Efficient Global Optimization Algorithm Research Articles

Vehicle Aerodynamic Optimization: On a Combination of Adjoint Method and Efficient Global Optimization Algorithm

Vehicle Aerodynamic Optimization: On a Combination of Adjoint Method and Efficient Global Optimization Algorithm

Efficient global optimization and modal strain energy coefficient-based algorithm for fast prediction of dynamic aeroelastic loads

Design optimization of airframes is conventionally conducted employing a deterministic set of critical load cases defined through performing a sheer number of aeroelastic analyses spanning the aircrafts’ design space. Due to its large computational cost, the latter process cannot be integrated within the structural optimization cycle, hindering the development of a multidisciplinary design optimization (MDO) framework. In this paper, we present an algorithm for the efficient estimation of critical dynamic aeroelastic loads, as a first step towards the development of an integrated MDO platform. The method is based on the Kriging metamodeling technique along with the Latin hypercube scheme for initial sampling, and the expected improvement function for subsequent selection of sample points, known together as the efficient global optimization (EGO) algorithm. Furthermore, the use of the element modal strain energy coefficient (MSEC) is investigated as an inexpensive indicator to determine if a substantial change in the loads is expected after structural modification, thus triggering the necessity for the re-exploration of the loads’ design space. A case study is presented to evaluate the performance of the proposed methodology versus a stand-alone Kriging interpolation; a reduction of over 40% was achieved in the total time of execution employing the proposed algorithm.

Surrogate-assisted microscopic traffic simulation-based optimisation of routing parameters

Reactive and predictive routing algorithms have to work fast and reliably for a large number of traffic participants. Therefore, simple rules and thresholds guide the routing decisions rather than extensive data collection and machine learning. In this paper, we optimise some of the thresholds governing the behaviour of a reactive and predictive routing algorithm by using the microscopic traffic simulator TraffSim. Microscopic traffic simulation is more exact than its macroscopic counterpart and very well suited to test the efficiency of a reactive and predictive routing algorithm. Unfortunately, it is also tremendously more computationally expensive, impairing the applicability of 'conventional' heuristic optimisation techniques like genetic algorithms or evolution strategies. Extensive use of surrogate models in an optimisation procedure is a promising alternative. Several variations of the efficient global optimisation (EGO) algorithm are tested and compared. Furthermore, a new type of surrogate model geared towards the parameter optimisation is presented.

Aerodynamic drag reduction in a vehicle based on efficient global optimisation

Vehicle aerodynamic shape optimisation is a typical non-linear and computationally expensive black box problem, which is severely limited by time and cost of the objective function evaluations during the global optimisation process. To solve the shortcomings of low efficiency and high cost of the existing vehicle drag reduction method, an improved efficient global optimisation (EGO) algorithm is used to optimise a four-dimensional aerodynamic drag reduction design of a vehicle combined with computational fluid dynamics numerical simulation technology. Moreover, data mining technologies are used to reveal the influence mechanisms of design variables on aerodynamic drag and to analyse the relationship between the variables. It is demonstrated that the improved EGO algorithm, based on the kriging response surface and expected improvement function, can achieve the global optimum with minimum function evaluations. The aerodynamic drag of the optimal design is 1.56% lower than that of the original vehicle. The data mining results showed that the engine hood inclination and the tail upturn angle play a leading role in the vehicle's aerodynamic drag, and the hood inclination has the greatest impact.

Efficient global optimization of constrained mixed variable problems

Due to the increasing demand for high performance and cost reduction within the framework of complex system design, numerical optimization of computationally costly problems is an increasingly popular topic in most engineering fields. In this paper, several variants of the Efficient Global Optimization algorithm for costly constrained problems depending simultaneously on continuous decision variables as well as on quantitative and/or qualitative discrete design parameters are proposed. The adaptation that is considered is based on a redefinition of the Gaussian Process kernel as a product between the standard continuous kernel and a second kernel representing the covariance between the discrete variable values. Several parameterizations of this discrete kernel, with their respective strengths and weaknesses, are discussed in this paper. The novel algorithms are tested on a number of analytical test-cases and an aerospace related design problem, and it is shown that they require fewer function evaluations in order to converge towards the neighborhoods of the problem optima when compared to more commonly used optimization algorithms.

Phasor particle swarm optimization: a simple and efficient variant of PSO

Particle swarm optimizer is a well-known efficient population and control parameter-based algorithm for global optimization of different problems. This paper focuses on a new and primary sample for PSO, which is named phasor particle swarm optimization (PPSO) and is based on modeling the particle control parameters with a phase angle (θ), inspired from phasor theory in the mathematics. This phase angle (θ) converts PSO algorithm to a self-adaptive, trigonometric, balanced, and nonparametric meta-heuristic algorithm. The performance of PPSO is tested on real-parameter optimization problems including unimodal and multimodal standard test functions and traditional benchmark functions. The optimization results show good and efficient performance of PPSO algorithm in real-parameter global optimization, especially for high-dimensional optimization problems compared with other improved PSO algorithms taken from the literature. The phasor model can be used to expand different types of PSO and other algorithms. The source codes of the PPSO algorithms are publicly available at https://github.com/ebrahimakbary/PPSO .

Optimization of BWB Aircraft Using Parallel Computing

Nacelle shape optimization for Blended Wing Body (BWB) is performed. The optimization procedure is based on numerical calculations of the Reynolds–averaged Navier–Stokes equations. For the Top Level Aircraft Requirements, formulated in AGILE project, the propulsion system was designed. The optimization procedure was divided in two steps. At first step, the isolated nacelle was designed and optimized for cruise regimes. This step is listed in paragraph 3. At second step the nacelles positions over airframe were optimized. To find the optimum solution, surrogate–based Efficient Global Optimization algorithm is used. An automatic structural computational mesh creation is realized for the effective optimization algorithm working. This whole procedure is considered in the context of the third generation multidisciplinary optimization techniques, developed within AGILE project. During the project, new techniques should be implemented for the novel aircraft configurations, chosen as test cases for application of AGILE technologies. It is shown that the optimization technology meets all requirements and is suitable for using in the AGILE project.

A multiple-data-based efficient global optimization algorithm and its parallel implementation for automotive body design

The purpose of this article is to improve the convergence efficiency of the traditional efficient global optimization method. Furthermore, we try a graphics processing unit–based parallel computing method to improve the computing efficiency of the efficient global optimization method for both mathematical and practical engineering problems. First, we propose a multiple-data-based efficient global optimization algorithm instead of the multiple-surrogates-based efficient global optimization algorithm. Second, a novel graphics processing unit–based general-purpose computing technology is adopted to accelerate the solution efficiency of our multiple-data-based efficient global optimization algorithm. Third, a hybrid parallel computing approach using the OpenMP and compute unified device architecture is adopted to further improve the solution efficiency of forward problems in practical application. This is accomplished by integrating the graphics processing unit–based finite element method numerical analysis system into the optimization software. The numerical results show that for the same problem, the optimal result of the multiple-data-based efficient global optimization algorithm is consistently better than the multiple-surrogates-based efficient global optimization algorithm with the same optimization iterations. In addition, the graphics processing unit–based parallel simulation system helps in the reduction of the calculation time for practical engineering problems. The multiple-data-based efficient global optimization method performs stably in both high-order mathematical functions and large-scale nonlinear practical engineering optimization problems. An added benefit is that the computational time and accuracy are no longer obstacles.

Surrogate-based visualization and sensitivity analysis of coronary stent performance: A study on the influence of geometric design.

The main goal of this numerical study is to assess the impact of geometric design perturbations on the performance of a representative coronary stent platform. In this context, first, a design parameterization model was defined for the stent under study. After, a set of metrics characterizing stent performance, namely, vessel injury, radial recoil, bending resistance, longitudinal resistance, radial strength, the risk of fracture, prolapse index, and dogboning were evaluated within the context of a finite element analysis. Afterwards, accurate surrogate models were developed, using the efficient global optimization algorithm, as predictive tools in the execution of tasks that normally require a high number of model evaluations, such as global sensitivity analysis and visualization. In the end, the dependence of the output response surfaces on the geometric parameters was mechanically interpreted, which allowed us to understand the complex interplay that exists between the considered design variables and the defined performance metrics.

A surrogate-assisted particle swarm optimization algorithm based on efficient global optimization for expensive black-box problems

ABSTRACTEvolutionary algorithms cannot effectively handle computationally expensive problems because of the unaffordable computational cost brought by a large number of fitness evaluations. Therefore, surrogates are widely used to assist evolutionary algorithms in solving these problems. This article proposes an improved surrogate-assisted particle swarm optimization (ISAPSO) algorithm, in which a hybrid particle swarm optimization (PSO) is combined with global and local surrogates. The global surrogate is not only used to predict fitness values for reducing computational burden but also regarded as a global searcher to speed up the global search process of PSO by using an efficient global optimization algorithm, while the local one is constructed for a local search in the neighbourhood of the current optimal solution by finding the predicted optimal solution of the local surrogate. Empirical studies on 10 widely used benchmark problems and a real-world structural design optimization problem of a driving axle show that the ISAPSO algorithm is effective and highly competitive.

Energy‐efficient power control for uplink spectrum‐sharing heterogeneous networks

SummaryThis article considers energy‐efficient power control schemes for interference management in uplink spectrum‐sharing heterogeneous networks that maximize the energy efficiency of users, protect the macro base station, and support users with QoS consideration. In the first scenario, we define the objective function as the weighted sum of the energy efficiencies and develop an efficient global optimization algorithm with global linear and local quadratic rate of convergence to solve the considered problem. To ensure fairness among individual user equipments (UEs) in terms of energy efficiency, we consider the max‐min problem, where the objective is defined as the weighted minimum of the energy efficiencies, and a fractional programming theory and the dual decomposition method are jointly used to solve the problem and investigate an iterative algorithm. As by‐products, we further discuss the global energy efficiency problem and consider near‐optimal schemes. Numerical examples are provided to demonstrate significant improvements of the proposed algorithms over existing interference management schemes.

Multi-surrogate-based Differential Evolution with multi-start exploration (MDEME) for computationally expensive optimization

In this paper, we present a new global optimization algorithm MDEME for black-box problems with computationally expensive objectives. Considering that Differential Evolution (DE) is an efficient global optimization algorithm but has difficulty in expensive optimization problems, we combine DE with three surrogate models Kriging, Radial Basis Function (RBF), and Quadratic Polynomial Response (QRS) to realize surrogate-based optimization. Although the three surrogates have different approximate effects that may generate diverse updating points, the surrogate-based DE may still get stuck in local optimal regions. In order to enhance its exploration capability, a multi-start optimization algorithm with a new selecting strategy is proposed. The multi-start optimization algorithm can capture and select several promising points from Kriging and RBF that always generate multiple local optimal solutions per optimization cycle. In the whole optimization process, DE and the proposed multi-start optimization are alternately carried out on the three surrogate models that are dynamically updated. Once no more satisfactory points can be obtained from Kriging and RBF, the multi-start optimization will explore the sparsely sampled area using the estimated mean square error of Kriging. After the comparison with 5 global optimization algorithms on 17 representative cases, MDEME shows its high efficiency, strong stability and good parallelism capability in dealing with expensive optimization problems. Finally, MDEME is used for the shape optimization of a blended-wing-body underwater glider, and the design performance gets significantly improved.

Variable-Fidelity Optimization of Film-Cooling Hole Arrangements Considering Conjugate Heat Transfer

In spite of its crucial importance, conjugate heat transfer has been ignored in most film-hole-array optimization studies due to the burdensome associated with added complexity and computational requirements. To cope with this issue and to consider the conduction cooling effects, the hierarchical kriging model was applied to optimize the film-cooling hole array on a high-pressure turbine nozzle. The hierarchical kriging model used in this study consists of three levels and was constructed effectively using both adiabatic-condition-based analyses and conjugate-heat-transfer analyses. The expected-improvement-based efficient global optimization algorithm was coupled with the hierarchical kriging model to improve the efficiency of the whole optimization process. As a result, the required computation time to obtain the optimum solution was markedly reduced to a quarter compared to the time without the hierarchical kriging model, and the viability of the method for highly nonlinear and time-consuming problems was proved. Additionally, the conjugate-heat-transfer-based optimum film-hole array showed that it has improved the overall cooling effectiveness and could have a different shape compared to the array obtained under the adiabatic wall condition. The detailed causes of the resultant hole arrangement were thoroughly examined with respect to both the external and internal cooling aspects.

Uncertainty quantification-based robust aerodynamic optimization of laminar flow nacelle

The aerodynamic performance of laminar flow nacelle is highly sensitive to uncertain working conditions, especially the surface roughness. An efficient robust aerodynamic optimization method on the basis of non-deterministic computational fluid dynamic (CFD) simulation and Efficient Global Optimization (EGO)algorithm was employed. A non-intrusive polynomial chaos method is used in conjunction with an existing well-verified CFD module to quantify the uncertainty propagation in the flow field. This paper investigates the roughness modeling behavior with the [Formula: see text]-Ret shear stress transport model including modeling flow transition and surface roughness effects. The roughness effects are modeled to simulate sand grain roughness. A Class-Shape Transformation-based parametrical description of the nacelle contour as part of an automatic design evaluation process is presented. A Design-of-Experiments (DoE) was performed and surrogate model by Kriging method was built. The new design nacelle process demonstrates that significant improvements of both mean and variance of the efficiency are achieved and the proposed method can be applied to laminar flow nacelle design successfully.

Defect localization and characterization in eddy current nondestructive testing by change detection and global optimization

PurposeThis paper aims to present a data-processing methodology combining kernel change detection (KCD) and efficient global optimization algorithms for solving inverse problem in eddy current non-destructive testing. The main purpose is to reduce the computation cost of eddy current data inversion, which is essentially because of the heavy forward modelling with finite element method and the non-linearity of the parameter estimation problem.Design/methodology/approachThe KCD algorithm is adapted and applied to detect damaged parts in an inspected conductive tube using probe impedance signal. The localization step allows in reducing the number of measurement data that will be processed for estimating the flaw characteristics using a global optimization algorithm (efficient global optimization). Actually, the minimized objective function is calculated from data related to defect detection indexes provided by KCD.FindingsSimulation results show the efficiency of the proposed methodology in terms of defect detection and localization; a significant reduction of computing time is obtained in the step of defect characterization.Originality/valueThis study is the first of its kind that combines a change detection method (KCD) with a global optimization algorithm (efficient global optimization) for defect detection and characterization. To show that such approach allows to reduce the numerical cost of ECT data inversion.

Kriging-based simulation optimization: An emergency medical system application

Metamodeling is a common subject in simulation optimization literature. It aims to estimate the actual value (simulated) even before the point is evaluated by a simulation model. However, most publications do not apply metamodeling to models with real world complexity and size. This paper sought to apply Kriging to minimize the average response time of a Medical Emergency System by allocating ambulances throughout several city bases. Kriging is considered the state-of-art technique in metamodeling as it provides, in addition to the new point estimation, the level of prediction uncertainty. The optimization process followed the Efficient Global Optimization algorithm (EGO) and the Reinterpolation Procedure to deal with a stochastic simulation model. Finally, EGO was used to obtain a curve that reflected the relationship between the minimum response time and the total number of ambulances allocated to the city, representing significant information for healthcare public systems managers.

Bi-Objective Optimization of Data-Parallel Applications on Homogeneous Multicore Clusters for Performance and Energy

Performance and energy are now the most dominant objectives for optimization on modern parallel platforms composed of multicore CPU nodes. The existing intra-node and inter-node optimization methods employ a large set of decision variables but do not consider problem size as a decision variable and assume a linear relationship between performance and problem size and between energy consumption and problem size. We demonstrate using experiments of real-life data-parallel applications on modern multicore CPUs that these relationships have complex (non-linear and even non-convex) properties and, therefore, that the problem size has become an important decision variable that can no longer be ignored. This key finding motivates our work in this paper. In this paper, we first formulate the bi-objective optimization problem for performance and energy (BOPPE) for data-parallel applications on homogeneous clusters of modern multicore CPUs. It contains only one but heretofore unconsidered decision variable, the problem size. We then present an efficient and exact global optimization algorithm called <i>ALEPH</i> that solves the <i>BOPPE</i> . It takes as inputs, discrete functions of performance and dynamic energy consumption against problem size and outputs the globally Pareto-optimal set of solutions. The solutions are the workload distributions, which achieve inter-node optimization of data-parallel applications for performance and energy. While existing solvers for <i>BOPPE</i> give only one solution when the problem size and number of processors are fixed, our algorithm gives a diverse set of globally Pareto-optimal solutions. The algorithm has time complexity of <inline-formula><tex-math notation="LaTeX">$O(m^2 \times p^2)$</tex-math></inline-formula> where <inline-formula> <tex-math notation="LaTeX">$m$</tex-math></inline-formula> is the number of points in the discrete speed/energy function and <inline-formula> <tex-math notation="LaTeX">$p$</tex-math></inline-formula> is the number of available processors. We experimentally study the efficiency and scalability of our algorithm for two data parallel applications, matrix multiplication and fast Fourier transform, on a modern multicore CPU and homogeneous clusters of such CPUs. Based on our experiments, we show that the average and maximum sizes of the globally Pareto-optimal sets determined by our algorithm are 15 and 34 and 7 and 20 for the two applications respectively. Comparing with load-balanced workload distribution solution, the average and maximum percentage improvements in performance and energy respectively demonstrated for the first application are (13%,97%) and (18%,71%). For the second application, these improvements are (40%,95%) and (22%,127%). Assuming 5 percent performance degradation from the optimal is acceptable, the average and maximum improvements in energy consumption demonstrated for the two applications respectively are 9 and 44 and 8 and 20 percent. Using the algorithm and its building blocks, we also present a study of interplay between performance and energy. We demonstrate how <i>ALEPH</i> can be combined with <i> DVFS</i> -based Multi-Objective Optimization (MOP) methods to give a better set of (globally Pareto-optimal) solutions.

Efficient global optimization for high-dimensional constrained problems by using the Kriging models combined with the partial least squares method

ABSTRACTIn many engineering optimization problems, the number of function evaluations is often very limited because of the computational cost to run one high-fidelity numerical simulation. Using a classic optimization algorithm, such as a derivative-based algorithm or an evolutionary algorithm, directly on a computational model is not suitable in this case. A common approach to addressing this challenge is to use black-box surrogate modelling techniques. The most popular surrogate-based optimization algorithm is the efficient global optimization (EGO) algorithm, which is an iterative sampling algorithm that adds one (or many) point(s) per iteration. This algorithm is often based on an infill sampling criterion, called expected improvement, which represents a trade-off between promising and uncertain areas. Many studies have shown the efficiency of EGO, particularly when the number of input variables is relatively low. However, its performance on high-dimensional problems is still poor since the Kriging models used are time-consuming to build. To deal with this issue, this article introduces a surrogate-based optimization method that is suited to high-dimensional problems. The method first uses the ‘locating the regional extreme’ criterion, which incorporates minimizing the surrogate model while also maximizing the expected improvement criterion. Then, it replaces the Kriging models by the KPLS(+K) models (Kriging combined with the partial least squares method), which are more suitable for high-dimensional problems. Finally, the proposed approach is validated by a comparison with alternative methods existing in the literature on some analytical functions and on 12-dimensional and 50-dimensional instances of the benchmark automotive problem ‘MOPTA08’.

An efficient global optimization algorithm for maximizing the sum of two generalized Rayleigh quotients

Maximizing the sum of two generalized Rayleigh quotients (SRQ) can be reformulated as a one-dimensional optimization problem, where the function value evaluations are reduced to solving semi-definite programming (SDP) subproblems. In this paper, we first use the dual SDP subproblem to construct an explicit overestimation and then propose a branch-and-bound algorithm to globally solve (SRQ). Numerical results demonstrate that it is even more efficient than the recent SDP-based heuristic algorithm.

An analysis of covariance parameters in Gaussian process-based optimization

Numerical optimization problems are at the core of many real-world applications in which the function to be optimized stems from a proprietary and computationally intensive simulation software. It is then preferable to handle the problem as a black-box optimization and to approximate the objective function by a surrogate. Among the methods developed for solving such problems, the Efficient Global Optimization (EGO) algorithm is regarded as a state-of-the-art algorithm. The surrogate model used in EGO is a Gaussian Process (GP) conditional on data points where the value of the objective function has already been calculated. The most important control on the efficiency of the EGO algorithm is the Gaussian process covariance function (or kernel) as it customizes the GP that is processed to create the optimization iterates. Traditionally, a parameterized family of covariance functions (e.g., squared exponential, Matern) is considered whose parameters are often estimated by maximum likelihood. However, the effect of these parameters on the performance of EGO has not been properly studied and needs further investigation. In this paper, we theoretically and empirically analyze the effect of the covariance parameters, the so-called “characteristic length-scale” and “nugget”, on the design of experiments generated by EGO and the associated optimization performance. More precisely, the behavior of EGO algorithms when the covariance parameters are fixed is compared to the standard setting where they are estimated, with a special focus on the case of very small or very large characteristic length-scale. The approach allows a deeper understanding of the influence of these parameters on the EGO iterates and addresses from a mixed practical/theoretical point of view questions that are relevant for EGO users. For instance, our numerical experiments show that choosing a “small” nugget should be preferred to its estimate by maximum likelihood. We prove that iterates stay at the best observed point when the length-scale tends to 0. Vice versa, when the length-scale tends to infinity, we prove that EGO degenerates into a minimization of the GP mean prediction which, itself, tends to the Lagrange interpolation polynomial if the GP kernel is sufficiently differentiable. Overall, this study contributes to a better understanding of a key optimization algorithm, EGO.