Surrogate-assisted Techniques Research Articles

Advanced Computational Methods for Simulating and Optimizing Stochastic Fracture: A Systematic Literature Review

Stochastic fracture processes, pervasive in diverse natural and engineered systems, pose intricate challenges for accurate simulation and optimization. This systematic literature review surveys the landscape of advanced computational methodologies to unravel and optimize stochastic fracture phenomena. Grounded in multidisciplinary perspectives spanning engineering, physics, and applied mathematics, the review navigates through the intricacies of simulation techniques and optimizations methods. From Finite Element Method (FEM) to Molecular Dynamics (MD) simulations, the review delineates the evolution and application of computational frameworks. It scrutinizes optimization strategies ranging from evolutionary algorithms to surrogate-assisted techniques, illuminating their efficacy in optimizing fracture properties amidst stochasticity. Drawing from applications in geological formations, engineered materials, and biomechanics, the review elucidates the diverse realms where advanced computational methods find resonance. Despite strides in computational prowess, challenges loom large, including computational complexity, validation dilemmas, and interdisciplinary communication barriers. Looking ahead, the review prognosticates on the integration of machine learning, novel algorithmic developments, and standardization endeavor’s to propel the frontier of stochastic fracture simulations towards unprecedented realms of understanding and optimization. Through synthesis and critique, this review engenders a roadmap for future research and underscores the transformative potential of advanced computational methods in deciphering stochastic fracture phenomena.

Surrogate Ensemble-Assisted Hyper-Heuristic Algorithm for Expensive Optimization Problems

This paper proposes a novel surrogate ensemble-assisted hyper-heuristic algorithm (SEA-HHA) to solve expensive optimization problems (EOPs). A representative HHA consists of two parts: the low-level and the high-level components. In the low-level component, we regard the surrogate-assisted technique as a type of search strategy and design the four search strategy archives: exploration strategy archive, exploitation strategy archive, surrogate-assisted estimation archive, and mutation strategy archive as low-level heuristics (LLHs), each archive contains one or more search strategies. Once the surrogate-assisted estimation archive is activated to generate the offspring individual, SEA-HHA first selects the dataset for model construction from three principles: All Data, Recent Data, and Neighbor, which correspond to the global and the local surrogate model, respectively. Then, the dataset is randomly divided into training and validation data, and the most accurate model built by polynomial regression (PR), support vector regression (SVR), and Gaussian process regression (GPR) cooperates with the infill sampling criterion is employed for solution estimation. In the high-level component, we design a random selection function based on the pre-defined probabilities to manipulate a set of LLHs. In numerical experiments, we compare SEA-HHA with six optimization techniques on 5-D, 10-D, and 30-D CEC2013 benchmark functions and three engineering optimization problems with only 1000 fitness evaluation times (FEs). The experimental and statistical results show that our proposed SEA-HHA has broad prospects for dealing with EOPs.

A parallel technique for multi-objective Bayesian global optimization: Using a batch selection of probability of improvement

Bayesian global optimization (BGO) is an efficient surrogate-assisted technique for problems involving expensive evaluations. A parallel technique can be used to parallelly evaluate the true-expensive objective functions in one iteration to boost the execution time. An effective and straightforward approach is to design an acquisition function that can evaluate the performance of a bath of multiple solutions, instead of a single point/solution, in one iteration. This paper proposes five alternatives of Probability of Improvement (PoI) with multiple points in a batch (q-PoI) for multi-objective Bayesian global optimization (MOBGO), taking the covariance among multiple points into account. Both exact computational formulas and the Monte Carlo approximation algorithms for all proposed q-PoIs are provided. Based on the distribution of the multiple points relevant to the Pareto-front, the position-dependent behavior of the five q-PoIs is investigated. Moreover, the five q-PoIs are compared with the other nine state-of-the-art and recently proposed batch MOBGO algorithms on twenty bio-objective benchmarks. The empirical experiments on different variety of benchmarks are conducted to demonstrate the effectiveness of two greedy q-PoIs ( q-PoI best and q-PoI all ) on low-dimensional problems and the effectiveness of two explorative q-PoIs ( q-PoI one and q-PoI worst ) on high-dimensional problems with difficult-to-approximate Pareto front boundaries.

Multi-objective optimization of semi-submersible platforms based on a support vector machine with grid search optimized mixed kernels surrogate model

Determination of optimal hull configurations in the semi-submersible platform (SEMI) should account for several objectives. These objectives are pertinent to hydrodynamic performances of SEMI under wave action but also total structure cost. They are often contradictory and cannot achieve the minimum simultaneously. Hence, a group of relative optimal and balanced solutions is introduced as optimization results, called Pareto-optimal solutions. This paper presents a surrogate-assisted technique to seek the optimal configuration of SEMI for minimal heave and roll response and the lightest weight. Design variables samples are generated by means of multidimensional Ladin hypercube design, and then these inputs are employed for hydrodynamic simulation to acquire the response data. To determine the relationship between objectives and hull structure size, Support Vector Machine with Grid Search optimized mixed kernels (SVM-GSM) is constructed as a surrogate model, and triple verification in terms of errors and robustness warrants its reliability. Three categories of Pareto optimal solutions are obtained by Non-dominated Sorting Genetic Algorithm II (NSGA-II), which correspond to three optimal goals. For optimization results, a presented comprehensive verification approach integrates frequency-domain analysis (FD), time-domain analysis (TD), convergence analysis, and main factors screening. This combination renders sufficient and reliable validation to optimization results. Results from FD and TD for SEMI indicate that the optimized effect of Pareto solutions is satisfactory. Besides, the main influence factors in design variables for hydrodynamic response are screened and investigated. Finally, the ranking of the influence degree of each variable is obtained and evaluated. The proposed framework in this paper provides a comprehensive validation idea for the construction of the surrogate model and optimization results for SEMI hull structure optimization.

A surrogate-assisted measurement correction method for accurate and low-cost monitoring of particulate matter pollutants

Air pollution involves multiple health and economic challenges. Its accurate and low-cost monitoring is important for developing services dedicated to reduce the exposure of living beings to the pollution. Particulate matter (PM) measurement sensors belong to the key components that support operation of these systems. In this work, a modular, mobile Internet of Things sensor for PM measurements has been proposed. Due to a limited accuracy of the PM detector, the measurement data are refined using a two-stage procedure that involves elimination of the non-physical signal spikes followed by a non-linear correction of the responses using a multiplicative surrogate model. The correction layer is derived from the sparse and non-uniform calibration data, i.e., a combination of the measurements from the PM monitoring station and the sensor obtained in the same location over a specified (relatively short) interval. The device and the method have been both demonstrated based on the data obtained during three measurement campaigns. The proposed correction scheme improves the fidelity of PM measurements by around two orders of magnitude w.r.t. the responses for which the post-processing has not been considered. Performance of the proposed surrogate-assisted technique has been favorably compared against the benchmark approaches from the literature.

Surrogate-Assisted Multistate Tuning-Driven EM Optimization for Microwave Tunable Filter

This article proposes a novel surrogate-assisted multistate tuning-driven electromagnetic (EM) optimization technique to address the challenges of microwave tunable filter design with multiple tuning states. The desired multiple tuning states are satisfied simultaneously using the proposed surrogate-assisted technique. The proposed surrogate model is composed of several subsurrogate models. Each subsurrogate model is developed to perform the optimization for each tuning state. The subsurrogate models share the same values of nontunable parameters and possess different values of tunable parameters. The overall surrogate model is developed to find a single set of optimal solutions for nontunable parameters and multiple sets of optimal solutions for tuning parameters simultaneously. Parallel computation scheme is exploited to generate the training samples for establishing the proposed surrogate model. Furthermore, a new trust-region updating formulation specifically for multistate tuning is proposed to improve the convergence of the proposed optimization algorithm. Using the proposed optimization technique, different tuning states are considered together and optimized simultaneously. The values of nontunable design parameters are constrained by all tuning states and consequently there is a higher chance that more suitable solutions can be found to satisfy all the desired tuning states simultaneously. The proposed technique for the tunable filter design with multiple tuning states has a better capability of avoiding local minima and can reach the optimal solution more effectively in comparison with the existing optimization method. Two microwave examples are used to validate the proposed technique.

Reduced‐cost electromagnetic‐driven optimisation of antenna structures by means oftrust‐region gradient‐search with sparse Jacobian updates

Numerical optimisation plays more and more important role in the antenna design. Because of lack of design-ready theoretical models, electromagnetic (EM)-simulation-driven adjustment of geometry parameters is a necessary step of the design process. At the same time, traditional parameter sweeping cannot handle complex topologies and large number of design variables. On the other hand, high computational cost of the conventional optimisation routines can be reduced using, e.g., surrogate-assisted techniques. Still, direct optimisation of EM simulation antenna models is required at certain level of fidelity. This work proposes a reduced cost trust-region algorithm with sparse updates of the antenna response Jacobian, decided based on relocation of the design variable vector between algorithm iterations and the update history. Our approach permits significant reduction of the optimisation cost (∼40% as compared to the reference algorithm) without affecting the design quality in a significant manner. Robustness of the proposed technique is validated using a set of benchmark antennas, statistical analysis of the algorithm performance over multiple initial designs, as well as investigating the effects of its control parameters that permit control efficiency vs. design quality trade-off. Selected designs were fabricated and measured to validate the computational models utilised in the optimisation process.

Fast surrogate‐assisted frequency scaling of planar antennas with circular polarisation

In this work, the problem of computationally efficient frequency scaling (re-design) of circular polarisation antennas is addressed using surrogate-assisted techniques. The task is challenging and requires the identification of the optimum geometry parameters to enable the operation of the re-designed structure at a selected (required) centre frequency. This involves handling several performance figures such as the antenna gain, the impedance bandwidth, as well as the axial ratio bandwidth. The design technique described here involves two types of surrogate models: an inverse surrogate (utilised to find the initial design) and a forward surrogate of the structure response sensitivities, necessary to realise post-scaling design correction. The entire re-design process is fast and only requires a few full-wave electromagnetic simulations of the antenna. The proposed dimension scaling method is demonstrated using a patch antenna with circular polarisation fed through a branch-line coupler. The structure is re-designed within the operating frequency range of 4.5–6.5 GHz. Numerical results are validated experimentally.

Multi‐fidelity EM simulations and constrained surrogate modelling for low‐cost multi‐objective design optimisation of antennas

In this study, a technique for low-cost multi-objective design optimisation of antenna structures has been proposed. The proposed approach is an enhancement of a recently reported surrogate-assisted technique exploiting variable-fidelity electromagnetic (EM) simulations and auxiliary kriging interpolation surrogate, the latter utilised to produce the initial approximation of the Pareto set. A bottleneck of the procedure for higher-dimensional design spaces is a large number of training data samples necessary to construct the surrogate. Here, the authors propose a procedure that allows us to confine the model domain to the subset spanned by the reference points, including the extreme Pareto-optimal designs obtained by optimising the individual objectives as well as an additional design that determines the Pareto front curvature. Setting up the surrogate in the constrained domain leads to a dramatic reduction of the required number of data samples, which results in lowering the overall cost of the optimisation process. Furthermore, the model domain confinement is generic, i.e. applicable for any number of design goals considered. The proposed technique is demonstrated using an ultra-wideband monopole antenna optimised with respect to three objectives. Significant reduction of the design cost is obtained as compared to the reference surrogate-assisted algorithm.

Domain segmentation for low‐cost surrogate‐assisted multi‐objective design optimisation of antennas

Information regarding the best possible design trade-offs of an antenna structure can be obtained through multi-objective optimisation (MO). Unfortunately, MO is extremely challenging if full-wave electromagnetic (EM) simulation models are used for performance evaluation. Yet, for the majority of contemporary antennas, EM analysis is the only tool that ensures reliability. This study introduces a procedure for accelerated MO design of antennas that exploits cheap data-driven surrogates, as well as MO evolutionary algorithm to yield an initial approximation of the Pareto set. The final Pareto set is found using output space mapping. The major contribution of this work is a further reduction of the computational cost of surrogate model construction using a design space segmentation mechanism, where a part of the space containing the Pareto front is first identified by means of single-objective optimisation runs and subsequently represented by a set of adjacent compartments with separate surrogate models established within them. Segmentation allows for significant reduction of the number of training points necessary to build a reliable surrogate and thus the overall optimisation cost. The presented technique is demonstrated using two antenna structures and compared with a state-of-the-art surrogate-assisted techniques. Experimental validation is also provided.

Rapid surrogate-assisted design optimization of minimum-size broadband branch-line couplers with variable topology

This work discusses simulation-driven design of miniaturized wideband branch-line couplers with a variable topology. Size reduction is enabled here by replacing uniform transmission lines of the original coupler with slow-wave structures in the form of cascaded compact cells and meander lines. The primary goal is to determine a number of cells in the cascade and particular cell dimensions for which the minimum size of the coupler as well as its required operating conditions are ensured. To this end, we employ a surrogate-assisted technique involving a trust-region gradient search framework. Computational efficiency of the design process stems from estimating the Jacobian of circuit responses at the level of a low-fidelity model of the cascade. The latter is composed in a circuit simulator from duplicated EM-evaluated data blocks of a single cell and is well correlated with the corresponding high-fidelity model. The key advantage of this work is the utilization of a reconfigurable, cheap, and well-aligned low-fidelity model. The proposed approach is demonstrated through design of a minimum-size two-section branch-line coupler with quasi-periodic dumbbell-shaped cells and meander lines. Excellent circuit performance as well as its small size showcase the reliability and usefulness of the presented method. Experimental verification is also provided.

Rapid simulation‐driven design of miniaturised dual‐band microwave couplers by means of adaptive response scaling

One of the major challenges in the design of compact microwave structures is the necessity of simultaneous handling of several objectives and the fact that expensive electromagnetic (EM) analysis is required for their reliable evaluation. Design of multi-band circuits where performance requirements are to be satisfied for several frequencies at the same time is even more difficult. In this work, a computationally efficient design of dual-band microstrip couplers is demonstrated by means of an adaptive response scaling (ARS) technique. ARS is a surrogate-assisted method that exploits a fast surrogate of the high-fidelity EM-simulation model of the coupler at hand constructed from its corrected equivalent circuit. ARS identifies nonlinear frequency and amplitude response scaling that accommodates the misalignment between the low- and high-fidelity models. Due to exploiting the knowledge embedded in the low-fidelity model ARS surrogate exhibits excellent generalisation capability. It is demonstrated here by optimisation of a dual-band microstrip coupler with enhanced bandwidth, working at 1 GHz and 2 GHz frequencies. The optimised design has been obtained at the cost of just a few high-fidelity EM simulations of the structure. Numerical comparisons indicate superiority of ARS over competitive surrogate-assisted techniques. Experimental validation is also provided.