State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

A Genetic Programming Based Heuristic to Simplify Rugged Landscapes Exploration

Some optimization problems are difficult to solve due to a considerable number of local optima, which may result in premature convergence of the optimization process. To address this problem, we propose a novel heuristic method for constructing a smooth surrogate model of the original function. The surrogate function is easier to optimize but maintains a fundamental property of the original rugged fitness landscape: the location of the global optimum. To create such a surrogate model, we consider a linear genetic programming approach coupled with a self-tuning fitness function. More specifically, to evaluate the fitness of the produced surrogate functions, we employ Fuzzy Self-Tuning Particle Swarm Optimization, a setting-free version of particle swarm optimization. To assess the performance of the proposed method, we considered a set of benchmark functions characterized by high noise and ruggedness. Moreover, the method is evaluated over different problems’ dimensionalities. The proposed approach reveals its suitability for performing the proposed task. In particular, experimental results confirm its capability to find the global argminimum for all the considered benchmark problems and all the domain dimensions taken into account, thus providing an innovative and promising strategy for dealing with challenging optimization problems. Doi: 10.28991/ESJ-2023-07-04-01 Full Text: PD

A Genetic Programming Based Heuristic to Simplify Rugged Landscapes Exploration

Some optimization problems are difficult to solve due to a considerable number of local optima, which may result in premature convergence of the optimization process. To address this problem, we propose a novel heuristic method for constructing a smooth surrogate model of the original function. The surrogate function is easier to optimize but maintains a fundamental property of the original rugged fitness landscape: the location of the global optimum. To create such a surrogate model, we consider a linear genetic programming approach coupled with a self-tuning fitness function. More specifically, to evaluate the fitness of the produced surrogate functions, we employ Fuzzy Self-Tuning Particle Swarm Optimization, a setting-free version of particle swarm optimization. To assess the performance of the proposed method, we considered a set of benchmark functions characterized by high noise and ruggedness. Moreover, the method is evaluated over different problems’ dimensionalities. The proposed approach reveals its suitability for performing the proposed task. In particular, experimental results confirm its capability to find the global argminimum for all the considered benchmark problems and all the domain dimensions taken into account, thus providing an innovative and promising strategy for dealing with challenging optimization problems

Uncertainty-Integrated Surrogate Modeling for Complex System Optimization

Approximation models such as surrogate models provide a tractable substitute to expensive physical simulations and an effective solution to the potential lack of quantitative models of system behavior. These capabilities not only enable the efficient design of complex systems, but is also essential for the effective analysis of physical phenomena/characteristics in the different domains of Engineering, Material Science, Biomedical Science, and various other disciplines. Since these models provide an abstraction of the real system behavior (often a low-fidelity representative) it is important to quantify the accuracy and the reliability of such approximation models without investing additional expensive system evaluations (simulations or physical experiments). Standard error measures, such as the mean squared error, the cross-validation error, and the Akaike\u27s information criterion however provide limited (often inadequate) information regarding the accuracy of the final surrogate model while other more effective dedicated error measures are tailored towards only one class of surrogate models. This lack of accuracy information and the ability to compare and test diverse surrogate models reduce the confidence in model application, restricts appropriate model selection, and undermines the effectiveness of surrogate-based optimization. A key contribution of this dissertation is the development of a new model-independent approach to quantify the fidelity of a trained surrogate model in a given region of the design domain. This method is called the Predictive Estimation of Model Fidelity (PEMF). The PEMF method is derived from the hypothesis that the accuracy of an approximation model is related to the amount of data resources leveraged to train the model . In PEMF, intermediate surrogate models are iteratively constructed over heuristic subsets of sample points. The median and the maximum errors estimated over the remaining points are used to determine the respective error distributions at each iteration. The estimated modes of the error distributions are represented as functions of the density of intermediate training points through nonlinear regression, assuming a smooth decreasing trend of errors with increasing sample density. These regression functions are then used to predict the expected median and maximum errors in the final surrogate models. It is observed that the model fidelities estimated by PEMF are up to two orders of magnitude more accurate and statistically more stable compared to those based on the popularly-used leave-one-out cross-validation method, when applied to a variety of benchmark problems. By leveraging this new paradigm in quantifying the fidelity of surrogate models, a novel automated surrogate model selection framework is also developed. This PEMF-based model selection framework is called the Concurrent Surrogate Model Selection (COSMOS). COSMOS, unlike existing model selection methods, coherently operates at all the three levels necessary to facilitate optimal selection, i.e., (1) selecting the model type, (2) selecting the kernel function type, and (3) determining the optimal values of the typically user-prescribed parameters. The selection criteria that guide optimal model selection are determined by PEMF and the search process is performed using a MINLP solver. The effectiveness of COSMOS is demonstrated by successfully applying it to different benchmark and practical engineering problems, where it offers a first-of-its-kind globally competitive model selection. In this dissertation, the knowledge about the accuracy of a surrogate estimated using PEMF is applied to also develop a novel model management approach for engineering optimization. This approach adaptively selects computational models (both physics-based models and surrogate models) of differing levels of fidelity and computational cost, to be used during optimization, with the overall objective to yield optimal designs with high-fidelity function estimates at a reasonable computational expense. In this technique, a new adaptive model switching (AMS) metric defined to guide the switching of model from one to the next higher fidelity model during the optimization process. The switching criterion is based on whether the uncertainty associated with the current model output dominates the latest improvement of the relative fitness function, where both the model output uncertainty and the function improvement (across the population) are expressed as probability distributions. This adaptive model switching technique is applied to two practical problems through Particle Swarm Optimization to successfully illustrate: (i) the computational advantage of this method over purely high-fidelity model-based optimization, and (ii) the accuracy advantage of this method over purely low-fidelity model-based optimization. Motivated by the unique capabilities of the model switching concept, a new model refinement approach is also developed in this dissertation. The model refinement approach can be perceived as an adaptive sequential sampling approach applied in surrogate-based optimization. Decisions regarding when to perform additional system evaluations to refine the model is guided by the same model-uncertainty principles as in the adaptive model switching technique. The effectiveness of this new model refinement technique is illustrated through application to practical surrogate-based optimization in the area of energy sustainability

Application of Surrogate Based Optimisation in the Design of Automotive Body Structures

The rapid development of automotive industry requires manufacturers to continuously reduce the development cost and time and to enhance the product quality. Thus, modern automotive design pays more attention to using CAE analysis based optimisation techniques to drive the entire design flow. This thesis focuses on the optimisation design to improve the automotive crashworthiness and fatigue performances, aiming to enhance the optimisation efficiency, accuracy, reliability, and robustness etc. The detailed contents are as follows: (1) To excavate the potential of crash energy absorbers, the concept of functionally graded structure was introduced and multiobjective designs were implemented to this novel type of structures. First, note that the severe deformation takes place in the tubal corners, multi-cell tubes with a lateral thickness gradient were proposed to better enhance the crashworthiness. The results of crashworthiness analyses and optimisation showed that these functionally graded multi-cell tubes are preferable to a uniform multi-cell tube. Then, functionally graded foam filled tubes with different gradient patterns were analyzed and optimized subject to lateral impact and the results demonstrated that these structures can still behave better than uniform foam filled structures under lateral loading, which will broaden the application scope of functionally graded structures. Finally, dual functionally graded structures, i.e. functionally graded foam filled tubes with functionally graded thickness walls, were proposed and different combinations of gradients were compared. The results indicated that placing more material to tubal corners and the maximum density to the outmost layer are beneficial to achieve the best performance. (2) To make full use of training data, multiple ensembles of surrogate models were proposed to maximize the fatigue life of a truck cab, while the panel thicknesses were taken as design variables and the structural mass the constraint. Meanwhile, particle swarm optimisation was integrated with sequential quadratic programming to avoid the premature convergence. The results illustrated that the hybrid particle swarm optimisation and ensembles of surrogates enable to attain a more competent solution for fatigue optimisation. (3) As the conventional surrogate based optimisation largely depends on the number of initial sample data, sequential surrogate modeling was proposed to practical applications in automotive industry. (a) To maximize the fatigue life of spot-welded joints, an expected improvement based sequential surrogate modeling method was utilized. The results showed that by using this method the performance can be significantly improved with only a relatively small number of finite element analyses. (c) A multiojective sequential surrogate modeling method was proposed to address a multiobjective optimisation of a foam-filled double cylindrical structure. By adding the sequential points and updating the Kriging model adaptively, more accurate Pareto solutions are generated. (4) While various uncertainties are inevitably present in real-life optimisations, conventional deterministic optimisations could probably lead to the violation of constraints and the instability of performances. Therefore, nondeterministic optimisation methods were introduced to solve the automotive design problems. (a) A multiobjective reliability-based optimisation for design of a door was investigated. Based on analysis and design responses surface models, the structural mass was minimized and the vertical sag stiffness was maximized subjected to the probabilistic constraint. The results revealed that the Pareto frontier is divided into the sensitive region and insensitive region with respect to uncertainties, and the decision maker is recommended to select a solution from the insensitive region. Furthermore, the reduction of uncertainties can help improve the reliability but will increase the manufacturing cost, and the tradeoff between the reliability target and performance should be made. (b) A multiobjective uncertain optimisation of the foam-filled double cylindrical structure was conducted by considering randomness in the foam density and wall thicknesses. Multiobjective particle swarm optimisation and Monte Carlo simulation were integrated into the optimisation. The results proved that while the performances of the objectives are sacrificed slightly, the nondeterministic optimisation can enhance the robustness of the objectives and maintain the reliability of the constraint. (c) A multiobjective robust optimisation of the truck cab was performed by considering the uncertainty in material properties. The general version of dual response surface model, namely dual surrogate model, was proposed to approximate the means and standard deviations of the performances. Then, the multiobjective particle optimisation was used to generate the well-distributed Pareto frontier. Finally, a hybrid multi-criteria decision making model was proposed to select the best compromise solution considering both the fatigue performance and its robustness. During this PhD study, the following ideas are considered innovative: (1) Surrogate modeling and multiobjective optimisation were integrated to address the design problems of novel functionally graded structures, aiming to develop more advanced automotive energy absorbers. (2) The ensembles of surrogates and hybrid particle swarm optimisation were proposed for the design of a truck cab, which could make full use of training points and has a strong searching capacity. (3) Sequential surrogate modeling methods were introduced to several optimisation problems in the automotive industry so that the optimisations are less dependent on the number of initial training points and both the efficiency and accuracy are improved. (4) The surrogate based optimisation method was implemented to address various uncertainties in real life applications. Furthermore, a hybrid multi-criteria decision making model was proposed to make the best compromise between the performance and robustness

Evolutionary model type selection for global surrogate modeling

Due to the scale and computational complexity of currently used simulation codes, global surrogate (metamodels) models have become indispensable tools for exploring and understanding the design space. Due to their compact formulation they are cheap to evaluate and thus readily facilitate visualization, design space exploration, rapid prototyping, and sensitivity analysis. They can also be used as accurate building blocks in design packages or larger simulation environments. Consequently, there is great interest in techniques that facilitate the construction of such approximation models while minimizing the computational cost and maximizing model accuracy. Many surrogate model types exist ( Support Vector Machines, Kriging, Neural Networks, etc.) but no type is optimal in all circumstances. Nor is there any hard theory available that can help make this choice. In this paper we present an automatic approach to the model type selection problem. We describe an adaptive global surrogate modeling environment with adaptive sampling, driven by speciated evolution. Different model types are evolved cooperatively using a Genetic Algorithm ( heterogeneous evolution) and compete to approximate the iteratively selected data. In this way the optimal model type and complexity for a given data set or simulation code can be dynamically determined. Its utility and performance is demonstrated on a number of problems where it outperforms traditional sequential execution of each model type

A hybrid swarm-based algorithm for single-objective optimization problems involving high-cost analyses

In many technical fields, single-objective optimization procedures in continuous domains involve expensive numerical simulations. In this context, an improvement of the Artificial Bee Colony (ABC) algorithm, called the Artificial super-Bee enhanced Colony (AsBeC), is presented. AsBeC is designed to provide fast convergence speed, high solution accuracy and robust performance over a wide range of problems. It implements enhancements of the ABC structure and hybridizations with interpolation strategies. The latter are inspired by the quadratic trust region approach for local investigation and by an efficient global optimizer for separable problems. Each modification and their combined effects are studied with appropriate metrics on a numerical benchmark, which is also used for comparing AsBeC with some effective ABC variants and other derivative-free algorithms. In addition, the presented algorithm is validated on two recent benchmarks adopted for competitions in international conferences. Results show remarkable competitiveness and robustness for AsBeC.Comment: 19 pages, 4 figures, Springer Swarm Intelligenc