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The optimal design of structures subjected to seismic loading poses significant challenges due to the presence of high nonlinearity and computational complexity. To address these challenges, this paper presents a novel methodology that combines Sequential Quadratic Programming with Trust-Region strategy (SQP-TR) and Endurance Time Method (ETM). SQP-TR is initially presented as a numerical optimization approach to address optimization problems by linearizing the constraints and approximating the objective function with Taylor expansion, as well as employing the filter method and trust region strategy to ensure convergence and feasibility. A five-story linear frame validates its effectiveness and demonstrates promising outcomes. ETM is successfully implemented as a seismic analysis approach to perform nonlinear time history analyses in order to capture the dynamic input feature of the seismic load and evaluate the nonlinear dynamic behaviors of structures. Its practical application is demonstrated by a nine-story structure with nonlinearity, which shows satisfactory results. Finally, the proposed methodology is applied to optimize a twelve-story three-Dimensional (3D) Reinforced Concrete (RC) nonlinear building under seismic load, and the results demonstrate that the method can accomplish optimal seismic design with high accuracy and efficiency. [ABSTRACT FROM AUTHOR]

A numerical optimization technique used to address nonlinear programming problems is the trust region (TR) method. TR uses a quadratic model, which may represent the function adequately, to create a neighbourhood around the current best solution as a trust region in each step, rather than searching for the original function's objective solution. This allows the method to determine the next local optimum. The TR technique has been utilized by numerous researchers to tackle multi‐objective optimization problems (MOOPs). But there is not any publication that discusses the issue of applying a chaotic search (CS) with the TR algorithm for solving multi‐objective (MO) problems. From this motivation, the main contribution of this study is to introduce trust‐region (TR) technique based on chaotic search (CS) for solving MOOPs. First, the reference point interactive approach is used to convert MOOP to a single objective optimization problem (SOOP). The search space is then randomly initialized with a set of initial points. Second, in order to supply locations on the Pareto boundary, the TR method solves the SOOP. Finally, all points on the Pareto frontier are obtained using CS. A range of MO benchmark problems have demonstrated the efficiency of the proposed algorithm (TR based CS) in generating Pareto optimum sets for MOOPs. Furthermore, a demonstration of the suggested algorithm's ability to resolve real‐world applications is provided through a practical implementation of the algorithm to improve an abrasive water‐jet machining process (AWJM). [ABSTRACT FROM AUTHOR]

Abstract In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust.

AbstractInconsistent topologies and oscillations during iterations are commonly observed when solving stress-constrained problems, indicating inadequate stability in topology optimization. The trust region based moving asymptotes (TRMA) method is proposed in this paper. To comprehensively investigate the stability of the TRMA method, the Trinity Evaluation Framework is proposed in this paper. It focuses on three types of dependencies in topology optimization, i.e. mesh dependence, parameter dependence, and initial topology dependence. The corresponding evaluation vector is proposed to measure the stability of the TRMA method. Numerical examples are given, indicating strong stability of the TRMA method in topology optimization of stress-constrained problems. [ABSTRACT FROM AUTHOR]

In this paper, a new appropriate diagonal matrix estimation of the Hessian is introduced by minimizing the Byrd and Nocedal function subject to the weak secant equation. The Hessian estimate is used to correct the framework of a nonmonotone trust region algorithm with the regularized quasi-Newton method. Moreover, to counteract the adverse effect of monotonicity, we introduce a new nonmonotone strategy. The global and superlinear convergence of the suggested algorithm is established under some standard conditions. The numerical experiments on unconstrained optimization test functions show that the new algorithm is efficient and robust. [ABSTRACT FROM AUTHOR]

Purpose: One of the most effective methods for solving unconstrained optimization problems is the trust region method. The strategy of determining the radius of the trust region has a significant effect on the efficiency of this method. On the other hand, imposing the monotonicity condition will decrease the convergence speed of this method. Therefore, improving and increasing the efficiency of this method is one of the most important issues and the attention of researchers. Methodology: Establishing a new adaptive trust region radius as well as combining the trust region method with a non- monotone strategy to avoid the adverse effects of monotonocity. Findings: A new adaptive trust region radius converged to zero is provided, and then a trust region combination is performed using a non-monotone strategy. Running the algorithm on a set of test functions shows that the new adaptive radius, along with the non-monotone strategy used, significantly improves the efficiency of the trust region method. Originality/Value: The presented non-monotone adaptive algorithm has a second-order convergence rate. In addition, it significantly reduces computational costs compared to traditional algorithms. On the other hand, the new adaptive radius avoids the ineffectiveness of the trust region close to the solution. [ABSTRACT FROM AUTHOR]

Using tail bounds, we introduce a new probabilistic condition for function estimation in stochastic derivative-free optimization (SDFO) which leads to a reduction in the number of samples and eases algorithmic analyses. Moreover, we develop simple stochastic direct-search and trust-region methods for the optimization of a potentially nonsmooth function whose values can only be estimated via stochastic observations. For trial points to be accepted, these algorithms require the estimated function values to yield a sufficient decrease measured in terms of a power larger than 1 of the algoritmic stepsize. Our new tail bound condition is precisely imposed on the reduction estimate used to achieve such a sufficient decrease. This condition allows us to select the stepsize power used for sufficient decrease in such a way that the number of samples needed per iteration is reduced. In previous works, the number of samples necessary for global convergence at every iteration k of this type of algorithm was O(\Delta 4 k), where Delta k is the stepsize or trust-region radius. However, using the new tail bound condition, and under mild assumptions on the noise, one can prove that such a number of samples is only O(\Delta 2 varepsilon k ), where varepsilon > 0 can be made arbitrarily small by selecting the power of the stepsize in the sufficient decrease test arbitrarily close to 1. In the common random number generator setting, a further improvement by a factor of Delta 2 k can be obtained. The global convergence properties of the stochastic direct-search and trust-region algorithms are established under the new tail bound condition. [ABSTRACT FROM AUTHOR]

In Baraldi (Math Program 20:1–40, 2022), we introduced an inexact trust-region algorithm for minimizing the sum of a smooth nonconvex function and a nonsmooth convex function in Hilbert space—a class of problems that is ubiquitous in data science, learning, optimal control, and inverse problems. This algorithm has demonstrated excellent performance and scalability with problem size. In this paper, we enrich the convergence analysis for this algorithm, proving strong convergence of the iterates with guaranteed rates. In particular, we demonstrate that the trust-region algorithm recovers superlinear, even quadratic, convergence rates when using a second-order Taylor approximation of the smooth objective function term. [ABSTRACT FROM AUTHOR]

In this paper, we propose a nonmonotone Alternative Direction Method (ADM) based on simple conic model for unconstrained optimization. Unlike traditional trust region method, the subproblem in our method is a simple conic model, where the Hessian of the objective function is replaced by a scalar approximation, the trust region subproblem is solved by ADM which was first proposed by Zhu and Ni. When the trial point isn't accepted by trust region, line search technique is used to find an acceptable point instead of resolving the trust region subproblem. The new method needs less memory capacitance and computational complexity. The global convergence of the algorithm is established under some mild conditions. Numerical results on a series of standard test problems are reported to show the new method is effective and robust. [ABSTRACT FROM AUTHOR]

Minimax problems have gained tremendous attentions across the optimization and machine learning community recently. In this paper, we introduce a new quasi-Newton method for the minimax problems, which we call J-symmetric quasi-Newton method. The method is obtained by exploiting the J-symmetric structure of the second-order derivative of the objective function in minimax problem. We show that the Hessian estimation (as well as its inverse) can be updated by a rank-2 operation, and it turns out that the update rule is a natural generalization of the classic Powell symmetric Broyden method from minimization problems to minimax problems. In theory, we show that our proposed quasi-Newton algorithm enjoys local Q-superlinear convergence to a desirable solution under standard regularity conditions. Furthermore, we introduce a trust-region variant of the algorithm that enjoys global R-superlinear convergence. Finally, we present numerical experiments that verify our theory and show the effectiveness of our proposed algorithms compared to Broyden's method and the extragradient method on three classes of minimax problems. [ABSTRACT FROM AUTHOR]

Multi-agent reinforcement learning (MARL) algorithms based on trust regions (TR) have achieved significant success in numerous cooperative multi-agent tasks. These algorithms restrain the Kullback–Leibler (KL) divergence (i.e., TR constraint) between the current and new policies to avoid aggressive update steps and improve learning performance. However, the majority of existing TR-based MARL algorithms are on-policy, meaning that they require new data sampled by current policies for training and cannot utilize off-policy (or historical) data, leading to low sample efficiency. This study aims to enhance the data efficiency of TR-based learning methods. To achieve this, an approximation of the original objective function is designed. In addition, it is proven that as long as the update size of the policy (measured by the KL divergence) is restricted, optimizing the designed objective function using historical data can guarantee the monotonic improvement of the original target. Building on the designed objective, a practical off-policy multi-agent stochastic policy gradient algorithm is proposed within the framework of centralized training with decentralized execution (CTDE). Additionally, policy entropy is integrated into the reward to promote exploration, and consequently, improve stability. Comprehensive experiments are conducted on a representative benchmark for multi-agent MuJoCo (MAMuJoCo), which offers a range of challenging tasks in cooperative continuous multi-agent control. The results demonstrate that the proposed algorithm outperforms all other existing algorithms by a significant margin. [ABSTRACT FROM AUTHOR]

Inaccurate models limit the performance of model‐based real‐time optimization (RTO) and even cause system instability. Therefore, a RTO framework that guarantees global convergence in the presence of plant‐model mismatch is desired. In this regard, the trust‐region framework is intuitive and simple to implement for unconstrained problems. Constrained RTO problems are converted to unconstrained ones by the penalty function, and global convergence is guaranteed if the penalty coefficient is large enough. However, a sufficiently large penalty coefficient is hard to determine and may lead to numerical difficulties. This paper addresses this issue and proposes a novel composite‐step trust‐region framework for constrained RTO problems that handles inequality constraints directly. The trial step is decomposed into a normal step that improves feasibility and a tangential step that reduces the cost function. A rigorous proof of its global convergence property is given. [ABSTRACT FROM AUTHOR]

We present a general version of bundle trust region method for minimizing convex functions. The trust region is constructed by generic p -norm with p ∈ [ 1 , + ∞ ] . In each iteration the algorithm solves a subproblem with a constraint involving p -norm. We show the convergence of the generic bundle trust region algorithm. In implementation, the infinity norm is chosen so that a linear programming subproblem is solved in each iteration. Preliminary numerical experiments show that our algorithm performs comparably with the traditional bundle trust region method and has advantages in solving large-scale problems. [ABSTRACT FROM AUTHOR]

We introduce Tadam (Trust region ADAptive Moment estimation), a new optimizer based on the trust region of the second-order approximation of the loss using the Fisher information matrix. Despite the enhanced gradient estimations offered by second-order approximations, their practical implementation requires sizable batch sizes to estimate the second-order approximation matrices and perform matrix inversions. Consequently, integrating second-order approximations entails additional memory consumption and imposes substantial computational demands due to the inversion of large matrices. In light of these challenges, we have devised a second-order approximation algorithm that mitigates these issues by judiciously approximating the pertinent large matrix, requiring only a marginal increase in memory usage while minimizing the computational burden. Tadam approximates the loss up to the second order using the Fisher information matrix. Since estimating the Fisher information matrix is expensive in both memory and time, Tadam approximates the Fisher information matrix and reduces the computational burdens to the O (N) level. Furthermore, Tadam employs an adaptive trust region scheme to reduce approximate errors and guarantee stability. Tadam evaluates how well it minimizes the loss function and uses this information to adjust the trust region dynamically. In addition, Tadam adjusts the learning rate internally, even if we provide the learning rate as a fixed constant. We run several experiments to measure Tadam's performance against Adam, AMSGrad, Radam, and Nadam, which have the same space and time complexity as Tadam. The test results show that Tadam outperforms the benchmarks and finds reasonable solutions fast and stably. [ABSTRACT FROM AUTHOR]

Bayesian optimization (BO) is an effective optimization technique for solving expensive black-box problems. Even though BO has remarkable success, its drawbacks are also obvious. First, the time complexity of the Gaussian process inference is higher than O(n3), where n is the number of samples. Consequently, the running time of BO increases rapidly with the problem size. Second, due to the non-convexity and multimodality of the acquisition function, it costs a lot to achieve good results. To address the above problems, we develop a local Bayesian optimization algorithm based on the trust region idea (TRLBO). In TRLBO, two trust regions with dynamically changing sizes are used to enhance the algorithm's exploitation ability, while at the same time retaining the exploration ability. Specifically, one trust region is used to reduce the number of samples in the Gaussian process. The other is used to restrict the solution space of the candidates. Furthermore, some theoretical results were provided to enlighten the efficiency of the proposed algorithm. Experimental results on both benchmark functions and real-world problems show that TRLBO compares favorably with the state-of-the-art algorithms. [ABSTRACT FROM AUTHOR]

As we know, conjugate gradient methods are widely used for unconstrained optimization because of the advantages of simple structure and small storage. For non-convex functions, the global convergence analysis of these methods are also crucial. But almost all of them require the gradient Lipschitz continuous condition. Based on the work of Hager and Zhang (Hager and Zhan in SIAM J. Optim. 16:170–192, 2005), Algorithm 1 and Algorithm 2 are proposed and analyzed for the optimization problems. The proposed algorithms possess the sufficient descent property and the trust region feature independent of line search technique. The global convergence of Algorithm 1 is obtained without the gradient Lipschitz continuous condition under the weak Wolfe-Powell inexact line search. Based on Algorithm 1, Algorithm 2 is further improved which global convergence can be obtained independently of line search technique. Numerical experiments are done for Muskingum model and image restoration problems [ABSTRACT FROM AUTHOR]

As for complex engineering structures, their single deterministic solutions need to be calculated with the help of computationintensive finite element software, and the corresponding computation time always lasts very long. When referring to robust design optimization of complex engineering structures, the above expensive job should be repeatedly carried out for a considerable amount of time during the full optimization process. Hence, such repetitive jobs may be difficult to complete for most engineering applications. Aiming at this problem, the paper proposes a general methodology for reliability-based robust design optimization (RBRDO). Firstly, the improved formulation of the RBRDO problem is proposed based on the conventional RBRDO form, and the original probabilistic constraint functions in the improved formulation are changed into the deterministic ones by means of employing the performance measure approach (PMA). Secondly, the above-mentioned improved RBRDO problem is approximately replaced by a new sequence of approximate suboptimizations. For each suboptimization, its original PMA functions are replaced by the approximate explicit form only concerning the deterministic design variables rather than random variables. In this way, each suboptimization is deterministic. Furthermore, the trust-region method is adopted to ensure that the new sequence of suboptimization converge to the original improved RBRDO problem. Lastly, a test problem and three applications are adopted to demonstrate the effectiveness and efficiency of the above-proposed methods. [ABSTRACT FROM AUTHOR]

The trust-region-based sequential convex programming (TSCP) method is designed to solve the nonlinear trajectory planning problem using successive linearization and trust region. The TSCP method has a good real-time performance suitable for onboard aerospace applications. However, the main challenge in practical applications is its poor convergence. In this article, we reveal an oscillation phenomenon, which is an important factor affecting the convergence. The main contribution of this article is threefold: 1) the oscillation phenomenon is proved to be an inherent property of the TSCP method for the nonlinear trajectory planning problem; 2) the oscillation condition that determines whether oscillation occurs is obtained; and 3) the oscillation-condition-based remedy to address the oscillation is presented. The effectiveness and robustness of the proposed remedy have been verified via a complex reentry trajectory planning problem. [ABSTRACT FROM AUTHOR]

This study employed the global optimization method called Modified Trusted Region Method (MTRM) to resolve the portfolio selection risk problem. An objective of unconstrained optimization problem was formulated with four sets of fund data. The relationship between the level of acceptable risk and the weighting factor was analyzed numerically. The return of portfolio increased along with the level of acceptable risk since a high return was always accompanied by higher risk. By contrast, the risk of portfolio decreased as the weighting factor increased. The MTRM could resolve the portfolio optimization problem. [ABSTRACT FROM AUTHOR]

This paper presents a novel computation-aware multi-fidelity surrogate-based optimization (MFSBO) methodology and a new sequential and adaptive sampling strategy based on expected improvement reduction (EIR). Given a fixed computational budget in each iteration, the EIR-based infill determines the data source and samples of infill by hypothetically interrogating the effect of samples and simulation fidelity on reducing the expected improvement, and enables low-fidelity batch infills within a dynamically varying trust-region to improve exploration as needed to accelerate the MFSBO process. The co-Kriging method is utilized to combine the data from different data sources with varying fidelities and computational costs. The EIR-based infill is then compared with other infill strategies in terms of convergence rate and design accuracy. Results indicate that the proposed method achieves a faster convergence rate and more accurate optimal design during MFSBO for all case studies. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

In this work an iterative method to solve the nonlinear multiobjective problem is presented. The goal is to find locally optimal points for the problem, that is, points that cannot simultaneously improve all functions when we compare the value at the point with those in their neighborhood. The algorithm uses a strategy developed in previous works by several authors but globalization is obtained through a nonmonotone technique. The construction of a new ratio between the actual descent and predicted descent plays a key role for selecting the new point and updating the trust region radius. On the other hand, we introduce a modification in the quadratic model used to determine if the point is accepted or not, which is fundamental for the convergence of the method. The combination of this strategy with a Newton-type method leads to an algorithm whose convergence properties are proved. The numerical experimentation is performed using a known set of test problems. Preliminary numerical results show that the nonmonotone method can be more efficient when it is compared to another algorithm that use the classic trust region approach. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new adaptive method for solving nonlinear semi-infinite programming(SIP). In the presented method, the continuous infinite inequality constraints are transformed into equivalent equality constraints in integral form. Based on penalty method and trust region strategy, we propose a modified quadratic subproblem, in which an adaptive parameter is considered. The acceptable criterion of the trial point is adjustable according to the value of this adaptive parameter and the improvements that made by the current iteration. Compared with the existing methods, our method is more flexible. Under some reasonable conditions, the convergent properties of the proposed algorithm are proved. The numerical results are reported in the end. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to develop a novel data-driven-based model that can accurately predict the decline curves and EUR (Estimated Ultimate Recovery) for new wells based on the data collected from nearby wells. This is because decline curves are easier and faster alternative to complex reservoir simulators which perform computationally expensive operations. In contrast to this, decline curves require only a few parameters in the equation which can be easily collected from the existing data of the wells. The predictor variables were successfully linked to SEDM (Stretched Exponential Decline Model) decline curve parameters (n and τ) in a random set of oil field well data. The relative influences of various well parameters were also examined to determine the hidden relationship between them. The novelty in this study lies in the algorithm and dataset that we used for the rate decline prediction in Eagle Ford data set. Although, this paper has referenced some previous papers where machine learning has been used to make prediction, but this paper presents use of new algorithm as well as a new dataset. As more data get available, there is definitely extra room for further data analysis and improved results. [ABSTRACT FROM AUTHOR]

Although deep learning algorithms have been widely used, their performance depends heavily on a good set of hyperparameters. This article presents an efficient Hyperband and trust-region-based mode-pursuing sampling hybrid method for hyperparameter optimization. First, Hyperband is modified and used to select the optimum quickly from a large number of random sampling points to construct a trust region. Secondly, mode-pursuing sampling is performed in the trust region to generate more points systematically around the minimum, and the location or size of the trust region is dynamically adjusted to accelerate its convergence. Thirdly, the process of selection and sampling is repeated until a termination criterion is met. Numerical examples are presented to verify the effectiveness of the hybrid method, the results of which are compared with those of five well-known algorithms. Comparison results show that better optimal solutions are obtained through the hybrid method, with a higher efficiency. [ABSTRACT FROM AUTHOR]

Uncertainty analysis is an essential procedure to evaluate reliability or robustness in uncertainty-based multidisciplinary optimization. Considering non-probabilistic interval uncertainties, this paper proposes a trust region-based sequential radial basis function (TR-SRBF) method for interval uncertainty analysis of multidisciplinary systems. First, the radial basis function neural network (RBFNN) is introduced to establish the correlation model between uncertain parameters and multidisciplinary outputs. After training a crude RBFNN via a small number of initial sample points, the proposed method sequentially collects sample points and updates the surrogate model according to the current accuracy. A trust region-based updating scheme is established to determine the sampling areas and guide the collection of new sample points. After successively updating, a satisfactory surrogate model will be obtained, based on which the extrema of multidisciplinary outputs can be obtained conveniently with some auxiliary algorithms. Further, to reduce the sample size, an alternant scheme is then presented to calculate the lower and upper bounds of the multidisciplinary outputs simultaneously. Finally, numerical examples are provided to demonstrate the effectiveness and applicability of TR-SRBF. By contrast with the static surrogate-based method, the results show that the proposed method can achieve better efficiency as well as high accuracy. The main contribution of this paper is to provide a novel dynamic surrogate-based interval uncertainty analysis method called TR-SRBF to calculate the upper and lower bounds of multidisciplinary outputs, in which the RBFNN is sequentially updated with the proposed trust region-based sampling scheme while the bounds are alternately calculated. [ABSTRACT FROM AUTHOR]

When solving large systems of nonlinear differential-algebraic equations by implicit schemes, each integration step requires the solution of a system of large nonlinear algebraic equations. The latter is solved by an inexact Newton method which, in its turn, leads to a set of large linear systems commonly solved by a Krylov subspace iterative method. The efficiency of the whole process depends on the initial guesses for the inexact Newton and the Krylov subspace methods. An inexpensive approach is proposed and justified that computes good initial guesses for these methods. It requires a subspace of small dimension and the use of line search and trust region for the inexact Newton method and Petrov-Galerkin for the Krylov subspace method. Numerical examples are included to illustrate the effectiveness of the proposed approach.

This article presents a discrete variable topology optimization method to solve the simplified convective heat transfer (SCHT) design optimization modeled by Newton's law of cooling. The discrete variable topology optimization is based on the proposed sequential approximate integer programming with trust‐region. Due to the discrete variables, identifying the convective boundary, and implementing this design‐dependent convective boundary condition can be precisely undertaken. As a result, the consistent precise temperature field compared with the commercial software is captured. Besides, the interpolation scheme of the convective coefficient is unnecessary to analyze this SCHT problem. Furthermore, an analytical sensitivity formulation that can simultaneously incorporate the conductive and convective effect is also deduced. Finally, several 2D and 3D valid thermal designs are presented to illustrate the effectiveness of the method. Based on the optimized designs, we find that favorable configurations for a simplified convective problem may be hollowed structure or the dense needle‐like structure. Further, the checkerboard pattern should be interpreted as a convection oscillatory feature but not the discretization error because it cannot be eliminated by using higher‐order elements. [ABSTRACT FROM AUTHOR]

Source localisation is an important component in the application of wireless sensor networks, and plays a key role in environmental monitoring, healthcare and battlefield surveillance and so on. In this article, the source localisation problem based on time-of-arrival measurements in asynchronous sensor networks is studied. Because of imperfect time synchronisation between the anchor nodes and the signal source node, the unknown parameter of start transmission time of signal source makes the localisation problem further sophisticated. The derived maximum-likelihood estimator cost function with multiple local minimum is non-linear and non-convex. A novel two-step method which can solve the global minimum is proposed. First, by leveraging dimensionality reduction, the maximum (minimum) distance maximum (minimum) time-of-arrival matching-based second-order Monte Carlo method is applied to find a rough initial position of the signal source with low computational complexity. Then, the rough initial position value is refined using trust region method to obtain the final positioning result. Comparative analysis with state-of-the-art semidefinite programming and min–max criterion-based algorithms are conducted. Simulations show that the proposed method is superior in terms of localisation accuracy and computational complexity, and can reach the optimality benchmark of Cramér–Rao Lower Bound even in high signal-to-noise ratio environments. [ABSTRACT FROM AUTHOR]

Abstract A precise detection of the fault feature parameter of motor current is a new research hotspot in the broken rotor bar (BRB) fault diagnosis of induction motors. Discrete Fourier transform (DFT) is the most popular technique in this field, owing to low computation and easy realization. However, its accuracy is often limited by the data window length, spectral leakage, fence effect, etc. Therefore, a new detection method based on a global optimization algorithm is proposed. First, a BRB fault current model and a residual error function are designed to transform the fault parameter detection problem into a nonlinear least-square problem. Because this optimization problem has a great number of local optima and needs to be resolved rapidly and accurately, a joint algorithm (called TR-MBPSO) based on a modified bare-bones particle swarm optimization (BPSO) and trust region (TR) is subsequently proposed. In the TR-MBPSO, a reinitialization strategy of inactive particle is introduced to the BPSO to enhance the swarm diversity and global search ability. Meanwhile, the TR is combined with the modified BPSO to improve convergence speed and accuracy. It also includes a global convergence analysis, whose result proves that the TR-MBPSO can converge to the global optimum with the probability of 1. Both simulations and experiments are conducted, and the results indicate that the proposed detection method not only has high accuracy of parameter estimation with short-time data window, e.g., the magnitude and frequency precision of the fault-related components reaches 10−4, but also overcomes the impacts of spectral leakage and non-integer-period sampling. The proposed research provides a new BRB detection method, which has enough precision to extract the parameters of the fault feature components.

The increasing complexities of multi energy-type micro energy grid (MEG) integrated with distributed renewable energy resources require more effective planning method. This paper presents an improved Kriging model for the planning of MEG to satisfy user's demands in cooling, heating, and electrical energy. First, a generic MEG model containing energy supply devices (combined cooling, heating, and power system, and energy storage systems) and energy supply networks is established. Second, the improved Kriging model combined with the Latin hypercube sampling method is proposed for searching the MEG optimal configuration to minimize the total annual cost. Third, for the sake of completeness and practicality, the sample points are updated by a novel mixed infill-sampling criterion comprised of minimum surrogate-model point criterion, trust region criterion, and mean square error criterion. The optimal configuration and operation schemes are obtained simultaneously in the case study. Eventually, the numerical results indicate that the proposed method could efficiently solve the optimal planning problem in contradistinction to three other scenarios regarding the Kriging model.

Space mapping (SM) methodology has been recognized as a powerful tool for accelerating electromagnetic (EM)-based yield optimization. This paper proposes a novel parallel space-mapping based yield-driven EM optimization technique incorporating trust region algorithm and polynomial chaos expansion (PCE). In this technique, a novel trust region algorithm is proposed to increase the robustness of the SM surrogate in each iteration during yield optimization. The proposed algorithm updates the trust radius of each design parameter based on the effectiveness of minimizing the l1 objective function using the surrogate, thereby increasing the robustness of the SM surrogate. Moreover, for the first time, parallel computation method is incorporated into SM-based yield-driven design to accelerate the overall yield optimization process of microwave structures. The use of parallel computation allows the surrogate developed in the proposed technique to be valid in a larger neighborhood than that in standard SM, consequently increasing the speed of finding the optimal yield solution in SM-based yield-driven design. Lastly, the PCE approach is incorporated into the proposed technique to further speed up yield verification on the fine model. Compared with the standard SM-based yield optimization technique with sequential computation, the proposed technique achieves a higher yield increase with shorter CPU time by reducing the number of SM iterations. The proposed technique is illustrated by two microwave examples.

Abstract It has turned out that the tensor expansion model has better approximation to the objective function than models of the normal second Taylor expansion. This paper conducts a study of the tensor model for nonlinear equations and it includes the following: (i) a three dimensional symmetric tensor trust-region subproblem model of the nonlinear equations is presented; (ii) the three dimensional symmetric tensor is replaced by interpolating function and gradient values from the most recent past iterate, which avoids the storage of the three dimensional symmetric tensor and decreases the workload of the computer; (iii) the limited BFGS quasi-Newton update is used instead of the second Jacobian matrix, which generates an inexpensive computation of a complex system; (iv) the global convergence is proved under suitable conditions. Numerical experiments are done to show that this proposed algorithm is competitive with the normal algorithm.