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Background: CT reconstruction is of essential importance in medical imaging. In 2022, the American Association of Physicists in Medicine (AAPM) sponsored a Grand Challenge to investigate the challenging inverse problem of spectral CT reconstruction, with the aim of achieving the most accurate reconstruction results. The authors of this paper participated in the challenge and won as a runner‐up team. Purpose: This paper reports details of our PROSPECT algorithm (Prior‐based Restricted‐variable Optimization for SPEctral CT) and follow‐up studies regarding the algorithm's accuracy and enhancement of its convergence speed. Methods: We formulated the reconstruction task as an optimization problem. PROSPECT employed a one‐step backward iterative scheme to solve this optimization problem by allowing estimation of and correction for the difference between the actual polychromatic projection model and the monochromatic model used in the optimization problem. PROSPECT incorporated various forms of prior information derived by analyzing training data provided by the Grand Challenge to reduce the number of unknown variables. We investigated the impact of projection data precision on the resulting solution accuracy and improved convergence speed of the PROSPECT algorithm by incorporating a beam‐hardening correction (BHC) step in the iterative process. We also studied the algorithm's performance under noisy projection data. Results: Prior knowledge allowed a reduction of the number of unknown variables by 85.9%$85.9\%$. PROSPECT algorithm achieved the average root of mean square error (RMSE) of 3.3×10−6$3.3\,\times \,10^{-6}$ in the test data set provided by the Grand Challenge. Performing the reconstruction with the same algorithm but using double‐precision projection data reduced RMSE to 1.2×10−11$1.2\,\times \,10^{-11}$. Including the BHC step in the PROSPECT algorithm accelerated the iteration process with a 40% reduction in computation time. Conclusions: PROSPECT algorithm achieved a high degree of accuracy and computational efficiency. [ABSTRACT FROM AUTHOR]

Autism Spectrum Disorder (ASD) is a complex neurodevelopmental disorder, and structural magnetic resonance imaging (sMRI) and functional magnetic resonance imaging (fMRI) provide information about brain structure and function, aiding in objective ASD diagnosis. However, existing ASD classification methods face challenges such as sample scarcity, inter‐imaging center variations, insufficient single‐modality information, and inconsistent feature dimensions. This study introduced a method based on the Local Global Multimodal Domain Adaptation (LGMDA)‐Sparse Adaptive Prior Coupled Dictionary Learning (SACDL) framework. Initially, the LGMDA method was introduced to achieve multi‐source DA. By minimizing differences between different data domains while maximizing inter‐class differences within the same domain, it expands the sample size of multi‐modal data, addressing the issues of sample scarcity and heterogeneity in ASD data. Subsequently, the SACDL method was employed for multimodal fusion. It initialized dictionaries using the ATGP algorithm, combined sMRI and fMRI data for dictionary learning, adaptively adjusted sparsity parameters, and integrated ASD phenotype data for constrained optimization. It enables joint learning of shared and modality‐specific features, balancing differences in feature dimensions. Experimental results show that this model effectively utilizes multi‐center, multi‐modal information to achieve better auxiliary diagnosis than single‐modal small samples. This method has the potential to provide effective solutions for ASD multi‐source and multi‐modal classification problems, which are significant for ASD research and clinical diagnosis. [ABSTRACT FROM AUTHOR]

This paper presents the development of an optimization and modeling method for the objective functions of output power, efficiency and weight of an outer rotor permanent magnet brushless DC (BLDC) motor based on radial basis function (RBF) approximation technique. The proposed RBF‐based Pareto optimization method requires less knowledge about electric/magnetic formulas and can replace conventional optimizations based on these equations with higher accuracy. To apply the proposed optimization method, the initial design should be developed using such equations. Therefore, RBFs are used to model and predict engine behavior. To optimize the objective functions, we used a genetic algorithm optimization technique with nonlinear electric and magnetic constraints to find the Pareto front set. The design obtained by the proposed radial basis function Pareto optimization (RBFPO) method was finally verified by Ansoft Maxwell. The results of optimal design using the RBFPO method have higher output power and efficiency. Also, in addition to the advantage of a favorable accuracy, RBF‐based models are significantly faster than models available in simulation tools. [ABSTRACT FROM AUTHOR]

Regulatory guidelines mandate the strong control of the familywise error rate in confirmatory clinical trials with primary and secondary objectives. Bonferroni tests are one of the popular choices for multiple comparison procedures and are building blocks of more advanced procedures. It is usually of interest to find the optimal weighted Bonferroni split for multiple hypotheses. We consider two popular quantities as the optimization objectives, which are the disjunctive power and the conjunctive power. The former is the probability to reject at least one false hypothesis and the latter is the probability to reject all false hypotheses. We investigate the behavior of each of them as a function of different Bonferroni splits, given assumptions about the alternative hypotheses and correlations between test statistics. Under independent tests, unique optimal Bonferroni weights exist; under dependence, optimal Bonferroni weights may not be unique based on a fine grid search. In general, we propose an optimization algorithm based on constrained nonlinear optimization and multiple starting points. The proposed algorithm efficiently identifies optimal Bonferroni weights to maximize the disjunctive or conjunctive power. In addition, we apply the proposed algorithm to graphical approaches, which include many Bonferroni‐based multiple comparison procedures. Utilizing the closed testing principle, we adopt a two‐step approach to find optimal graphs using the disjunctive power. We also identify a class of closed test procedures that optimize the conjunctive power. We apply the proposed algorithm to a case study to illustrate the utility of optimal graphical approaches that reflect study objectives. [ABSTRACT FROM AUTHOR]

Based on the hierarchical control structure, optimization and control problems of large‐scale and multivariate plants are solved sequentially. The economic performance of the plant plays an essential role in the plant‐wide modern industry. The optimal operating conditions will change as the economic criteria changes throughout the operation of the plant as the result of variations in raw material prices, product prices, production demand, market fluctuations, disturbances, and so forth. In reality, soft constraints are frequently used to denote the production requirements of various operating conditions. In order to improve economic performance and guarantee feasibility for the entire plant operation, a novel economic model predictive control (EMPC) strategy is proposed to control the constrained multi‐variable process system with varying economic performance criteria under soft constraints. By incorporating the transient steady‐state and two categories of slack variables for soft constraints, a modified economic performance index is optimized to cope with the changing criteria. In addition, a contractive constraint is added to the closed‐loop system to guarantee stability for non‐dissipative stage costs. This approach ensures recursive feasibility and asymptotic stability. The effectiveness of the proposed method is demonstrated by numerical examples and the fluid catalytic cracking unit (FCCU) process. [ABSTRACT FROM AUTHOR]

This article investigates the distributed Nash equilibrium seeking problem of quadratic time‐varying games with Euler–Lagrange (EL) players, where external disturbances and parametric uncertainties are involved. A gradient‐based hierarchical algorithm consisting of a game layer and a control layer is proposed. Specifically, in the game layer, EL players communicate with neighbors through a graph to reach the consensus on potential aggregate values, which will be employed to calculate the gradient of each player's objective function, and then, a gradient‐based sliding mode controller is developed to track time‐varying gradient in the control layer. Thus, the convergence results are hierarchically obtained through the Lyapunov stability method. In addition, the hierarchical control strategy is extended to address the constrained problems through the utilization of a smooth penalty function. By appropriately choosing control parameters, the Nash equilibrium seeking errors can be arbitrarily small. The relation between the optimal solutions of the original problem and the dual one is further discussed. Finally, the proposed methods are numerically verified. [ABSTRACT FROM AUTHOR]

The accelerated failure time (AFT) model offers an important and useful alternative to the conventional Cox proportional hazards model, particularly when the proportional hazards assumption for a Cox model is violated. Since an AFT model is basically a log‐linear model, meaningful interpretations of covariate effects on failure times can be made directly. However, estimation of a semiparametric AFT model imposes computational challenges even when it only has time‐fixed covariates, and the situation becomes much more complicated when time‐varying covariates are included. In this paper, we propose a penalised likelihood approach to estimate the semiparametric AFT model with right‐censored failure time, where both time‐fixed and time‐varying covariates are permitted. We adopt the Gaussian basis functions to construct a smooth approximation to the nonparametric baseline hazard. This model fitting method requires a constrained optimisation approach. A comprehensive simulation study is conducted to demonstrate the performance of the proposed method. An application of our method to a motor neuron disease data set is provided. [ABSTRACT FROM AUTHOR]

Summary: This paper proposes a reinforcement learning‐based guidance law for Mars powered descent phase, which is an effective online calculation method that handles the nonlinearity caused by the mass variation and avoids collisions. The reinforcement learning method is designed to solve the constrained nonlinear optimization problem by using a critic neural network. Specifically, to cope with the position constraint (i.e., glide‐slope constraint) and the thrust force limit constraint, a modified cost function is proposed, and the associated Hamilton‐Jacobi‐Bellman equation is solved online without using an actor neural network, which significantly reduces the computational burden. The convergence of the critic neural network is proven. Simulation results show the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

With the rise of quantum mechanical/molecular mechanical (QM/MM) methods, the interest in the calculation of molecular assemblies has increased considerably. The structures and dynamics of such assemblies are usually governed to a large extend by intermolecular interactions. As a result, the corresponding potential energy surfaces are topological rich and possess many shallow minima. Therefore, local structure optimizations of QM/MM molecular assemblies can be challenging, in particular if optimization constraints are imposed. To overcome this problem, structure optimization in normal coordinate space is advocated. To do so, the external degrees of freedom of a molecule are separated from the internal ones by a projector matrix in the space of the Cartesian coordinates. Here we extend this approach to Cartesian constraints. To this end, we devise an algorithm that adds the Cartesian constraints directly to the projector matrix and in this way eliminates them from the reduced coordinate space in which the molecule is optimized. To analyze the performance and stability of the constrained optimization algorithm in normal coordinate space, we present constrained minimizations of small molecular systems and amino acids in gas phase as well as water employing QM/MM constrained optimizations. All calculations are performed in the framework of auxiliary density functional theory as implemented in the program deMon2k. [ABSTRACT FROM AUTHOR]

Incomplete data, whether realized from nonresponse in survey data or counterfactual outcomes in observational studies, may lead to biased estimation of study variables. Nonresponse and selection bias may be mitigated with techniques that weight the incomplete data to match characteristics of the partially unobserved complete data. Inverse probability weighting is a widely used method in causal inference that relies on a propensity model to construct adjusted weights; whereas calibration is a common method used by survey statisticians to use constrained optimization to construct adjusted weights. This article reviews inverse probability weighting and entropy balancing calibration by distinguishing them in the statistical sense of variable balancing, extending propensity score construction to include generalized boosting models, and demonstrating the use of inverse probability weighting and calibration separately and together through a widely cited simulation study evaluation. This article is categorized under:Statistical and Graphical Methods of Data Analysis > SamplingData: Types and Structure > Categorical DataStatistical Learning and Exploratory Methods of the Data Sciences > Modeling Methods [ABSTRACT FROM AUTHOR]

In order to enhance the resource utilisation of the netted radar system, a receiving resource allocation (RRA) strategy for target localisation is developed in this article. Receiving resource refers to the receiving node and the processing approach adopted. The aim of the proposed RAA strategy is to select the receiver node and corresponding processing approach to minimise the resource cost while satisfying the desired target localisation accuracies. The resource cost includes the implementation cost of the processing approaches and the distance cost of data transmission. The Cramer‐Rao bound (CRB) incorporating the above controllable parameters is derived and used as the target localisation performance metric in the netted radar system. Whereafter, the RRA problem is modelled as a non‐convex constrained optimisation problem with the discrete variables. A scheme based on the modified depth‐first search is proposed to solve this problem. Simulation results demonstrate that the proposed scheme can effectively reduce resource consumption under the desired target localisation performance constraints. [ABSTRACT FROM AUTHOR]

Background: High dose rate (HDR) brachytherapy is commonly used to treat prostate cancer. Existing HDR planning systems solve the dwell time problem for predetermined catheters and a single energy source. Purpose: Additional degrees of freedom can be obtained by relaxing the catheters' pre‐designation and introducing more source types, and may have a dosimetric benefit, particularly in improving conformality to spare the urethra. This study presents a novel analytical approach to solving the corresponding HDR planning problem. Methods: The catheter and dual‐energy source selection problem was formulated as a constrained optimization problem with a non‐convex group sparsity regularization. The optimization problem was solved using the fast‐iterative shrinkage‐thresholding algorithm (FISTA). Two isotopes were considered. The dose rates for the HDR 4140 Ytterbium (Yb‐169) source and the Elekta Iridium (Ir‐192) HDR Flexisource were modeled according to the TG‐43U1 formalism and benchmarked accordingly. Twenty‐two retrospective HDR prostate brachytherapy patients treated with Ir‐192 were considered. An Ir‐192 only (IRO), Yb‐169 only (YBO), and dual‐source (DS) plan with optimized catheter location was created for each patient with N catheters, where N is the number of catheters used in the clinically delivered plans. The DS plans jointly optimized Yb‐169 and Ir‐192 dwell times. All plans and the clinical plans were normalized to deliver a 15 Gy prescription (Rx) dose to 95% of the clinical treatment volume (CTV) and evaluated for the CTV D90%, V150%, and V200%, urethra D0.1cc and D1cc, bladder V75%, and rectum V75%. Dose‐volume histograms (DVHs) were generated for each structure. Results: The DS plans ubiquitously selected Ir‐192 as the only treatment source. IRO outperformed YBO in organ at risk (OARs) OAR sparing, reducing the urethra D0.1cc and D1cc by 0.98% (p=2.22∗10−9$p\ = \ 2.22*{10^{ - 9}}$) and 1.09% (p=1.22∗10−10$p\ = \ 1.22*{10^{ - 10}}$) of the Rx dose, respectively, and reducing the bladder and rectum V75% by 0.09 (p=0.0023$p\ = \ 0.0023$) and 0.13 cubic centimeters (cc) (p=0.033$p\ = \ 0.033$), respectively. The YBO plans delivered a more homogenous dose to the CTV, with a smaller V150% and V200% by 3.20 (p=4.67∗10−10$p\ = \ 4.67*{10^{ - 10}}$) and 1.91 cc (p=5.79∗10−10$p\ = \ 5.79*{10^{ - 10}}$), respectively, and a lower CTV D90% by 0.49% (p=0.0056$p\ = \ 0.0056$) of the prescription dose. The IRO plans reduce the urethral D1cc by 2.82% (p=1.38∗10−4$p\ = \ 1.38*{10^{ - 4}}$) of the Rx dose compared to the clinical plans, at the cost of increased bladder and rectal V75% by 0.57 (p=0.0022$p\ = \ 0.0022$) and 0.21 cc (p=0.019$p\ = \ 0.019$), respectively, and increased CTV V150% by a mean of 1.46 cc (p=0.010$p\ = \ 0.010$) and CTV D90% by an average of 1.40% of the Rx dose (p=8.80∗10−8$p\ = \ 8.80*{10^{ - 8}}$). While these differences are statistically significant, the clinical differences between the plans are minimal. Conclusions: The proposed analytical HDR planning algorithm integrates catheter and isotope selection with dwell time optimization for varying clinical goals, including urethra sparing. The planning method can guide HDR implants and identify promising isotopes for specific HDR clinical goals, such as target conformality or OAR sparing. [ABSTRACT FROM AUTHOR]

The additive hazards model specifies the effect of covariates on the hazard in an additive way, in contrast to the popular Cox model, in which it is multiplicative. As the non‐parametric model, additive hazards offer a very flexible way of modeling time‐varying covariate effects. It is most commonly estimated by ordinary least squares. In this paper, we consider the case where covariates are bounded, and derive the maximum likelihood estimator under the constraint that the hazard is non‐negative for all covariate values in their domain. We show that the maximum likelihood estimator may be obtained by separately maximizing the log‐likelihood contribution of each event time point, and we show that the maximizing problem is equivalent to fitting a series of Poisson regression models with an identity link under non‐negativity constraints. We derive an analytic solution to the maximum likelihood estimator. We contrast the maximum likelihood estimator with the ordinary least‐squares estimator in a simulation study and show that the maximum likelihood estimator has smaller mean squared error than the ordinary least‐squares estimator. An illustration with data on patients with carcinoma of the oropharynx is provided. [ABSTRACT FROM AUTHOR]

A dynamic treatment regime (DTR) is a sequence of decision rules that provide guidance on how to treat individuals based on their static and time‐varying status. Existing observational data are often used to generate hypotheses about effective DTRs. A common challenge with observational data, however, is the need for analysts to consider "restrictions" on the treatment sequences. Such restrictions may be necessary for settings where (1) one or more treatment sequences that were offered to individuals when the data were collected are no longer considered viable in practice, (2) specific treatment sequences are no longer available, or (3) the scientific focus of the analysis concerns a specific type of treatment sequences (eg, "stepped‐up" treatments). To address this challenge, we propose a restricted tree–based reinforcement learning (RT‐RL) method that searches for an interpretable DTR with the maximum expected outcome, given a (set of) user‐specified restriction(s), which specifies treatment options (at each stage) that ought not to be considered as part of the estimated tree‐based DTR. In simulations, we evaluate the performance of RT‐RL versus the standard approach of ignoring the partial data for individuals not following the (set of) restriction(s). The method is illustrated using an observational data set to estimate a two‐stage stepped‐up DTR for guiding the level of care placement for adolescents with substance use disorder. [ABSTRACT FROM AUTHOR]

Background: The intensities (i.e., number of protons in monitor unit [MU]) of deliverable proton spots need to be either zero or meet a minimum‐MU (MMU) threshold, which is a nonconvex problem. Since the dose rate is proportionally associated with the MMU threshold, higher‐dose‐rate proton radiation therapy (RT) (e.g., efficient intensity modulated proton therapy (IMPT) and ARC proton therapy, and high‐dose‐rate‐induced FLASH effect needs to solve the MMU problem with larger MMU threshold, which however makes the nonconvex problem more difficult to solve. Purpose: This work will develop a more effective optimization method based on orthogonal matching pursuit (OMP) for solving the MMU problem with large MMU thresholds, compared to state‐of‐the‐art methods, such as alternating direction method of multipliers (ADMM), proximal gradient descent method (PGD), or stochastic coordinate descent method (SCD). Methods: The new method consists of two essential components. First, the iterative convex relaxation (ICR) method is used to determine the active sets for dose‐volume planning constraints and decouple the MMU constraint from the rest. Second, a modified OMP optimization algorithm is used to handle the MMU constraint: the non‐zero spots are greedily selected via OMP to form the solution set to be optimized, and then a convex constrained subproblem is formed and can be conveniently solved to optimize the spot weights restricted to this solution set via OMP. During this iterative process, the new non‐zero spots localized via OMP will be adaptively added to or removed from the optimization objective. Results: The new method via OMP is validated in comparison with ADMM, PGD and SCD for high‐dose‐rate IMPT, ARC, and FLASH problems of large MMU thresholds, and the results suggest that OMP substantially improved the plan quality from PGD, ADMM and SCD in terms of both target dose conformality (e.g., quantified by max target dose and conformity index) and normal tissue sparing (e.g., mean and max dose). For example, in the brain case, the max target dose for IMPT/ARC/FLASH was 368.0%/358.3%/283.4% respectively for PGD, 154.4%/179.8%/150.0% for ADMM, 134.5%/130.4%/123.0% for SCD, while it was <120% in all scenarios for OMP; compared to PGD/ADMM/SCD, OMP improved the conformity index from 0.42/0.52/0.33 to 0.65 for IMPT and 0.46/0.60/0.61 to 0.83 for ARC. Conclusions: A new OMP‐based optimization algorithm is developed to solve the MMU problems with large MMU thresholds, and validated using examples of IMPT, ARC, and FLASH with substantially improved plan quality from ADMM, PGD, and SCD. [ABSTRACT FROM AUTHOR]

The ideal gas molecular movement (IGMM) as a metaheuristic optimization method is a prominent option for solving optimization problems. However, in some complex cases, IGMM may possess premature convergence or get trapped in local optima. Therefore, to tackle these issues, this paper indicates a new modified IGMM algorithm named opposition‐based IGMM, which has been incorporated with opposition based learning (OBL), Cauchy mutation (CM), velocity clamping (VC), and mirror operator (MO) to enhance its performance. OBL, VC, and MO improve the convergence of IGMM, whereas CM assists IGMM to escape local optima. The effect of each strategy, OBL, CM, VC, and MO, on IGMM, is confirmed through 30 low and high‐dimensional benchmarks, including 23 well‐known mathematical problems and CEC2017 as complex test functions and three engineering problems. Analysis results represent that integration IGMM with OBL, CM, VC, and MO has the best performance among other IGMM variants and eventually improved IGMM in exploration, exploitation, accelerating convergence, and local optima avoidance. [ABSTRACT FROM AUTHOR]

The optimization of offshore wind farms is mainly performed through the deployment of wind farms and submarine cables to maximize power output and minimize cable costs. However, the above results are affected by the wake effect, equipment layout, and the cost of cables. To effectively complete the deployment of wind turbines and submarine cable lines, first, a bi‐level constrained optimization model based on maximum profit and the shortest route of cable is proposed in this paper; then, a differential evolution and improved Prim algorithm (IPADE) are used to optimize the upper‐ and lower‐level objective function, respectively. Moreover, the fitness values are used to divide the population, and a surrogate model is used to evaluate approximate fitness values for the sub‐population with poor performance; the best individual is selected as the offspring individual according to the approximate fitness values. Next, a clustering method is used to divide the position of the wind farm, and a Prim algorithm based on roulette wheel selection is designed to deploy submarine cables of every subwind farm. Finally, the proposed algorithm is compared with five other popular algorithms under the two wind conditions. The simulation experimental results show that algorithm IPADE performs better than other algorithms in terms of the power output, profit, and the length of cables. [ABSTRACT FROM AUTHOR]

This paper proposes a tube‐based robust model predictive control (TMPC) scheme with an optimal tube for disturbance‐affected linear systems. In the literature on TMPC, there is no proper methodology to handle the considerable effects of the tube size on the closed‐loop system performance. There is usually a trade‐off between the disturbance rejection level and the amount of control effort available for the MPC problem. In some applications, it is nearly impossible to find a feasible TMPC to have a sufficient amount of states and inputs feasible sets for the MPC optimization problem. It would be a vital contribution to the TMPC designs if an algorithm is demonstrated which can investigate the suitability of TMPC for a specific system. This paper provides a solution for the mentioned challenges by introducing the concept of Quasi‐H∞ criterion and proposing a constrained optimization problem. The optimization problem is then reformulated and simplified to present an efficient methodology for the TMPC designers. The proposed TMPC scheme could benefit from a larger terminal region and result in a larger region of attraction. The achievements in TMPC designs are shown by simulations and comparisons with the previously used techniquesover numerical case studies. [ABSTRACT FROM AUTHOR]

In this paper, we focus on solving a distributed convex aggregative optimization problem in a network, where each agent has its own cost function which depends not only on its own decision variables but also on the aggregated function of all agents' decision variables. The decision variable is constrained within a feasible set. In order to minimize the sum of the cost functions when each agent only knows its local cost function, we propose a distributed Frank–Wolfe algorithm based on gradient tracking for the aggregative optimization problem where each node maintains two estimates, namely an estimate of the sum of agents' decision variable and an estimate of the gradient of global function. The algorithm is projection‐free, but only involves solving a linear optimization to get a search direction at each step. We show the convergence of the proposed algorithm for convex and smooth objective functions over a time‐varying network. Finally, we demonstrate the convergence and computational efficiency of the proposed algorithm via numerical simulations. [ABSTRACT FROM AUTHOR]

Background: Periodic and slow target motion is tracked by synchronous motion of the treatment beams in robotic stereotactic body radiation therapy (SBRT). However, spontaneous, non‐periodic displacement or drift of the target may completely change the treatment geometry. Simple motion compensation is not sufficient to guarantee the best possible treatment, since relative motion between the target and organs at risk (OARs) can cause substantial deviations of dose in the OARs. This is especially evident when considering the temporally heterogeneous dose delivery by many focused beams which is typical for robotic SBRT. Instead, a reoptimization of the remaining treatment plan after a large target motion during the treatment could potentially reduce the actually delivered dose to OARs and improve target coverage. This reoptimization task, however, is challenging due to time constraints and limited human supervision. Purpose: To study the detrimental effect of spontaneous target motion relative to surrounding OARs on the delivered dose distribution and to analyze how intra‐fractional constrained replanning could improve motion compensated robotic SBRT of the prostate. Methods: We solve the inverse planning problem by optimizing a linear program. When considering intra‐fractional target motion resulting in a change of geometry, we adapt the linear program to account for the changed dose coefficients and delivered dose. We reduce the problem size by only reweighting beams from the reference treatment plan without motion. For evaluation we simulate target motion and compare our approach for intra‐fractional replanning to the conventional compensation by synchronous beam motion. Results are generated retrospectively on data of 50 patients. Results: Our results show that reoptimization can on average retain or improve coverage in case of target motion compared to the reference plan without motion. Compared to the conventional compensation, coverage is improved from 87.83 % to 94.81 % for large target motion. Our approach for reoptimization ensures fixed upper constraints on the dose even after motion, enabling safer intra‐fraction adaption, compared to conventional motion compensation where overdosage in OARs can lead to 21.79 % higher maximum dose than planned. With an average reoptimization time of 6 s for 200 reoptimized beams our approach shows promising performance for intra‐fractional application. Conclusions: We show that intra‐fractional constrained reoptimization for adaption to target motion can improve coverage compared to the conventional approach of beam translation while ensuring that upper dose constraints on VOIs are not violated. [ABSTRACT FROM AUTHOR]

Expert knowledge is an important information source for reliability assessment of those systems with limited time‐to‐failure data. For a better understanding of the degradation profiles of systems, multiple experts are oftentimes invited to express their judgments and the associated uncertainties on the reliability‐related measures of the system. Evidential variables, as an alternative of uncertainty quantification, have been extensively used in expert systems to quantify the epistemic uncertainty of the elicited expertise. When eliciting the reliability‐related information by evidential variables, experts only need to express the possible ranges of reliability‐related measures and their associated probabilities. Such a type of information well caters to the experts' elicitation process. In this article, an evidential network (EN)‐based reliability assessment method is put forth by fusing multi‐source evidential information. The proposed method mainly contains three steps. In the first place, the multi‐source evidential information related to all components is elicited from experts in the form of evidential variables. Next, the evidential variable of the component reliability is assessed via a constrained optimization model by treating all pieces of multi‐source evidential information as constraints. The component reliability results are transformed into pieces of mass functions of the components' states under the theory of belief functions. The system reliability‐box and the reliability‐box over time are, therefore, calculated by the EN model by inputting all mass functions of components' states. A pipeline system and a chip cutting system are exemplified to examine the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

In this article, we deal with a numerical method for the approximation of a class of coupled shape optimization problems, which consist in minimizing an appropriate general volume cost functional subjected to coupled boundary value problems by means of a Neumann boundary transmission condition. We show the existence of the shape derivative of the cost functional and express it by means of support functions, using a new formula of shape derivative on a family of convex domains. This allows us to avoid the disadvantages related to the classical shape derivative method using vectors field. Then the numerical discretization is performed using the dual reciprocity boundary element method in order to avert the remeshing task required for the finite element method. Finally, we give some numerical results, based on the gradient method, showing the efficiency of the proposed approach. [ABSTRACT FROM AUTHOR]

Logos are one of the most important graphic design forms that use an abstracted shape to clearly represent the spirit of a community. Among various styles of abstraction, a particular golden‐ratio design is frequently employed by designers to create a concise and regular logo. In this context, designers utilize a set of circular arcs with golden ratios (i.e., all arcs are taken from circles whose radii form a geometric series based on the golden ratio) as the design elements to manually approximate a target shape. This error‐prone process requires a large amount of time and effort, posing a significant challenge for design space exploration. In this work, we present a novel computational framework that can automatically generate golden ratio logo abstractions from an input image. Our framework is based on a set of carefully identified design principles and a constrained optimization formulation respecting these principles. We also propose a progressive approach that can efficiently solve the optimization problem, resulting in a sequence of abstractions that approximate the input at decreasing levels of detail. We evaluate our work by testing on images with different formats including real photos, clip arts, and line drawings. We also extensively validate the key components and compare our results with manual results by designers to demonstrate the effectiveness of our framework. Moreover, our framework can largely benefit design space exploration via easy specification of design parameters such as abstraction levels, golden circle sizes, etc. [ABSTRACT FROM AUTHOR]

Bio‐inspired algorithms have become popular due to their capability of finding good solutions for complex optimization problems in an acceptable computational time. The Grey Wolf Optimizer is a nature‐inspired, population‐based metaheuristic that simulates the social hierarchy and the hunting strategy observed in a grey wolf pack. Although the Grey Wolf Optimizer has been successfully applied to solve different optimization problems, it may suffer from premature convergence and get stuck in local optima. In order to overcome these drawbacks, this paper proposes a chaotic version of the Grey Wolf Optimizer that differs from the original algorithm and previously published modified versions because it does not add a chaotic variable in the parameters that control the execution of the algorithm. Instead, the proposed model uses a chaotic variable to define the wolves in the pack that will be used to guide the hunting process in each iteration of the algorithm. Numerical experiments using 20 benchmark functions are carried out. The performance of the proposed model is compared with the performance of the original Grey Wolf Optimizer and other well‐known algorithms, namely the Particle Swarm Optimization, the Genetic Algorithm, the Symbiotic Organisms Search, and the Teaching‐Learning Based Optimization. Nine chaotic maps reported in the literature are tested. The results show that the proposed algorithm has a very competitive performance, and the Chebyshev map presented the best performance among the chaotic maps simulated. The proposed algorithm can be integrated into other modified versions of the Grey Wolf Optimizer in a straightforward way. [ABSTRACT FROM AUTHOR]

We consider frequency‐weighted damping optimization for vibrating systems described by a second‐order differential equation. The goal is to determine viscosity values such that eigenvalues are kept away from certain undesirable areas on the imaginary axis. To this end, we present two complementary techniques. First, we propose new frameworks using nonsmooth constrained optimization problems, whose solutions both damp undesirable frequency bands and maintain the stability of the system. These frameworks also allow us to weight, which frequency bands are the most important to damp. Second, we also propose a fast new eigensolver for the structured quadratic eigenvalue problems (QEPs) that appear in such vibrating systems. In order to be efficient, our new eigensolver exploits special properties of diagonal‐plus‐rank‐one (DPR1) complex symmetric matrices, which we leverage by showing how each QEP can be transformed into a short sequence of such linear eigenvalue problems. The result is an eigensolver that is substantially faster than standard techniques. By combining this new solver with our new optimization frameworks, we obtain our overall algorithm for fast computation of optimal viscosities. The efficiency and performance of our new approach are verified and illustrated on several numerical examples. [ABSTRACT FROM AUTHOR]

Time‐varying covariates can be important predictors when model based predictions are considered. A Cox model that includes time‐varying covariates is usually referred to as an extended Cox model. When only right censoring is presented in the observed survival times, the conventional partial likelihood method is still applicable to estimate the regression coefficients of an extended Cox model. However, if there are interval‐censored survival times, then the partial likelihood method is not directly available unless an imputation, such as the middle point imputation, is used to replaced the left‐ and interval‐censored data. However, such imputation methods are well known for causing biases. This paper considers fitting of the extended Cox models using the maximum penalised likelihood method allowing observed survival times to be partly interval censored, where a penalty function is used to regularise the baseline hazard estimate. We present simulation studies to demonstrate the performance of our proposed method, and illustrate our method with applications to two real datasets from medical research. [ABSTRACT FROM AUTHOR]

Nonlinear optimization problems arise in the context of many engineering processes and other real‐world applications. Depending on the complexity of modeled phenomena and constraints, such problems can feature multiple local solutions of different nature. Primarily, the quality of a solution is measured by the value of an objective function, and hence, one aims to find a global optimum. In many cases, however, additional criteria arise. For instance, nonlinear programs, in addition to decision variables, might depend on parameters undergoing perturbations. Such disturbances might be caused by noisy measurement data, changes in the environment in a real‐time setting or other factors. In this case, apart from good optimality, a practitioner might be interested in the behaviour of a solution under changes in parameters. Recently, the parametric stability score was introduced as a quality measure for solutions of unconstrained problems with respect to the influence of parameter perturbations. In this paper, we extend the concept to constrained optimization problems. The score is defined as the largest magnitude of a perturbation for which the perturbed solution does not deviate from the nominal one beyond an allowed tolerance. Our work is based on the results of parametric sensitivity analysis. This framework enables us to give a formal definition of the parametric stability score and provides tools for its efficient numerical approximation. We illustrate the approach with an example and discuss possible application scenarios for the concept. [ABSTRACT FROM AUTHOR]

The FE2 method, cf. [1], a direct micro‐macro homogenization approach, has become a standard procedure for scale‐transition applications. Therein, the modeling of a micro‐heterogeneous material described by a representative volume element (RVE) based on realistic microstructures can give rise to a barely unmanageable computational effort. Alternatively, statistically similar RVEs (SSRVEs) can be used, which are constructed based on morphological information of the real microstructure and lead to a reduction of computational cost, see [2]. In their construction, a least‐square functional is used to minimize the deviation of statistical properties, such as volume fraction, spectral density and lineal‐path function, of the SSRVE and the real microstructure. The application of SSRVEs has been shown to lead to an adequate representation of the mechanical behavior of the real microstructure. The first part of the talk will give an overview on the construction of SSRVEs and present examples of multiscale analyses using the FE2 approach with simplified microstructures in different engineering applications of steel material. The paper also focusses on the details of the microstructure and discusses crystal plasticity models, see e.g. [3], in order to account for the material anisotropy induced by the texture of the crystalline structure of steel. It is well known that for rate independent single crystal plasticity, the ambiguity of the choice of active slip systems and linear dependency of slip criteria may cause instabilities in the algorithm. Classical perturbation methods are often used to solve the problem as well as rate dependent algorithms which model the rate independent case as the limit of vanishing viscosity. However, this leads to stiff constitutive equations and thus requires small time increments. In [4], an alternative approach has been proposed recently which is based on handling the constrained optimization problem in the framework of infeasible primal‐dual interior point methods (IPDIPM). We modify the original constrained optimization problem using slack variables in order to stabilize the algorithm and allow for temporary violation of the constraints. Numerical examples are presented for crystalline structures with face centered cubic properties. [ABSTRACT FROM AUTHOR]

The analytic connectivity (AC), defined via solving a series of constrained polynomial optimization problems, serves as a measure of connectivity in hypergraphs. How to compute such a quantity efficiently is important in practice and of theoretical challenge as well due to the non‐convex and combinatorial features in its definition. In this article, we first perform a careful analysis of several widely used structured hypergraphs in terms of their properties and heuristic upper bounds of ACs. We then present an affine‐scaling method to compute some upper bounds of ACs for uniform hypergraphs. To testify the tightness of the obtained upper bounds, two possible approaches via the Pólya theorem and semidefinite programming respectively are also proposed to verify the lower bounds generated by the obtained upper bounds minus a small gap. Numerical experiments on synthetic datasets are reported to demonstrate the efficiency of our proposed method. Further, we apply our method in hypergraphs constructed from social networks and text analysis to detect the network connectivity and rank the keywords, respectively. [ABSTRACT FROM AUTHOR]

Bald Eagle Search optimization (BES) is introduced recently, which mimics the bald eagles' hunting and food searching behaviour. The capability of a BES algorithm is enhanced in this paper by avoiding local optima stagnation and premature convergence problems. The BES algorithm is modified to enhance the performance of the algorithm and the modified algorithm is called the Self Adaptive Bald Eagle Search (SABES) algorithm. Dynamic‐opposite Learning (DOL) method is invoked in the initialization phase to increase the population diversity and convergence speed. To find better global solutions, the exploitation capability of the SBES algorithm is enhanced by considering the dynamic‐opposite solutions. In addition, the algorithmic parameter values of the BES algorithm have been determined using the linear and non‐linear time‐varying adaption strategy to create a balance between the search abilities which promotes the overall performance of the algorithm. The performance of the SABES algorithm is validated by comparing the results of 50 benchmark functions and CEC2017 functions with different erstwhile algorithms. The proposed algorithm achieves the best results in 80% of the benchmark functions, whereas the BES only gets the best results in 56% of functions. For the CEC2017, the SABES algorithm achieves optimal results for 20 functions which are highest in comparison to state‐of‐the‐art algorithms. The feasibility and effectiveness of the proposed algorithm are checked using the 15 CEC2020 competition real‐world single‐objective constrained optimization problems. The SABES achieves a 100% success rate and 100% feasibility rate in comparison to other well‐regarded algorithms. The statistical significance of the algorithm has been proved using Friedman's mean rank and Wilcoxon sign rank test. [ABSTRACT FROM AUTHOR]

Practical industrial process is usually a dynamic process including uncertainty. Stochastic constraints can be used for industrial process modeling, when system sate and/or control input constraints cannot be strictly satisfied. Thus, optimal control of nonlinear systems with stochastic constraints can be available to address practical industrial process problems with integer‐valued control inputs. In general, obtaining an analytical solution of this optimal control problem is very difficult due to the discrete nature of the control inputs and the complexity of stochastic constraints. To obtain a numerical solution, this problem is formulated as a finite dimensional static constrained optimization problem. First, the integer‐valued control input is relaxed into a continuous‐valued control input by imposing a penalty term on the objective function. Convergence results show that the relaxed solution obtained is an integer solution as long as the penalty parameter is sufficiently large. In addition, it should be noted that no any constraint is introduced in the novel relaxation technique, which can effectively avoid introducing any extra extreme point for the original optimal control problem. Next, a novel smooth approximation function is used to construct a subset of feasible region for this optimal control problem. It is proved that the smooth approximation can converge uniformly to the stochastic constraints as the adjusting parameter reduces. Following that, a numerical computation method is proposed for solving the original optimal control problem. Finally, in order to illustrate the effectiveness of the proposed method, an electric vehicle energy management problem is extended by considering some stochastic constraints. The numerical results show that the proposed method is less conservative compared with the existing typical approaches and can obtain a stable and robust performance when considering the initial condition small perturbations. [ABSTRACT FROM AUTHOR]

In this study, a new optimization algorithm is proposed based on swarm intelligence theory. In the algorithm, the movement of each individual toward the best member of the population is not represented as a linear vector; instead, it can change nonlinearly according to the discrete‐time that is represented by the iteration number. By implementing this change, the speed of each member of the population can be controlled, which results in finding a better solution. As there is a dependency on the iteration number, it is named the Iteration Dependent Optimizer (IDO). The performance of the proposed algorithm is evaluated based on unconstrained unimodal and multimodal benchmark functions and constrained engineering optimization problems. Then the algorithm is used to solve a practical problem in civil engineering, in which unknown parameters of the model of a large‐scale magnetorheological (MR) damper, which is commonly used in structural control, are identified. The results of statistical study and direct comparisons demonstrate the advantages and capabilities of the proposed model and indicate that IDO can compete favorably with some other well‐studied algorithms. [ABSTRACT FROM AUTHOR]

Over the years, seismic amplitude variation with offset has been successfully applied for predicting the elastic properties of the subsurface. Nevertheless, the solution of the amplitude inversion is not stable due to insufficient information in the recorded seismic data. To enhance the stability, various amplitude inversions under a Bayesian framework have been introduced and most of which are based on single‐component a priori probability densities, which can be solved deterministically. For multi‐component a priori densities, Monte Carlo sampling methods are often used to obtain the posterior distribution of the inverted parameters. The variational methods, on the other hand, provide the gradients of the parameters with respect to the data. Here, we present an inversion framework that uses the gradients of the variational inference as regularization. Due to the ill‐posedness of the amplitude inversion, solving the likelihood of the data leads to solutions that may exist within the low‐probability regions of the a priori density. The rule of the regularization (variational inference gradient) is, therefore, to force solutions within the high‐probability regions that enhance the stability of the inversion process. The performance of the regularization is tested using synthetic and field data examples to jointly estimate the elastic and Thomsen's anisotropy parameters. The proposed constrained optimization successfully predicts the P‐wave velocity, S‐wave velocity and P‐wave anisotropy and preferably constrains the density and near‐vertical anisotropy parameters. [ABSTRACT FROM AUTHOR]

Approximations in the moist thermodynamics of atmospheric models can often be inconsistent; different parts of numerical models may handle the thermodynamics in different ways, or the approximations may disagree with the laws of thermodynamics. To address these problems, all relevant thermodynamic quantities may be derived from a defined thermodynamic potential; approximations are instead made to the potential itself—this guarantees self‐consistency, as well as flexibility. Previous work showed that this concept is viable for vapour and liquid water mixtures in a moist atmospheric system using the Gibbs potential. However, on extension to include the ice phase, an ambiguity is encountered at the triple point. To resolve this ambiguity, here the internal energy is used instead. Constrained maximisation methods on the entropy can then be used to solve for the system equilibrium state. Nevertheless, a further extension is necessary for realistic atmospheric systems, where many important non‐equilibrium processes take place; for example, freezing of supercooled water and evaporation into subsaturated air. To capture processes such as these fully, the equilibrium method must be reformulated to involve finite rates of approach towards equilibrium. Here the principles of non‐equilibrium thermodynamics are used, beginning with a set of phenomenological equations, to show how non‐equilibrium moist processes may be coupled to a semi‐implicit semi‐Lagrangian dynamical core. Standard bubble test cases and simulations of idealised cloudy thermals are presented to demonstrate the viability of the approach for the equilibrium regime. Further details and results for non‐equilibrium regimes are presented in Part II. [ABSTRACT FROM AUTHOR]

We propose a tree‐based algorithm (μCART) for classification and regression problems in the context of functional data analysis, which allows to leverage measure learning and multiple splitting rules at the node level, with the objective of reducing error while retaining the interpretability of a tree. For each internal node, our main contribution is the idea of learning a weighted functional L2 space by means of constrained convex optimization, which is then used to extract multiple weighted integral features from the functional predictors, in order to determine the binary split. The approach is designed to manage multiple functional predictors and/or responses, by defining suitable splitting rules and loss functions that can depend on the specific problem and can also be combined with additional scalar and categorical predictors, as the tree is grown with the original greedy CART algorithm. We focus on the case of scalar‐valued functional predictors defined on unidimensional domains and illustrate the effectiveness of our method in both classification and regression tasks, through a simulation study and four real‐world applications. [ABSTRACT FROM AUTHOR]

Life cycle assessment (LCA) is a method to evaluate the environmental impacts of technologies from cradle to grave. However, LCAs are commonly defined in terms of the consumption of a single unit of a product and thus ignore scaling issues in large‐scale deployment of technologies. Such product‐level LCAs often do not consider capital manufacturing capacity and supply chain bottlenecks that may hinder the rapid, widespread uptake of emerging technologies entering the market; emerging technologies often require the expansion of existing supply chains or the development of entirely new supply chains, such as the manufacturing of novel materials. As a result, such LCA studies are limited in their ability to realistically assess impacts at the macro‐scale and thus to guide large‐scale decisions. In this work, we present ECOPT2, a generalized adaptable model that combines these constraints to the LCA approach using a mathematical programming approach and dynamic stock modeling. ECOPT2 combines LCA factors with transition scenarios from energy systems models to determine the environmentally optimal deployment of new technologies while accounting for material circularity constraints and barriers to uptake. We also introduce the structure of the software tool and demonstrate its features using a stylized vehicle electrification scenario. [ABSTRACT FROM AUTHOR]

The vertical alignment optimization is about developing a minimum cost curvilinear vertical profile of constrained grade sections and appropriate non‐overlapping vertical curves passing through fixed control points with elevation constraints. Variations in ground profile and discreteness in unit cutting and filling costs make it a non‐convex, noisy, constrained optimization problem with many local minima. Further, the gradient related constraints and vertical curvature are non‐linear. This paper presents an innovative exploring and exploiting ant colony optimization (E&E‐ACO) algorithm with an appropriate point sampling, vertical curve fitting strategies, and an intuitive feasible region identification approach for solving the vertical alignment optimization problem. The E&E‐ACO algorithm extensively explores the feasible search space to generate a set of potential solutions and effectively exploit the space around the potential solutions for developing the optimized vertical alignment. The efficacy of the proposed method is demonstrated using two case studies. In one case study, the optimized solution by the proposed method had a marginally better objective function value and about three times lesser computational time than the solution by the mesh adaptive direct search method. The optimized alignment satisfied the elevation constraints of fixed control points and imitated the manually designed real‐world vertical alignment. The linearly varying exploration and exploitation parameters had better convergence rate than the other tested variations. Further, the proposed method at the end of 1000 iterations yielded about six times better result than the traditional ACO algorithm. [ABSTRACT FROM AUTHOR]

This work proposed a new metaheuristic dubbed as Chaotic Lévy flight distribution (CLFD) algorithm, to address physical world engineering optimization problems that incorporate the chaotic maps in the elementary Lévy flight distribution (LFD). Hybridization aims to increase the LFD rate of convergence while also providing a problem‐free optimization approach. The proposed methodology is investigated for five case studies of constrained optimization issues followed by shape optimization of structural design. The outcomes from the CFLD algorithm are further contrasted with its fundamental version and other distinguished recently introduced algorithms. The computational analysis illustrates the dominance of CLFD over other considered optimizers. Moreover, the present investigation shows that CLFD is a robust technique that can efficiently find optimal mechanical design problems with a proper chaotic map selection. [ABSTRACT FROM AUTHOR]

This article presents a new refinement design routine aimed at solving the robust multivariable tracking error problem with reduced conservatism. The prevailing multivariable quantitative feedback theory (QFT) approach is to implicitly overbound the model‐error tracking set frequency response in magnitude using the triangle inequality, with the intention of arriving at a set of univariate design constraints that independently describe the feedback controller solution space. While this method is effective in the low‐frequency range (where the loop gain tends to be large), the mid‐ to high‐frequency design regions (where diagonal dominance is not possible in general) suffers from arbitrarily large design conservatism. This inhibits minimum gain‐phase solutions and necessitates undesirable over‐design in the frequency band that can contribute to large, expensive control action. The proposed method follows a refinement approach that makes use of information from an a priori feedback control design. In this way, the tracking error problem is reposed as a differential design, and gain‐phase information from the previous iteration can be captured to reduce the conservatism imposed when applying the triangle inequality. Additionally, a constrained optimization routine is used to select a prototype feedforward filter that can relax the constraint set, thereby increasing the accessible solution space of the diagonal feedback controller. Finally, a nondiagonal, multivariable feedforward filter bound generation routine is defined that relies on existence conditions and is free of induced design conservatism. The viability of this design methodology is demonstrated on two benchmark problems of varying complexity, in order to demonstrate the widespread efficacy. [ABSTRACT FROM AUTHOR]

Time‐to‐event data in medical studies may involve some patients who are cured and will never experience the event of interest. In practice, those cured patients are right censored. However, when data contain a cured fraction, standard survival methods such as Cox proportional hazards models can produce biased results and therefore misleading interpretations. In addition, for some outcomes, the exact time of an event is not known; instead an interval of time in which the event occurred is recorded. This article proposes a new computational approach that can deal with both the cured fraction issues and the interval censoring challenge. To do so, we extend the traditional mixture cure Cox model to accommodate data with partly interval censoring for the observed event times. The traditional method for estimation of the model parameters is based on the expectation‐maximization (EM) algorithm, where the log‐likelihood is maximized through an indirect complete data log‐likelihood function. We propose in this article an alternative algorithm that directly optimizes the log‐likelihood function. Extensive Monte Carlo simulations are conducted to demonstrate the performance of the new method over the EM algorithm. The main advantage of the new algorithm is the generation of asymptotic variance matrices for all the estimated parameters. The new method is applied to a thin melanoma dataset to predict melanoma recurrence. Various inferences, including survival and hazard function plots with point‐wise confidence intervals, are presented. An R package is now available at Github and will be uploaded to R CRAN. [ABSTRACT FROM AUTHOR]

This article studies the extremum seeking control (ESC) problem for a class of constrained nonlinear systems. Specifically, we focus on a family of constraints that allows to reformulate the original nonlinear system in the so‐called input–output normal form. To steer the system to optimize a performance function without knowing its explicit form, we propose a novel numerical optimization‐based extremum seeking control (NOESC) design consisting of a constrained numerical optimization method and an inversion‐based feedforward controller. In particular, a projected gradient descent algorithm is exploited to produce the state sequence to optimize the performance function, whereas a suitable boundary value problem accommodates the finite‐time state transition between each two consecutive points of the state sequence. Compared to available NOESC methods, the proposed approach (i) can explicitly deal with output constraints; (ii) can consider a direct dependence on the states of the internal dynamics in the performance function; (iii) the internal dynamics do not have to be necessarily stable. The effectiveness of the proposed ESC scheme is shown through extensive numerical simulations and design of antilock braking systems. [ABSTRACT FROM AUTHOR]

Reliable predictions of surface chemical reaction energetics require an accurate description of both chemisorption and physisorption. Here, we present an empirical approach to simultaneously optimize semi‐local exchange and nonlocal correlation of a density functional approximation to improve these energetics. A combination of reference data for solid bulk, surface, and gas‐phase chemistry and physical exchange‐correlation model constraints leads to the VCML‐rVV10 exchange‐correlation functional. Owing to the variety of training data, the applicability of VCML‐rVV10 extends beyond surface chemistry simulations. It provides optimized gas phase reaction energetics and an accurate description of bulk lattice constants and elastic properties. [ABSTRACT FROM AUTHOR]

The interconnection of multiple microgrids can effectively improve the operating efficiency of the system and reduce the cost of power generation. First, establish an economic environment optimal dispatch model based on the regional interconnected multi‐microgrids system, and formulate a dispatch strategy based on the time‐of‐use electricity price and the supply‐demand relationship between microgrids; Secondly, in order to solve this constrained optimization problem, a whale algorithm improved with five strategies including adaptive inertial weights, dynamic spiral search and generalized opposition‐based learning is proposed to obtain higher solution accuracy and anti‐premature convergence ability; Finally, combined 12 test functions to test the effectiveness of the improved algorithm, and use the improved algorithm to solve the example model containing two microgrids, and analyze it in two states of interconnection operation and non‐interconnection operation. The simulation results show that the regional interconnection operation of the microgrid under the established dispatching strategy can effectively reduce the overall operating cost of the system, and at the same time show the effectiveness of the improved algorithm to solve the optimal dispatching problem. © 2022 Institute of Electrical Engineers of Japan. Published by Wiley Periodicals LLC. [ABSTRACT FROM AUTHOR]

Over the last decades, many efforts have been made toward the understanding of the convergence rate of the gradient‐based method for both constrained and unconstrained optimization. The cases of the strongly convex and weakly convex payoff function have been extensively studied and are nowadays fully understood. Despite the impressive advances made in the convex optimization context, the nonlinear non‐convex optimization problems are still not fully exploited. In this paper, we are concerned with the nonlinear, non‐convex optimization problem under system dynamic constraints. We apply our analysis to parameter identification of systems governed by general nonlinear differential equations. The considered inverse problem is presented using optimal control tools. We tackle the optimization through the use of Fletcher‐Reeves nonlinear conjugate gradient method satisfying strong Wolfe conditions with inexact line search. We rigorously establish a convergence analysis of the method and report a new linear convergence rate which forms the main contribution of this work. The theoretical result reported in our analysis requires that the second derivative of the payoff functional be continuous and bounded. Numerical evidence on a selection of popular nonlinear models is presented as a direct application of parameter identification to support the theoretical findings. [ABSTRACT FROM AUTHOR]

Modern CAD tools represent 3D designs not only as geometry, but also as a program composed of geometric operations, each of which depends on a set of parameters. Program representations enable meaningful and controlled shape variations via parameter changes. However, achieving desired modifications solely through parameter editing is challenging when CAD models have not been explicitly authored to expose select degrees of freedom in advance. We introduce a novel bidirectional editing system for 3D CAD programs. In addition to editing the CAD program, users can directly manipulate 3D geometry and our system infers parameter updates to keep both representations in sync. We formulate inverse edits as a set of constrained optimization objectives, returning plausible updates to program parameters that both match user intent and maintain program validity. Our approach implements an automatically differentiable domain‐specific language for CAD programs, providing derivatives for this optimization to be performed quickly on any expressed program. Our system enables rapid, interactive exploration of a constrained 3D design space by allowing users to manipulate the program and geometry interchangeably during design iteration. While our approach is not designed to optimize across changes in geometric topology, we show it is expressive and performant enough for users to produce a diverse set of design variants, even when the CAD program contains a relatively large number of parameters. [ABSTRACT FROM AUTHOR]

We propose a simple yet effective method to perform surface remeshing with hard constraints, such as bounding approximation errors and ensuring Delaunay conditions. The remeshing is formulated as a constrained optimization problem, where the variables contain the mesh connectivity and the mesh geometry. To solve it effectively, we adopt traditional local operations, including edge split, edge collapse, edge flip, and vertex relocation, to update the variables. Central to our method is an evolutionary vertex optimization algorithm, which is derivative‐free and robust. The feasibility and practicability of our method are demonstrated in two applications, including error‐bounded Delaunay mesh simplification and error‐bounded angle improvement with a given number of vertices, over many models. Compared to state‐of‐the‐art methods, our method achieves higher remeshing quality. [ABSTRACT FROM AUTHOR]

The parameter optimization coupled with the control strategy and target driving cycle directly affects the performance of vehicles. This paper proposes an optimization approach for a plug‐in hybrid electric truck (PHET), which considers comprehensive performances including fuel economy, emissions, vehicle drivability, safety, and dynamics. First, 10 initial design parameters are selected from powertrain components and a real‐time energy management strategy (EMS). Then, a definitive screening design (DSD) is proposed to simplify the design parameters. Finally, non‐dominated sorting genetic algorithm‐III (NSGA‐III) is proposed to solve a constrained many‐objective optimization problem with 9 objectives, and the design space is refined through a sensitivity analysis. Simulation results demonstrate that the proposed optimization approach can achieve significant improvements regarding both the comprehensive performances, power repartition, and system efficiency. The simulation is conducted both on Chinese Heavy‐Duty Commercial Vehicle Test Cycle (CHTC) and Urban Dynamometer Driving Schedule for Heavy‐Duty Vehicles (UDDSHDV). In addition, to guide a decision maker (DM) to make trade‐offs among many objectives, preferences are also incorporated into the solutions. [ABSTRACT FROM AUTHOR]

Purpose: Spectral computed tomography (CT) based on the photon‐counting detection system has the capability to produce energy‐discriminative attenuation maps of objects with a single scan. However, the insufficiency of photons collected into the narrow energy bins results in high quantum noise levels causing low image quality. This work aims to improve spectral CT image quality by developing a novel regularization based on framelet tensor prior. Methods: First, similar patches are extracted from highly correlated interchannel images in spectral and spatial domains, and stacked to form a third‐order tensor after vectorization along the energy channels. Second, the framelet tensor nuclear norm (FTNN) is introduced and applied to construct the regularization to exploit the sparsity embedded in nonlocal similarity of spectral images, and thus the reconstruction problem is modeled as a constrained optimization. Third, an iterative algorithm is proposed by utilizing the alternating direction method of multipliers framework in which efficient solvers are developed for each subproblem. Results: Both numerical simulations and real data verifications were performed to evaluate and validate the proposed FTNN‐based method. Compared to the analytic, TV‐based, and the state‐of‐the‐art tensor‐based methods, the proposed method achieves higher numerical accuracy on both reconstructed CT images and decomposed material maps in the mouse data indicating the capability in noise suppression and detail preservation of the proposed method. Conclusions: A framelet tensor sparsity–based iterative algorithm is proposed for spectral reconstruction. The qualitative and quantitative comparisons show a promising improvement of image quality, indicating its promising potential in spectral CT imaging. [ABSTRACT FROM AUTHOR]

This article investigates the distributed constrained optimization with hybrid linear constraints for multi-agent networks, in which all the agents collaboratively minimize the global objective function with a sum of convex local objective functions, while the constraints aremore general with local and global restrictions on the agents. Based on matrix and graph theories, a discrete-time algorithm under distributedmanner is designed to dealwith the organized problems. In addition, the optimality of the presented algorithm is obtained under certain initial restriction for the agents. By virtue of a novel Lyapunov function and the optimal conditions, rigorous analysis shows the convergence of the multi-agent networks with undirected and connected graphs. Finally, two simulation examples are presented to validate the theoretical consequence. [ABSTRACT FROM AUTHOR]

Regression models describing the joint distribution of multivariate responses conditional on covariate information have become an important aspect of contemporary regression analysis. However, a limitation of such models are the rather simplistic assumptions often made, for example, a constant dependence structure not varying with covariates or the restriction to linear dependence between the responses. We propose a general framework for multivariate conditional transformation models that overcomes these limitations and describes the entire distribution in a tractable and interpretable yet flexible way conditional on nonlinear effects of covariates. The framework can be embedded into likelihood‐based inference, including results on asymptotic normality, and allows the dependence structure to vary with covariates. In addition, it scales well‐beyond bivariate response situations, which were the main focus of most earlier investigations. We illustrate the benefits in a trivariate analysis of childhood undernutrition and demonstrate empirically that complex truly multivariate data‐generating processes can be inferred from observations. [ABSTRACT FROM AUTHOR]