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Ammonia is a promising carbon‐free energy vector. Small‐scale renewable power‐to‐ammonia (P2A) is particularly suited for isolated agricultural areas where ammonia can be used as fuel and fertilizer. This work compares two approaches to simulate and optimize the steady‐state behavior of a novel small‐scale P2A process: Aspen Plus® and MOSAIC®. Aspen Plus® is a commercial flow sheeting software whereas MOSAIC® is a freeware where equations and thermochemical properties need to be specified by hand. It can be shown that the results of MOSAIC® and Aspen Plus® are qualitatively comparable, but not identical. This suggests that the model in MOSAIC® can be improved further, starting with the implementation of a more accurate numeric reactor kinetics and equation of state. [ABSTRACT FROM AUTHOR]

Imitation learning enables synthesis of controllers for systems with complex objectives and uncertain plant models. However, ensuring an imitation learned controller is stable requires copious amounts of data and/or a known plant model. In this paper, we explore an input–output (IO) stability approach to imitation learning, which achieves stability with sparse data sets while only requiring coarse knowledge of the energy characteristics of the plant. A constrained optimization problem is developed, in which the controller learns to mimic expert data while maintaining stabilizing energy characteristics induced by the plant. While the learning objective is nonconvex, iterative convex overbounding (ICO) and projected gradient descent (PGD) are explored as methods to learn the controller. In numerical examples, it is shown that with little knowledge of the plant model and a small data set, the dissipativity constrained learned controller achieves closed loop stability and successfully mimics the behavior of the expert controller, while other methods often fail to maintain stability and achieve good performance. [ABSTRACT FROM AUTHOR]

This study introduces a constrained many‐objective optimization approach for the optimal design of 20 MW direct drive (DD) permanent magnet synchronous generators (PMSGs). Designing a high‐performance, competitive DD‐PMSG requires considering the generator's performance as well as its weight and material cost. Therefore, we focus on four main characteristics as our design objectives: (1) specific power (power per weight), (2) power‐per‐cost, (3) efficiency, and (4) power factor. To achieve this, we apply an advanced constrained nondominated sorting genetic algorithm III (NSGA‐III), a many‐objective optimization method utilizing evolutionary computation, capable of optimizing four or more objectives with constraints. Additionally, the electromagnetic finite element method is employed to evaluate the generator's characteristics. Through our proposed design process, we optimize three distinct 20 MW DD‐PMSG configurations: a 320‐pole/300‐slot, a 350‐pole/300‐slot, and a 350‐pole/336‐slot topology. Following this optimization, we perform additional multiphysics simulations (covering electromagnetic, structural, overload, and thermal aspects) and control response simulations on four selected models from the Pareto‐optimal solutions to validate their effectiveness as preliminary DD‐PMSG designs. Finally, we conduct a comprehensive analysis of all simulation results. [ABSTRACT FROM AUTHOR]

Communication plays a pivotal role in distributed optimization problems, where unavoidable communication delays are presented. This research studies the distributed constrained optimization problem concerning second‐order multi‐agent systems with double‐integrator under time‐varying communication delays. An adaptive distributed optimization algorithm using multi‐agent system consensus technique and Karush–Kuhn–Tucker conditions is developed to deal with this problem. The local constraint term is solved adaptively through local dual Lagrange multipliers. When the cost function is strongly convex, and the communication topology is undirected and connected, we employ the Lasalle invariance principle to analyze the delay effects on convergence analysis. Moreover, we give an upper bound on communication delay. Finally, the provided numerical simulation examples demonstrate that the developed method is robust for the limited communication delay and the derived results are conservative. [ABSTRACT FROM AUTHOR]

Serverless computing has nowadays become a mainstream paradigm to develop cloud‐native applications owing to its high scalability, ease of usage and cost‐effectiveness. Nevertheless, because of its poor infrastructure transparency, two main challenges emerge when users migrate their applications to a serverless platform: the lack of an effective analytical model for performance and billing, and the trade‐off problem between them. In this paper, we formally define a serverless workflow and introduce the concept of execution instances. Based on them, a probabilistic performance and cost evaluation model is built to obtain their expected values for an input serverless workflow. Then, we design a tailored evolutionary optimization algorithm called EASW to tackle budget‐constrained performance optimization and performance‐constrained cost optimization problems. Extensive experiments were carried out to test the proposed model and optimization algorithm on AWS Lambda. Results reveal that our model can achieve an accuracy over 98% and EASW can yield a better memory configuration solution than existing methods for constrained optimization. [ABSTRACT FROM AUTHOR]

This paper investigates the robust stabilization problem of linear delay systems with parametric uncertainty. First, by means of the argument principle, a delay‐dependent sufficient condition is derived for designing a feedback controller, with which the closed‐loop system can achieve robust stability. Then, based on the fundamental matrix of the linear delay systems, a constrained optimization problem is formulated for solving the feedback gain matrices. The effectiveness of the proposed method is verified by some simulation results. [ABSTRACT FROM AUTHOR]

Topology optimization (TO) has recently emerged as an advanced design method. To ensure practical reliability in the design process, it is imperative to incorporate considerations of uncertainty. Consequently, performing reliability analysis (RA) during the design phase becomes necessary. However, RA itself constitutes an optimization problem. Combining these two optimization problems can result in inefficiency. To address this challenge, we propose a decoupled approach that integrates deterministic topology optimization (DTO) and RA cycles. The reliability‐based stress‐constrained TO (RBSCTO) problem is considered in this paper. The DTO constraint is derived based on shifting vectors derived from the previous cycle's RA outcomes, enabling low‐reliability constraint shift towards the feasible direction. The DTO is solved based on solid‐isotropic‐material‐with‐penalization (SIMP) and augmented Lagrangian method. Meanwhile, the optimization problem in RA is addressed using finite differences and the interior point method. To reduce the errors resulting from linear approximation and optimization in RA when the target reliability is very low, an outlier handling method is employed. Meantime, we utilize a probabilistic neural network to enhance the efficiency of reliability assessment. Comparative studies against traditional methods across four RBSCTO tasks are demonstrated to validate its effectiveness. Monte Carlo simulations are used to validate the reliability of results. [ABSTRACT FROM AUTHOR]

In this work, for unconstrained optimization, we introduce an improved Dai‐Liao‐style hybrid conjugate gradient method based on the hybridization‐based self‐adaptive technique, and the search direction generated fulfills the sufficient descent and trust region properties regardless of any line search. The global convergence is established under standard Wolfe line search and common assumptions. Then, combining the hyperplane projection technique and a new self‐adaptive line search, we extend the proposed conjugate gradient method and obtain an improved Dai‐Liao‐style hybrid conjugate gradient projection method to solve constrained nonlinear monotone equations. Under mild conditions, we obtain its global convergence without Lipschitz continuity. In addition, the convergence rates for the two proposed methods are analyzed, respectively. Finally, numerical experiments are conducted to demonstrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a novel high‐order shock tracking method and provide a proof of concept. Our method leverages concepts from implicit shock tracking and extended discontinuous Galerkin methods, primarily designed for solving partial differential equations featuring discontinuities. To address this challenge, we solve a constrained optimization problem aiming at accurately fitting the zero iso‐contour of a level set function to the discontinuities. Additionally, we discuss various robustness measures inspired by both numerical experiments and existing literature. Finally, we showcase the capabilities of our method through a series of two‐dimensional problems, progressively increasing in complexity. [ABSTRACT FROM AUTHOR]

During terminal guidance, the attack platform is provided with a high‐resolution image of the target area through the application of synthetic aperture radar. Additionally, the stealth trajectory with low observability can significantly impact mission success. This paper considers both the performance of missile‐borne synthetic aperture radar imaging and stealth performance as influencing factors for terminal trajectory optimization, which is modelled as a constrained multi‐objective optimization problem. The application of the pseudospectral method in the solution of optimal control problems has led to the proposal of the hybrid genetic algorithm pseudospectral optimization framework. The problem is decomposed into several single‐objective optimal control problems, which can generate a specific initial population for the genetic algorithm to obtain a set of Pareto‐optimal solutions. Finally, the numerical simulations demonstrate the effectiveness of the proposed optimization approach compared with the benchmark scheme. [ABSTRACT FROM AUTHOR]

Objective: Designing physiologically adequate microvascular trees is of crucial relevance for bioengineering functional tissues and organs. Yet, currently available methods are poorly suited to replicate the morphological and topological heterogeneity of real microvascular trees because the parameters used to control tree generation are too simplistic to mimic results of the complex angiogenetic and structural adaptation processes in vivo. Methods: We propose a method to overcome this limitation by integrating a conditional deep convolutional generative adversarial network (cDCGAN) with a local fractal dimension‐oriented constrained constructive optimization (LFDO‐CCO) strategy. The cDCGAN learns the patterns of real microvascular bifurcations allowing for their artificial replication. The LFDO‐CCO strategy connects the generated bifurcations hierarchically to form microvascular trees with a vessel density corresponding to that observed in healthy tissues. Results: The generated artificial microvascular trees are consistent with real microvascular trees regarding characteristics such as fractal dimension, vascular density, and coefficient of variation of diameter, length, and tortuosity. Conclusions: These results support the adoption of the proposed strategy for the generation of artificial microvascular trees in tissue engineering as well as for computational modeling and simulations of microcirculatory physiology. [ABSTRACT FROM AUTHOR]

This study focuses on the precise model estimation for a position control problem actuated by a shape memory alloy (SMA) wire. Because the hysteresis characteristic of SMA introduces complexities in system modelling and adds degrees of freedom, a model with reduced order is implemented for controller design. This model is online updated by calculating a complementary term from the measured data to compensate for the SMA actuator dynamics and other parametric uncertainties. The position controller, derived from the formulated reduced‐order model, adapts itself to real conditions and is cost‐effective due to the use of only displacement sensor. The saturation of the control input is modelled within the structure of a constrained optimization problem solved by Karush–Kuhn–Tucker theorem. The boundedness of mean and covariance of tracking error and its derivative is demonstrated by stochastic analysis. The experimental results conducted on a platform incorporating a SMA wire show the efficiency of the proposed system in precisely controlling the position by admissible voltage range. The comparative results with a sliding mode controller indicate higher accuracy for the proposed controller to reduce the effect of uncertainties. [ABSTRACT FROM AUTHOR]

The key motivation of this paper lies in the development of a high‐level decision‐making framework for autonomous overtaking maneuvers on two‐lane country roads with dynamic oncoming traffic. To generate an optimal and safe decision sequence for such scenario, an innovative high‐level decision‐making framework that combines model predictive control (MPC) and switching control methodologies is introduced. Specifically, the autonomous vehicle is abstracted and modelled as a switched system. This abstraction allows vehicle to operate in different modes corresponding to different high‐level decisions. It establishes a crucial connection between high‐level decision‐making and low‐level behaviour of the autonomous vehicle. Furthermore, barrier functions and predictive models that account for the relationship between the autonomous vehicle and oncoming traffic are incorporated. This technique enables us to guarantee the satisfaction of constraints, while also assessing performance within a prediction horizon. By repeatedly solving the online constrained optimization problems, we not only generate an optimal decision sequence for overtaking safely and efficiently but also enhance the adaptability and robustness. This adaptability allows the system to respond effectively to potential changes and unexpected events. Finally, the performance of the proposed MPC framework is demonstrated via simulations of four driving scenarios, which shows that it can handle multiple behaviours. [ABSTRACT FROM AUTHOR]

An optimization algorithm is presented for the deconvolution of a complex field to improve the resolution and accuracy of quantitative phase imaging (QPI). A high‐resolution phase map can be recovered by solving a constrained optimization problem of deconvolution using a complex gradient operator. The method is demonstrated on phase measurements of samples using a white light based phase shifting interferometry (WLPSI) method. The application of the algorithm on real and simulated objects shows a significant resolution and contrast improvement. Experiments performed on Escherichia coli bacterium have revealed its sub‐cellular structures that were not visible in the raw WLPSI images obtained using a five phase shifting method. These features can give valuable insights into the structures and functioning of biological cells. The algorithm is simple in implementation and can be incorporated into other QPI modalities. [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]

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]

In this article, we propose non‐parametric estimations of robustness and reliability measures approximation error, employed in the context of constrained multi‐objective optimisation under uncertainty (OUU). These approximations with tunable accuracy permit to capture the Pareto front in a parsimonious way, and can be exploited within an adaptive refinement strategy. First, we illustrate an efficient approach for obtaining joint representations of the robustness and reliability measures, allowing sharper discrimination of Pareto‐optimal designs. A specific surrogate model of these objectives and constraints is then proposed to accelerate the optimisation process. Secondly, we propose an adaptive refinement strategy, using these tunable accuracy approximations to drive the computational effort towards the computation of the optimal area. To this extent, an adapted Pareto dominance rule and Pareto optimal probability computation are formulated. The performance of the proposed strategy is assessed on several analytical test‐cases against classical approaches. We also illustrate the method on an engineering application, performing shape OUU of an Organic Rankine Cycle turbine. [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]

A system of fast moving quadcopters has a high risk of collisions with neighboring quadcopters or obstacles. The objective of this work is to develop a control strategy for collision and obstacle avoidance of multiple quadcopters. In this paper, the problem of distributed dynamic matrix control (DMC) for collision avoidance among a team of multiple quadcopters attempting to reach consensus in the horizontal plane and yaw direction (x,y$$ x,y $$, and ψ$$ \psi $$) is investigated. Violations of a predetermined safety radius generates output constraints on the DMC optimization function, which has not been dealt with in the literature. Different from past works, the proposed strategy can perform collision avoidance in the x$$ x $$, y$$ y $$, and z$$ z $$‐directions. In addition, logarithmic barrier functions are implemented as input rate constraints on the control actions. Extensive simulation studies for a team of quadcopters illustrate promising results of the proposed control strategy and case variations. In addition, DMC parameter effects on the system performance are studied, and a successful study for obstacle avoidance is presented. [ABSTRACT FROM AUTHOR]

Quantum annealing is a promising method for solving hard optimization problems by transforming them into quadratic unconstrained binary optimization (QUBO) problems. However, when constraints are involved, particularly multiple inequality constraints, incorporating them into the objective function poses challenges. In this paper, the authors present two novel approaches for solving problems with multiple inequality constraints on a quantum annealer and apply them to the set cover problem (SCP). The first approach uses the augmented Lagrangian method to represent the constraints, while the second approach employs a higher‐order binary optimization (HUBO) formulation. The experiments show that both approaches outperform the standard approach for solving the SCP on the D‐Wave Advantage quantum annealer. The HUBO formulation performs slightly better than the augmented Lagrangian method in solving the SCP, but its scalability in terms of embeddability in the quantum chip is worse. The results demonstrate that the proposed augmented Lagrangian and HUBO methods can successfully implement a large number of inequality constraints, making them applicable to a broad range of constrained problems beyond the SCP. [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]

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]

Digital economy development is driving the profound revolution in omnichannel retail, yet digital technology inevitably raises privacy concerns. This paper examines the optimal pricing and service strategies for a traditional single‐channel retailer transitioning to omnichannel sales when the market has privacy issues. We construct a nonlinear constrained optimization model to discuss the retailer's optimal gains and pricing when faced with profit‐seeking and privacy‐sensitive consumers during the discount and full‐price periods. Besides, we analyze the influence of item privacy attributes and clients' profit‐seeking or strategic behavior. Several valuable findings are as follows. First, the product's privacy attributes significantly influence retailer's pricing decisions. High‐privacy value goods benefit them in the full‐price period, while common items with low‐privacy attributes are profitable in all sales periods. Second, profit‐seeking (myopic) consumers are the mainstay of the discount period, whereas privacy‐sensitive (strategic) consumers prefer to act in the full‐price period. Lastly, when supported by appropriate privacy services, the strategic actions of privacy consumers also help retailers to optimize profits. [ABSTRACT FROM AUTHOR]

Summary: This article extends the analysis of optimal control based on a generalized Hamiltonian which covers situations of nonconvexity. The approach offers several key advantages. First, by identifying a global solution to a constrained optimization problem, the generalized Hamiltonian approach solves the problem of distinguishing between a global optimum and the (possibly many) nonoptimal points satisfying the Pontryagyn principle under nonconvexity. Second, in our generalized approach, interpreting the slopes of the separating hypersurface as shadow prices of the states continues to hold. Third, we discuss how the generalized Hamiltonian approach can be used in solving dynamic optimization problems under nonconvexity. [ABSTRACT FROM AUTHOR]

This paper proposes a near‐optimal controller design for the constrained nonlinear affine systems based on a Recurrent Neural Network (RNN) and Extended State Observers (ESOs). For this purpose, after defining a finite‐horizon integral‐type performance index, the prediction over the horizon is performed using the Taylor expansion that converts the primary problem into a finite‐dimensional optimization. In comparison with other controllers of the similar structure, the proposed method is capable of dealing with output constraints by employing the Control Barrier Function (CBF). The class of the output and input constraints are of the box‐type. Moreover, whereas several safe control approaches are proposed regardless of the performance of the closed‐loop system, this paper aims at achieving a near‐optimal performance as far as the constraints permit. As a result, a constrained optimization problem is achieved, where the online solution is obtained using a rapidly convergent RNN. Stability and the ease of implementation are some of the advantages of this network making the algorithm more reliable. Moreover, integrated stability analysis of the closed‐loop system that includes the dynamic RNN reveals that the closed‐loop system is stable in the sense of the Lyapunov stability theory. The effectiveness of the proposed control method in terms of the tracking performance and constraint satisfaction is illustrated through a simulating example of two‐inverted pendulums system. The results indicated advantages of the proposed method as compared with the recently published methods in well‐known literature. [ABSTRACT FROM AUTHOR]

Quantum approximate optimization algorithm (QAOA) is a promising variational quantum algorithm for combinatorial optimization problems. However, the implementation of QAOA is limited due to the requirement that the problems be mapped to Ising Hamiltonians and the nonconvex optimization landscapes. Although the Ising Hamiltonians for many NP hard problems have been obtained, a general method to obtain the Ising Hamiltonians for constrained combinatorial optimization problems (CCOPs) has not yet been investigated. In this paper, a general method is introduced to obtain the Ising Hamiltonians for CCOPs and the Metropolis‐Hastings warm‐starting algorithm for QAOA is presented which can provably converge to the global optimal solutions. The effectiveness of this method is demonstrated by tackling the minimum weight vertex cover (MWVC) problem, the minimum vertex cover (MVC) problem, and the maximal independent set problem as examples. The Ising Hamiltonian for the MWVC problem is obtained first time by using this method. The advantages of the Metropolis‐Hastings warm‐starting algorithm presented here is numerically analyzed through solving 30 randomly generated MVC cases with 1‐depth QAOA. [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]

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]

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]

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]

Constrained Markov decision process (CMDP) is a methodology that has not seen wide applications in the literature, but is a more natural specification for modeling preferences in modern service systems. In this paper we present a general framework for solving two‐class CMDPs. In particular, we show that CMDPs can be solved by using the Lagrangian dual to specify a particular unconstrained problem. If an appropriate Lagrange multiplier can be discerned, structural results can be exploited to solve the original CMDP with the appropriate structure. We show that for two queues in parallel or two queues in series, the framework leads to simple threshold‐like optimal policies. The results in each case are used to develop heuristics for analogous problems with abandonments with applications to health care, call centers, and manufacturing systems. The efficacy of the heuristics is verified in each case via a detailed numerical study. [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]

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]

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]

Several applications on fractional order (FO) control have gained considerable significance in the recent years, which led to the evolution of novel tuning strategies of the generalized order FO controllers. Some of the methods in available literatures are based on constrained minimization optimization techniques or analytical method defined only for specific plants. They are valid only for some special model cases. On the contrary, in this technical note, a generalized non‐integer order internal model control (IMC) framework is realized for any order non‐minimum phase (NMP) plants with right half plane (RHP) zero as well as time delayed plants having any finite relative order. Its parameters are graphically interpreted satisfying the frequency domain design stipulations for single input and single output (SISO) higher order linear time invariant (LTI) plants. The performance of the same on a bioreactor fermentation process for its temperature control is found to have outperformed in contrast to its integer order (IO)‐IMC. It is therefore inferred here that this new approach pledges to impart unique solution of the controller parameters, formulating a highly efficient tool outperforming the existing paradigms. Simulation and real time experimentation are presented to validate the method put forward providing satisfactory performance in reference tracking, disturbance rejection, and robustness to various plant parameter perturbations. [ABSTRACT FROM AUTHOR]

Purpose: Varian Ethos utilizes novel intelligent‐optimization‐engine (IOE) designed to automate the planning. However, this introduced a black box approach to plan optimization and challenge for planners to improve plan quality. This study aims to evaluate machine‐learning‐guided initial reference plan generation approaches for head & neck (H&N) adaptive radiotherapy (ART). Methods: Twenty previously treated patients treated on C‐arm/Ring‐mounted were retroactively re‐planned in the Ethos planning system using a fixed 18‐beam intensity‐modulated radiotherapy (IMRT) template. Clinical goals for IOE input were generated using (1) in‐house deep‐learning 3D‐dose predictor (AI‐Guided) (2) commercial knowledge‐based planning (KBP) model with universal RTOG‐based population criteria (KBP‐RTOG) and (3) an RTOG‐based constraint template only (RTOG) for in‐depth analysis of IOE sensitivity. Similar training data was utilized for both models. Plans were optimized until their respective criteria were achieved or DVH‐estimation band was satisfied. Plans were normalized such that the highest PTV dose level received 95% coverage. Target coverage, high‐impact organs‐at‐risk (OAR) and plan deliverability was assessed in comparison to clinical (benchmark) plans. Statistical significance was evaluated using a paired two‐tailed student t‐test. Results: AI‐guided plans were superior to both KBP‐RTOG and RTOG‐only plans with respect to clinical benchmark cases. Overall, OAR doses were comparable or improved with AI‐guided plans versus benchmark, while they increased with KBP‐RTOG and RTOG plans. However, all plans generally satisfied the RTOG criteria. Heterogeneity Index (HI) was on average <1.07 for all plans. Average modulation factor was 12.2 ± 1.9 (p = n.s), 13.1 ± 1.4 (p = <0.001), 11.5 ± 1.3 (p = n.s.) and 12.2 ± 1.9 for KBP‐RTOG, AI‐Guided, RTOG and benchmark plans, respectively. Conclusion: AI‐guided plans were the highest quality. Both KBP‐enabled and RTOG‐only plans are feasible approaches as clinics adopt ART workflows. Similar to constrained optimization, the IOE is sensitive to clinical input goals and we recommend comparable input to an institution's planning directive dosimetric criteria. [ABSTRACT FROM AUTHOR]

This study demonstrates how the linear constrained optimization approach can be used to design a health benefits package (HBP) which maximises the net disability adjusted life years (DALYs) averted given the health system constraints faced by a country, and how the approach can help assess the marginal value of relaxing health system constraints. In the analysis performed for Uganda, 45 interventions were included in the HBP in the base scenario, resulting in a total of 26.7 million net DALYs averted. When task shifting of pharmacists' and nutrition officers' tasks to nurses is allowed, 73 interventions were included in the HBP resulting in a total of 32 million net DALYs averted (a 20% increase). Further, investing only $58 towards hiring additional nutrition officers' time could avert one net DALY; this increased to $60 and $64 for pharmacists and nurses respectively, and $100,000 for expanding the consumable budget, since human resources present the main constraint to the system. [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]

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]

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]

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]

Objective: To simulate the impact on population mental health indicators of allowing people to book some Medicare‐subsidised sessions with psychologists and other mental health care professionals without a referral (direct access), and of increasing the annual growth rate in specialist mental health care capacity (consultations). Design: System dynamics model, calibrated using historical time series data from the Australian Bureau of Statistics, HealthStats NSW, the Australian Institute of Health and Welfare, and the Australian Early Development Census. Parameter values that could not be derived from these sources were estimated by constrained optimisation. Setting: New South Wales, 1 September 2021 – 1 September 2028. Main outcome measures: Projected mental health‐related emergency department presentations, hospitalisations following self‐harm, and deaths by suicide, both overall and for people aged 15–24 years. Results: Direct access (for 10–50% of people requiring specialist mental health care) would lead to increases in the numbers of mental health‐related emergency department presentations (0.33–1.68% of baseline), hospitalisations with self‐harm (0.16–0.77%), and deaths by suicide (0.19–0.90%), as waiting times for consultations would increase, leading to disengagement and consequently to increases in adverse outcomes. Increasing the annual rate of growth of mental health service capacity (two‐ to fivefold) would reduce the frequency of all three outcomes; combining direct access to a proportion of services with increased growth in capacity achieved substantially greater gains than an increase in service capacity alone. A fivefold increase in the annual service growth rate would increase capacity by 71.6% by the end of 2028, compared with current projections; combined with direct access to 50% of mental health consultations, 26 616 emergency department presentations (3.6%), 1199 hospitalisations following self‐harm (1.9%), and 158 deaths by suicide (2.1%) could be averted. Conclusion: The optimal combination of increased service capacity growth (fivefold) and direct access (50% of consultations) would have double the impact over seven years of accelerated capacity growth alone. Our model highlights the risks of implementing individual reforms without knowledge of their overall system effect. [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]