickly and efficiently. To this end, an explicit dynamic extended FEM with circular/elliptical void enrichments is implemented to model the propagation of elastic waves in the detecting window domain. To avoid wave reflections, we consider the window as an unbounded domain with the option of full‐infinite/semi‐infinite/quarter‐infinite domains and employ a simple multi‐dimensional absorbing boundary layer technique. A spatially varying Rayleigh damping is proposed to eliminate spurious wave reflections at the artificial model boundaries. In the process of flaw detection, two phases are proposed: (i) pre‐analysis—identification of rough damage regions through a data‐driven approach, and (ii) post‐analysis‐–identification of the true flaw parameters by a two‐stage optimization technique. The ‘pre‐analysis’ phase considers the information contained in the ‘pseudo’ healthy structure and the scattered wave signals, providing an admissible initial guess for the optimization process. Then a two‐stage optimization approach (the simplex method and a damped Gauss–Newton algorithm) is carried out in the ‘post‐analysis’ phase for convergence to the true flaw parameters. A weighted sum of the least squares, of the residuals between the measured and simulated waves, is used to construct the objective function for optimization. Several benchmark examples are numerically illustrated to test the performance of the proposed sweeping methodology for detection of multiple flaws in an unbounded elastic domain. Copyright © 2015 John Wiley & Sons, Ltd.     

Structural shape optimization using equivalent static loads transformed from dynamic loads

In structural optimization, static loads are generally utilized although real external forces are dynamic. Dynamic loads have been considered only in small‐scale problems. Recently, an algorithm for dynamic response optimization using transformation of dynamic loads into equivalent static loads has been proposed. The transformation is conducted to match the displacement fields from dynamic and static analyses. This algorithm can be applied to large‐scale problems. However, the application has been limited to size optimization. The present study applies the algorithm to shape optimization. Because the number of degrees of freedom of finite element models is usually very large in shape optimization, it is difficult to conduct dynamic response optimization with conventional methods that directly treat dynamic response in the time domain. The optimization process is carried out by interfacing an optimization system and an analysis system for structural dynamics. Various examples are solved to verify the algorithm. The results are compared to the results from static loads. It is found that the algorithm using static loads transformed from dynamic loads based on displacement is valid for very large‐scale shape optimization problems. Copyright © 2005 John Wiley & Sons, Ltd.     

Towards Robust Rain Removal with Unet++

Image deraining has become a hot topic in the field of computer vision. It is the process of removing rain streaks from an image to reconstruct a high-quality background. This study aims at improving the performance of image rain streak removal and reducing the disruptive effects caused by rain. To better fit the rain removal task, an innovative image deraining method is proposed, where a kernel prediction network with Unet++ is designed and used to filter rainy images, and rainy-day images are used to estimate the pixel-level kernel for rain removal. To minimize the gap between synthetic and real data and improve the performance in real rainy image handling, a loss function and an effective data optimization method are suggested. In contrast with other methods, the loss function consists of Structural Similarity Index loss, edge loss, and L1 loss, and it is adopted to improve performance. The proposed algorithm can improve the Peak Signal-to-Noise ratio by 1.3% when compared to conventional approaches. Experimental results indicate that the proposed method can achieve a better efficiency and preserve more image structure than several classical methods.     

Displacement back analysis for underground engineering based on immunized continuous ant colony optimization

The objective function of displacement back analysis for rock parameters in underground engineering is a very complicated nonlinear multiple hump function. The global optimization method can solve this problem very well. However, many numerical simulations must be performed during the optimization process, which is very time consuming. Therefore, it is important to improve the computational efficiency of optimization back analysis. To improve optimization back analysis, a new global optimization, immunized continuous ant colony optimization, is proposed. This is an improved continuous ant colony optimization using the basic principles of an artificial immune system and evolutionary algorithm. Based on this new global optimization, a new displacement optimization back analysis for rock parameters is proposed. The computational performance of the new back analysis is verified through a numerical example and a real engineering example. The results show that this new method can be used to obtain suitable parameters of rock mass with higher accuracy and less effort than previous methods. Moreover, the new back analysis is very robust.     

An efficient memetic algorithm for 3D shape matching problems

Shape representation plays a vital role in any shape optimization exercise. The ability to identify a shape with good functional properties is dependent on the underlying shape representation scheme, the morphing mechanism and the efficiency of the optimization algorithm. This article presents a novel and efficient methodology for morphing 3D shapes via smart repair of control points. The repaired sequence of control points are subsequently used to define the 3D object using a B-spline surface representation. The control points are evolved within the framework of a memetic algorithm for greater efficiency. While the authors have already proposed an approach for 2D shape matching, this article extends it further to deal with 3D shape matching problems. Three 3D examples and a real customized 3D earplug design have been used as examples to illustrate the performance of the proposed approach and the effectiveness of the repair scheme. Complete details of the problems are presented for future work in this direction.     

A new approach to solving problems of multi‐state system reliability optimization

Usually engineers try to achieve the required reliability level with minimal cost. The problem of total investment cost minimization, subject to reliability constraints, is well known as the reliability optimization problem. When applied to multi‐state systems (MSS), the system has many performance levels, and reliability is considered as a measure of the ability of the system to meet the demand (required performance). In this case, the outage effect will be essentially different for units with different performance rate. Therefore, the performance of system components, as well as the demand, should be taken into account. In this paper, we present a technique for solving a family of MSS reliability optimization problems, such as structure optimization, optimal expansion, maintenance optimization and optimal multistage modernization. This technique combines a universal generating function (UGF) method used for fast reliability estimation of MSS and a genetic algorithm (GA) used as an optimization engine. The UGF method provides the ability to estimate relatively quickly different MSS reliability indices for series‐parallel and bridge structures. It can be applied to MSS with different physical nature of system performance measure. The GA is a robust, universal optimization tool that uses only estimates of solution quality to determine the direction of search. Copyright © 2001 John Wiley & Sons, Ltd.     

A surrogate-model based multi-modal optimization algorithm

In this article a new algorithm for optimization of multi-modal, nonlinear, black-box objective functions is introduced. It extends the recently-introduced adaptive multi-modal optimization by incorporating surrogate modelling features similar to response surface methods. The resulting algorithm has reduced computational intensity and is well-suited for optimization of expensive objective functions. It relies on an adaptive, multi-resolution mesh to obtain an initial estimation of the objective function surface. Local surrogate models are then constructed and used to generate additional trial points around the local minima discovered. The steps of mesh refinement and surrogate modelling continue until convergence is achieved. The algorithm produces progressively accurate surrogate models, which can be used for post-optimization studies such as sensitivity and tolerance analyses with minimal computational effort. This article demonstrates the effectiveness of the algorithm using comparative optimization of several multi-modal objective functions, and shows an engineering application of the design of a power electronic converter.     

A multiobjective mesh optimization framework for mesh quality improvement and mesh untangling

We propose a multiobjective mesh optimization framework for mesh quality improvement and mesh untangling. Our framework combines two or more competing objective functions into a single objective function to be solved using one of various multiobjective optimization methods. Methods within our framework are able to optimize various aspects of the mesh such as the element shape, element size, associated PDE interpolation error, and number of inverted elements, but the improvement is not limited to these categories. The strength of our multiobjective mesh optimization framework lies in its ability to be extended to simultaneously optimize any aspects of the mesh and to optimize meshes with different element types. We propose the exponential sum, objective product, and equal sum multiobjective mesh optimization methods within our framework; these methods do not require articulation of preferences. However, the solutions obtained satisfy a sufficient condition of weak Pareto optimality. Experimental results show that our multiobjective mesh optimization methods are able to simultaneously optimize two or more aspects of the mesh and also are able to improve mesh qualities while eliminating inverted elements. We successfully apply our methods to real‐world applications such as hydrocephalus treatment and shape optimization. Copyright © 2013 John Wiley & Sons, Ltd.     

A structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme

Structural optimization methods based on the level set method are a new type of structural optimization method where the outlines of target structures can be implicitly represented using the level set function, and updated by solving the so‐called Hamilton–Jacobi equation based on a Eulerian coordinate system. These new methods can allow topological alterations, such as the number of holes, during the optimization process whereas the boundaries of the target structure are clearly defined. However, the re‐initialization scheme used when updating the level set function is a critical problem when seeking to obtain appropriately updated outlines of target structures. In this paper, we propose a new structural optimization method based on the level set method using a new geometry‐based re‐initialization scheme where both the numerical analysis used when solving the equilibrium equations and the updating process of the level set function are performed using the Finite Element Method. The stiffness maximization, eigenfrequency maximization, and eigenfrequency matching problems are considered as optimization problems. Several design examples are presented to confirm the usefulness of the proposed method. Copyright © 2010 John Wiley & Sons, Ltd.     

Applying multiple objective tabu search to continuous optimization problems with a simple neighbourhood strategy

One of the first multiple objective versions of the tabu search (TS) algorithm is proposed by the author. The idea of applying TS to multiple objective optimization is inspired from its solution structure. TS works with more than one solution (neighbourhood solutions) at a time and this situation gives the opportunity to evaluate multiple objectives simultaneously in one run. The selection and updating stages are modified to enable the original TS algorithm to work with more than one objective. In this paper, the multiple objective tabu search (MOTS) algorithm is applied to multiple objective non‐linear optimization problems with continuous variables using a simple neighbourhood strategy. The algorithm is applied to four mechanical components design problems. The results are compared with several other solution techniques including multiple objective genetic algorithms. It is observed that MOTS is able to find better and much wider spread of solutions than the reported ones. Copyright © 2005 John Wiley & Sons, Ltd.     

A multiple surrogate assisted evolutionary algorithm for optimization involving iterative solvers

In many real-world optimization problems, the underlying objective and constraint function(s) are evaluated using computationally expensive iterative simulations such as the solvers for computational electro-magnetics, computational fluid dynamics, the finite element method, etc. The default practice is to run such simulations until convergence using termination criteria, such as maximum number of iterations, residual error thresholds or limits on computational time, to estimate the performance of a given design. This information is used to build computationally cheap approximations/surrogates which are subsequently used during the course of optimization in lieu of the actual simulations. However, it is possible to exploit information on pre-converged solutions if one has the control to abort simulations at various stages of convergence. This would mean access to various performance estimates in lower fidelities. Surrogate assisted optimization methods have rarely been used to deal with such classes of problem, where estimates at various levels of fidelity are available. In this article, a multiple surrogate assisted optimization approach is presented, where solutions are evaluated at various levels of fidelity during the course of the search. For any solution under consideration, the choice to evaluate it at an appropriate fidelity level is derived from neighbourhood information, i.e. rank correlations between performance at different fidelity levels and the highest fidelity level of the neighbouring solutions. Moreover, multiple types of surrogates are used to gain a competitive edge. The performance of the approach is illustrated using a simple 1D unconstrained analytical test function. Thereafter, the performance is further assessed using three 10D and three 20D test problems, and finally a practical design problem involving drag minimization of an unmanned underwater vehicle. The numerical experiments clearly demonstrate the benefits of the proposed approach for such classes of problem.     

An adaptive metamodel-based global optimization algorithm for black-box type problems

In this article, an adaptive metamodel-based global optimization (AMGO) algorithm is presented to solve unconstrained black-box problems. In the AMGO algorithm, a type of hybrid model composed of kriging and augmented radial basis function (RBF) is used as the surrogate model. The weight factors of hybrid model are adaptively selected in the optimization process. To balance the local and global search, a sub-optimization problem is constructed during each iteration to determine the new iterative points. As numerical experiments, six standard two-dimensional test functions are selected to show the distributions of iterative points. The AMGO algorithm is also tested on seven well-known benchmark optimization problems and contrasted with three representative metamodel-based optimization methods: efficient global optimization (EGO), GutmannRBF and hybrid and adaptive metamodel (HAM). The test results demonstrate the efficiency and robustness of the proposed method. The AMGO algorithm is finally applied to the structural design of the import and export chamber of a cycloid gear pump, achieving satisfactory results.