Surrogate-assisted Optimization Algorithm Research Articles

A Multi-level Surrogate-assisted Algorithm for Expensive Optimization Problems

With the development of computer science, more and more complex problems rely on the help of computers for solving. When facing the parameter optimization problem of complex models, traditional intelligent optimization algorithms often require multiple iterations on the target problem. It can bring unacceptable costs and resource costs in dealing with these complex problems. In order to solve the parameter optimization of complex problems, in this paper we propose a multi-level surrogate-assisted optimization algorithm (MLSAO). By constructing surrogate models at different levels, the algorithm effectively explores the parameter space, avoiding local optima and enhancing optimization efficiency. The method combines two optimization algorithms, differential evolution (DE) and Downhill simplex method. DE is focused on global level surrogate model optimization. Downhill simplex is concentrated on local level surrogate model update. Random forest and inverse distance weighting (IDW) are constructed for global and local level surrogate model respectively. These methods leverage their respective advantages at different stages of the algorithm. The MLSAO algorithm is evaluated against other state-of-the-art approaches using benchmark functions of varying dimensions. Comprehensive results from the comparisons showcase the superior performance of the MLSAO algorithm in addressing expensive optimization problems. Moreover, we implement the MLSAO algorithm for tuning precipitation parameters in the Community Earth System Model (CESM). The outcomes reveal its effective enhancement of CESM's simulation accuracy for precipitation in the North Indian Ocean and the North Pacific region. These experiments demonstrate that MLSAO can better address parameter optimization problems under complex conditions.

An online surrogate-assisted neighborhood search algorithm based on deep neural network for thermal layout optimization

Thermal layout optimization problems are common in integrated circuit design, where a large number of electronic components are placed on the layout, and a low temperature (i.e., high efficiency) is achieved by optimizing the positions of the electronic components. The operating temperature value of the layout is obtained by measuring the temperature field from the expensive simulation. Based on this, the thermal layout optimization problem can be viewed as an expensive combinatorial optimization problem. In order to reduce the evaluation cost, surrogate models have been widely used to replace the expensive simulations in the optimization process. However, facing the discrete decision space in thermal layout problems, generic surrogate models have large prediction errors, leading to a wrong guidance of the optimization direction. In this work, the layout scheme and its temperature field are represented by images whose relation can be well approximated by a deep neural network. Therefore, we propose an online deep surrogate-assisted optimization algorithm for thermal layout optimization. First, the iterative local search is developed to explore the discrete decision space to generate new layout schemes. Then, we design a deep neural network to build an image-to-image mapping model between the layout and the temperature field as the approximated evaluation. The operating temperature of the layout can be measured by the temperature field predicted by the mapping model. Finally, a segmented fusion model management strategy is proposed to online updates the parameters of the network. The experimental results on three kinds of layout datasets demonstrate the effectiveness of our proposed algorithm, especially when the required computational budget is limited.

A practical tutorial on solving optimization problems via PlatEMO

PlatEMO is an open-source platform for solving complex optimization problems, which provides a variety of metaheuristics including evolutionary algorithms, swarm intelligence algorithms, multi-objective optimization algorithms, surrogate-assisted optimization algorithms, and many others. Due to the problem-independent nature of most metaheuristics, they are versatile for solving problems with various difficulties such as multimodal landscapes, discrete search spaces, multiple objectives, strict constraints, and expensive evaluations, regardless of the fields the problems belong to. Since PlatEMO was published in 2017, it has been used by many researchers from both academia and industry in the computational intelligence community. However, the basic terms and concepts about optimization may confuse practitioners and junior researchers new to metaheuristics. Hence, this paper presents a practical introduction to the use of PlatEMO 4.0, focusing on the procedures of defining problems, selecting suitable metaheuristics, and collecting results. Note, however, that a description of the technical details of metaheuristics is beyond the scope of this paper and interested readers may refer to the cited references.

Early termination strategies with asynchronous parallel optimization in application to automatic calibration of groundwater PDE models

Automatic calibration is widely used to estimate parameters in hydrological models. The main idea is to use optimization algorithms to minimize the discrepancy between field data and simulation prediction. This process involves iterative exchanges of a parameter set chosen by the optimization and simulation. However, for computationally expensive models, such as groundwater flow and transport models, the calibration process may be extremely computationally demanding. In this study, we introduce and demonstrate a new asynchronous parallel surrogate-assisted optimization algorithm with an early truncation feature and different knowledge extraction strategies (SO-AET-k). Results show that our asynchronous algorithm performs significantly better than the synchronous analogue (SO-SP), requiring only 40%–70% of the computation time to achieve the same averaged results. In addition, various knowledge extraction strategies of the asynchronous SO-AET-k are tested. In comparisons with two other algorithms, SCE-UA and APPSPACK, asynchronous SO-AET-k shows significantly better performance in terms of both efficiency and robustness.

A neural network learning-based global optimization approach for aero-engine transient control schedule

Transient performance of aero-engine determines the maneuverability of aircraft. The optimal control schedule can tap the potential transient performance with subject to each constraint. Thus the transient time can be minimized with the optimal transient control schedule. This transient schedule is described by a strong constrained and nonlinear problem. It is therefore challenging to present an optimal method to achieve the best transient schedule. Motivated by solving this problem, a surrogate-assisted optimization framework is presented by using the learning capability of neural networks. It is achieved by presenting a sequential ensemble radial basis function (RBF) neural network-based optimization (SERO) algorithm. The advantage of the RBF neural network such as excellent prediction accuracy is taken and integrated into the surrogate-assisted optimization algorithm to improve the algorithm performance. With the application of the proposed scheme, the global optimization schedule is guaranteed for aero-engine transient control. Numerical validation is finally carried out by applying the presented optimization framework to a mixed-flow aero-engine transient control schedule. It is demonstrated that the SERO approach can minimize the transient process time despite any constraint at any time.

Surrogate-assisted optimization for augmentation of finite element techniques

The application of finite element techniques for the analysis and optimization of complex thermo-mechanical structures typically involves highly nonlinear models for material characterization, tribological contact, large deformation, damage, etc. These nonlinearities usually call for a higher order spatio-temporal discretization, including a large number of elements and time-steps in order to provide good convergence and sufficiently accurate simulation results. Unfortunately, this inevitably leads to many expensive simulations in terms of cost and time if an optimization or adaption of design parameters has to be done. In this work, a surrogate-assisted optimization algorithm is utilized to find the setting of design parameters, which would lead to maximum damage in a simple tensile testing scenario involving a notched specimen with as few FEM simulations as possible.

An improved assisted evolutionary algorithm for data-driven mixed integer optimization based on Two_Arch

Most of the existing data-driven surrogate-assisted optimization algorithms are developed to solve continuous optimization problems, but there are many problems in reality belong to combinatorial optimization/discrete optimization problems, especially (subdivided into) mixed-integer optimization problems. However, there are few researches based on online data-driven mixed-integer linear programming. Therefore, in this work, we solve a kind of expensive data-driven constrained multi-objective mixed-integer optimization problem, the objectives and constraints are derived based on a large number of calculations. In order to solve this kind of problem, we proposed the use of a random forest classifier (RF) as a surrogate model to approximate the objective and constraints. At the same time, to balance the convergence, diversity, and complexity of the objective, this paper proposes a new improvement strategy that combines the surrogate-assisted model and the Two_Arch method, which assigns different selection principles to the two files, and a dual structure multi-objective maintenance program based on Hypervolume district size (HD) indicators. To further improve the accuracy and performance of the model, this paper also adopts a new crossover operator. To verify the effectiveness of the algorithm, tests are carried out on ten benchmark problems of multi-objective knapsack, and comprehensive comparison with several well-known algorithms is carried out. Experimental results show that the improved algorithm is effective in solving data-driven multi-objective mixed-integer optimization problems.

Variable-Fidelity Simulation Models and Sparse Gradient Updates for Cost-Efficient Optimization of Compact Antenna Input Characteristics.

Design of antennas for the Internet of Things (IoT) applications requires taking into account several performance figures, both electrical (e.g., impedance matching) and field (gain, radiation pattern), but also physical constraints, primarily concerning size limitation. Fulfillment of stringent specifications necessitates the development of topologically complex structures described by a large number of geometry parameters that need tuning. Conventional optimization procedures are typically too expensive when the antenna is evaluated using high-fidelity electromagnetic (EM) analysis, otherwise required to ensure accuracy. This paper proposes a novel surrogate-assisted optimization algorithm for computationally efficient design optimization of antenna structures. In the paper, the optimization of antenna input characteristic is presented, specifically, minimization of the antenna reflection coefficient in a given bandwidth. Our methodology involves variable-fidelity EM simulations as well as a dedicated procedure to reduce the cost of estimating the antenna response gradients. The latter is based on monitoring the variations of the antenna response sensitivities along the optimization path. The procedure suppresses the finite-differentiation-based sensitivity updates for variables that exhibit stable gradient behavior. The proposed algorithm is validated using three compact wideband antennas and demonstrated to outperform both the conventional trust region algorithm and the pattern search procedure, as well as surrogate-based procedures while retaining acceptable design quality.

Two-Level Surrogate-Assisted Differential Evolution Multi-Objective Optimization of Electric Machines Using 3-D FEA

A two-level surrogate-assisted optimization algorithm is proposed for electric machine design using 3-D finite-element analysis (FEA). The algorithm achieves the optima with much fewer FEA evaluations than conventional methods. It is composed of interior and exterior levels. The exploration is performed mainly in the interior level, which evaluates hundreds of designs employing affordable kriging models. Then, the most promising designs are evaluated in the exterior loop with expensive 3-D FEA models. The sample pool is constructed in a self-adjustable and dynamic way. A hybrid stopping criterion is used to avoid unnecessary expensive function evaluations.

Multiple Surrogate-Assisted Many-Objective Optimization for Computationally Expensive Engineering Design

Engineering design often involves problems with multiple conflicting performance criteria, commonly referred to as multi-objective optimization problems (MOP). MOPs are known to be particularly challenging if the number of objectives is more than three. This has motivated recent attempts to solve MOPs with more than three objectives, which are now more specifically referred to as “many-objective” optimization problems (MaOPs). Evolutionary algorithms (EAs) used to solve such problems require numerous design evaluations prior to convergence. This is not practical for engineering applications involving computationally expensive evaluations such as computational fluid dynamics and finite element analysis. While the use of surrogates has been commonly studied for single-objective optimization, there is scarce literature on its use for MOPs/MaOPs. This paper attempts to bridge this research gap by introducing a surrogate-assisted optimization algorithm for solving MOP/MaOP within a limited computing budget. The algorithm relies on principles of decomposition and adaptation of reference vectors for effective search. The flexibility of function representation is offered through the use of multiple types of surrogate models. Furthermore, to efficiently deal with constrained MaOPs, marginally infeasible solutions are promoted during initial phases of the search. The performance of the proposed algorithm is benchmarked with the state-of-the-art approaches using a range of problems with up to ten objective problems. Thereafter, a case study involving vehicle design is presented to demonstrate the utility of the approach.

Comparison between efficient global optimization and output space mapping technique

The optimization of electromagnetic devices by direct use of finite element models is computationally expensive. This paper presents two effective surrogate-assisted optimization algorithms: Output Space Mapping and Efficient Global Optimization which are employed with regard to a minimum number of finite element model evaluations. A parallel between the two algorithms is made through a single phase safety isolating transformer optimization problem using 3D finite element models.