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

Numerical optimization has been ubiquitous in antenna design for over a decade or so. It is indispensable in handling of multiple geometry/material parameters, performance goals, and constraints. It is also challenging as it incurs significant CPU expenses, especially when the underlying computational model involves full-wave electromagnetic (EM) analysis. In most practical cases, the latter is imperative to ensure evaluation reliability. The numerical challenges are even more pronounced when global search is required, which is most often carried out using nature-inspired algorithms. Population-based procedures are known for their ability to escape from local optima, yet their computational efficiency is poor, which makes them impractical when applied directly to EM models. A common workaround is the utilization of surrogate modeling techniques, typically in the form of iterative prediction-correction schemes, where the accumulated EM simulation data is used to identify the promising regions of the parameter space and to refine the surrogate model predictive power at the same time. Notwithstanding, implementation of surrogate-assisted procedures is often intricate, whereas their efficacy may be hampered by the dimensionality issues and considerable nonlinearity of antenna characteristics. This work investigates the benefits of incorporating variable-resolution EM simulation models into nature-inspired algorithms for optimization of antenna structures, where the model resolution pertains to the level of discretization density of an antenna structure in the full-wave simulation model. The considered framework utilizes EM simulation models which share the same physical background and are selected from a continuous spectrum of allowable resolutions. The early stages of the search process are carried out with the use of the lowest fidelity model, which is subsequently automatically increased to finally reach the high-fidelity antenna representation (i.e., considered as sufficiently accurate for design purposes). Numerical validation is executed using several antenna structures of distinct types of characteristics, and a particle swarm optimizer as the optimization engine. The results demonstrate that appropriate resolution adjustment profiles permit considerable computational savings (reaching up to eighty percent in comparison to high-fidelity-based optimization) without noticeable degradation of the search process reliability. The most appealing features of the presented approach—apart from its computational efficiency—are straightforward implementation and versatility.

Purpose Development of techniques for expedited design optimization of complex and numerically expensive electromagnetic (EM) simulation models of antenna structures validated both numerically and experimentally. The paper aims to discuss these issues. Design/methodology/approach The optimization task is performed using a technique that combines gradient search with adjoint sensitivities, trust region framework, as well as EM simulation models with various levels of fidelity (coarse, medium and fine). Adaptive procedure for switching between the models of increasing accuracy in the course of the optimization process is implemented. Numerical and experimental case studies are provided to validate correctness of the design approach. Findings Appropriate combination of suitable design optimization algorithm embedded in a trust region framework, as well as model selection techniques, allows for considerable reduction of the antenna optimization cost compared to conventional methods. Research limitations/implications The study demonstrates feasibility of EM-simulation-driven design optimization of antennas at low computational cost. The presented techniques reach beyond the common design approaches based on direct optimization of EM models using conventional gradient-based or derivative-free methods, particularly in terms of reliability and reduction of the computational costs of the design processes. Originality/value Simulation-driven design optimization of contemporary antenna structures is very challenging when high-fidelity EM simulations are utilized for performance utilization of structure at hand. The proposed variable-fidelity optimization technique with adjoint sensitivity and trust regions permits rapid optimization of numerically demanding antenna designs (here, dielectric resonator antenna and compact monopole), which cannot be achieved when conventional methods are of use. The design cost of proposed strategy is up to 60 percent lower than direct optimization exploiting adjoint sensitivities. Experimental validation of the results is also provided.

The paper addresses simulation-driven design optimization of compact antennas involving variable-fidelity electromagnetic (EM) simulation models. Comprehensive investigations are carried out concerning selection of the coarse model discretization density. The effects of the low-fidelity model setup on the reliability and computational complexity of the optimization process are determined using a benchmark set of three ultra-wideband antennas designed for the best matching and for the minimum size. The optimization algorithm of choice is trust-region gradient search with low-fidelity model correction realized through frequency scaling and multiplicative output space mapping. The results indicate that appropriate low-fidelity model setup can be assessed using a correlation analysis based on the selected characteristic points of the antenna responses and sparsely allocated test designs, and the results are consistent across the considered benchmark set.

In this paper, a novel structure of a compact UWB slot antenna and its design optimization procedure has been presented. In order to achieve a sufficient number of degrees of freedom necessary to obtain a considerable size reduction rate, the slot is parameterized using spline curves. All antenna dimensions are simultaneously adjusted using numerical optimization procedures. The fundamental bottleneck here is a high cost of the electromagnetic (EM) simulation model of the structure that includes (for reliability) an SMA connector. Another problem is a large number of geometry parameters (nineteen). For the sake of computational efficiency, the optimization process is therefore performed using variable-fidelity EM simulations and surrogate-assisted algorithms. The optimization process is oriented towards explicit reduction of the antenna size and leads to a compact footprint of 199 mm2 as well as acceptable matching within the entire UWB band. The simulation results are validated using physical measurements of the fabricated antenna prototype.

We present an efficient technique for design optimization of antenna structures. Our approach exploits coarse-discretization electromagnetic (EM) simulations of the antenna of interest that are used to create its fast initial model (a surrogate) through kriging. During the design process, the predictions obtained by optimizing the surrogate are verified using high-fidelity EM simulations, and this high-fidelity data is used to enhance the surrogate through co-kriging technique that accommodates all EM simulation data into one surrogate model. The co-kriging-based optimization algorithm is simple, elegant and is capable of yielding a satisfactory design at a low cost equivalent to a few high-fidelity EM simulations of the antenna structure. To our knowledge, this is a first application of co-kriging to antenna design. An application example is provided.

Surrogate-based method can dramatically reduce the number of expensive function evaluations in real-world multi- objective optimization problems (MOP). When the number of objectives is small, using surrogate models combined with expected hypervolume improvement (EHVI) infill sampling criterion (ISC) has been proved to be efficient to provide a set of solutions with good diversity and good proximity to the Pareto front (PF) in aerodynamic shape optimization. However, traditional hypervolume-based infilling strategies use only one kind of ISC to generate one or multiple sample points, the advantages of various kinds of ISC cannot be comprehensively utilized and the parallelization is not easy to implement. This paper proposes a combined multi-point infilling strategy based on Kriging models and develops an efficient global multi-objective constrained optimization method (EGMOCO) to solve multi- objective aerodynamic shape optimization with complex constraints. Multiple sample points are generated by using four ISC considering hypervolume at each iteration and then evaluated in parallel. Firstly, the performance of EGMOCO is compared with that of single criterion EHVI strategy on six benchmarks within the same computational budget to prove its effectiveness, and then EGMOCO is implemented in an aerodynamic shape optimization problem with complex constraints. The result shows that EGMOCO has good performance in balancing local exploitation and global exploration with faster convergence rate and high robustness, the whole PF can be fully explored in limited evaluations and the constraint handling is effective especially for real-world problems with complex and nonlinear constraints, the comprehensive aerodynamic performance of the airfoil is greatly improved. It can be confirmed that Kriging-based multi-objective optimization method combined with multi-point infilling strategy performs better than single infilling criterion EHVI, since different sample infilling criteria can complement with each other, both local exploitation and global exploration can be considered and well balanced.

A simple yet robust methodology for rapid multiobjective design optimization of antenna structures has been presented. The key component of our approach is sequential domain patching of the design space, which is a stencil-based search that aims at creating a path that connects the extreme Pareto-optimal designs, obtained by means of single-objective optimization runs. The patching process yields the initial approximation of the Pareto set representing the best possible tradeoffs between conflicting design objectives. It is realized-for the sake of computational efficiency-at the level of coarse-discretization electromagnetic (EM) simulation model. The final Pareto front is subsequently obtained using surrogate-assisted optimization where the EM simulation data acquired at the initial design stage is reused.

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.

Multiobjective optimization plays an increasingly important role in modern applications, where several criteria are often of equal importance. The task in multiobjective optimization and multiobjective optimal control is therefore to compute the set of optimal compromises (the Pareto set) between the conflicting objectives. The advances in algorithms and the increasing interest in Pareto-optimal solutions have led to a wide range of new applications related to optimal and feedback control, which results in new challenges such as expensive models or real-time applicability. Since the Pareto set generally consists of an infinite number of solutions, the computational effort can quickly become challenging, which is particularly problematic when the objectives are costly to evaluate or when a solution has to be presented very quickly. This article gives an overview of recent developments in accelerating multiobjective optimal control for complex problems where either PDE constraints are present or where a feedback behavior has to be achieved. In the first case, surrogate models yield significant speed-ups. Besides classical meta-modeling techniques for multiobjective optimization, a promising alternative for control problems is to introduce a surrogate model for the system dynamics. In the case of real-time requirements, various promising model predictive control approaches have been proposed, using either fast online solvers or offline-online decomposition. We also briefly comment on dimension reduction in many-objective optimization problems as another technique for reducing the numerical effort.

Groundwater management involves a complex decision‐making process, often with the need to balance the trade‐off between meeting society's demand for water and environmental protection. Therefore effective management of groundwater resources often involves some form of multi‐objective optimization (MOO). Many existing software tools offer simulation model‐enabled optimization, including evolutionary algorithms, for solving MOO problems. However, such analyses involve a huge amount of numerical process‐based model runs, which require significant computational effort, depending on the nonlinearity and dimensionality of the problem, in order to seek the optimal trade‐off function known as the Pareto front. Surrogate modeling, through techniques such as Gaussian Process Regression (GPR), is an emerging approach to significantly reduce the number of these model evaluations thereby speeding up the optimization process. Yet, surrogate model predictive uncertainty remains a profound challenge for MOO, as it could mislead surrogate‐assisted optimization, which may result in either little computational savings from excessive retraining, or lead to suboptimal and/or infeasible solutions. In this work, we present probabilistic Pareto dominance criteria that considers the uncertainty of GPR emulation during MOO, producing a “cloudy” Pareto front which provides an efficient decision space sampling mechanism for retraining the GPR. We then developed a novel acquisition strategy to manage the solution repository from this cloud and generate an ensemble of infill points for retraining. We demonstrate the capabilities of the algorithm through benchmark test functions and a typical density‐dependent coastal groundwater management problem.

BACKGROUND Dual‐reflux pressure swing adsorption (DR‐PSA) is an advanced variant of conventional PSA systems, capable of simultaneously producing two high‐purity products with high recovery. However, inherent trade‐offs among purity, productivity, and cycle work necessitate multi‐objective optimization (MOO) to balance performance. This study investigates the MOO of the DR‐PSA process for biogas upgrading using artificial neural networks (ANNs) as surrogate models. Single‐hidden‐layer ANNs were developed with various structures and training algorithms and integrated into the non‐dominated sorting genetic algorithm‐II to solve MOO problems. RESULTS Different DR‐PSA performance metrics require distinct ANN architectures and algorithms, indicating no universal model selection. The Adam‐ selu‐ 446 model for CH 4 purity in light product (LP) and the Adam‐ relu ‐398 model for cycle work, both developed on a large dataset, exhibited high accuracy, with of 0.9975 and 0.9959, respectively. Meanwhile, the Adam‐ elu ‐212 model for bed productivity, developed using a small dataset, achieved an of 0.9988. The Pareto front for maximizing CH 4 purity in LP and bed productivity revealed a sharp knee region, indicating a significant trade‐off. Under constrained bed productivity and cycle work, distinct Pareto fronts emerged at different CH 4 purity levels (>91% and 91.5%), with fewer feasible solutions at higher purity. Ultimately, the optimized conditions resulted in an enhancement in CH 4 purity in LP by at least 17%, a reduction in bed productivity by as much as 34%, and a reduction in cycle work by at least 30%, compared to the base case. CONCLUSION ANN‐assisted MOO optimizes DR‐PSA performance, offering insights into ANN model development, Pareto front mapping, and identification of feasible operational regions. © 2025 Society of Chemical Industry (SCI).

Stormwater runoff is a major concern in urban areas which is mostly the result of vast urbanization. To reduce urban stormwater runoff and improve water quality, low impact development (LID) is used in urban areas. Therefore, it is vital to find the optimal combination of LID controls to achieve maximum reduction in both stormwater runoff and pollutants with optimal cost. In this study, a simulation-optimization model was developed by linking the EPA Storm Water Management Model (SWMM) to the Multi-Objective Particle Swarm Optimization (MOPSO) using MATLAB. The coupled model could carry out multi-objective optimization (MOO) and find potential solutions to the optimization objectives using the SWMM simulation model outputs. The SWMM model was developed using data from the BUNUS catchment in Kuala Lumpur, Malaysia. The total suspended solids (TSS) and total nitrogen (TN) were selected as pollutants to be used in the simulation model. Vegetated swale and rain garden were selected as LID controls for the study area. The LID controls were assigned to the model using the catchment characteristics. The target objectives were to minimize peak stormwater runoff, TSS, and TN with the minimum number of LID controls applications. The LID combination scenarios were also tested in SWMM to identify the best LID types and combination to achieve maximum reduction in both peak runoff and pollutants. This study found that the peak runoff, TSS, and TN were reduced by 13%, 38%, and 24%, respectively. The optimal number of LID controls that could be used at the BUNUS catchment area was also found to be 25.

Summary CO2-water-alternating-gas (CO2-WAG) is a reservoir development method that can simultaneously enhance oil recovery and achieve CO2 storage. However, improperly designed parameters for CO2 injection and oil production may significantly reduce the oil displacement efficiency and CO2 storage. Furthermore, optimizing the injection parameters is computationally expensive due to the high computational cost of the compositional simulation. This work aims to propose an efficient optimization method to obtain a series of well-control schemes that balance maximizing net present value (NPV) and CO2 storage for decision-makers. Given the number of CO2-WAG cycles and the duration of each cycle, we optimize the water injection rate, gas injection rate, and half-cycle for the injection well and the bottomhole pressure (BHP) for the production well. In this paper, a two-stage optimization strategy is proposed to enhance the optimization efficiency. The first stage performs the surrogate-assisted single-objective optimizations of each considered objective. It is designed to find the endpoints of the Pareto front that connect all solutions of the multiobjective optimization; this stage not only provides important search directions for the subsequent multiobjective optimization but also improves the accuracy of the surrogate model near the Pareto front. The second stage is the surrogate-assisted multiobjective optimization, which aims to find all the solutions along the Pareto front based on the Pareto endpoints obtained from the first stage. In addition, this study successfully combines the gradient of the objective functions with the meta-heuristic algorithm during the multiobjective optimization, which ensures a faster convergence to the global optimum. The proposed multiobjective optimization algorithm shows faster convergence than the conventional optimization methods when applied to the three multiobjective optimization test functions. Finally, a comparison with the conventional multiobjective optimization is conducted based on one test function and two benchmark reservoir simulation models to verify the correctness and efficiency of the proposed method. It is confirmed that the proposed method outperforms the conventional ones for the optimization of CO2-WAG injection.

Pressure swing adsorption (PSA) is an energy-efficient technology for gas separation, while the multi-objective optimization of PSA is a challenging task. To tackle this, we propose a hybrid optimization framework, which integrates three steps. In the first step, we establish surrogate models for the constraints using Gaussian processes (GPs) and employ multi-objective Bayesian optimization to search for feasible points that satisfy the constraints. In the second step, we establish surrogate models for the objective function and constraints using GPs and utilize constrained multi-objective Bayesian optimization to search for an approximate Pareto front. In the third step, we perform a local search based on the approximate Pareto front. By employing the trust region filter method, we construct quadratic models for each constraint and objective function and refine the Pareto front to achieve local optimality. This framework demonstrates the efficiency of Bayesian optimization and the local optimality of the trust region method. A comparison with the popular evolutionary algorithm, Nondominated Sorting Genetic Algorithm II (NSGA-II), showed that this framework had a higher hypervolume of the Pareto front while halving the runtime and reducing the number of simulations by a factor of 20.

This research proposes a multi-objective optimization methodology to enhance the curving and tangent performance of forced-steering passenger trains. Using the Non-dominated Sorting Genetic Algorithm-III (NSGA-III), we optimize a set of parameters — primary suspension stiffness (longitudinal and lateral) and steering linkage — to minimize wheelset unloading, derailment risk, rail rollover risk, and car body lateral acceleration. A 167-degree-of-freedom high-fidelity simulation model of the train is developed and validated against conventional rail vehicle data. Sensitivity analysis via the Sobol’ method identifies key design parameters, reducing the number of variables for optimization. A Kriging surrogate model is then employed to approximate the simulation model, making optimization feasible. Post-optimization, the robustness of the Pareto optimal solutions is evaluated under varying track conditions. Key findings reveal that steering ratio and longitudinal primary suspension stiffness are critical, while yoke-to-yoke parameters have minimal impact. The optimization results show a trade-off between curving performance and car body lateral acceleration, with solutions varying based on lateral stiffness. Two out of four Pareto optimal sets demonstrated improved robustness under varying curve radii and equivalent conicity, while all Pareto optimal sets exhibit equal robustness and significant improvements in performance under varying track friction. These findings emphasize the importance of robust design optimization across different operational conditions to achieve balanced performance.