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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]

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]

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]

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]

We propose a likelihood ratio test to assess that sampling has been completed in closed population size estimation studies. More precisely, we assess if the expected number of subjects that have never been sampled is below a user‐specified threshold. The likelihood ratio test statistic has a nonstandard distribution under the null hypothesis. Critical values can be easily approximated and tabulated, and they do not depend on model specification. We illustrate in a simulation study and three real data examples, one of which involves ascertainment bias of amyotrophic lateral sclerosis in Gulf War veterans. [ABSTRACT FROM AUTHOR]

Summary: Recently, workflow applications are increasingly migrated to Function‐as‐a‐Service platforms which are easy to manage, highly‐scalable, and pay‐as‐you‐go. Meanwhile, users face challenges in migration of serverless applications because of the lack of efficient algorithm for workflow memory configuration to optimize the performance. To this end, this article proposes a heuristic urgency‐based algorithm UWC and a meta‐heuristic hybrid algorithm BPSO to tackle the time‐cost tradeoff. UWC sorts functions and allocates each function an appropriate memory size by greedy strategy. BPSO hybridizes particle swarm optimization as well as beetle antennae search algorithm to guide particles to search directionally and utilizes nonlinear inertia weight to avoid local premature convergence. Extensive experiments with classical serverless application demonstrate that UWC and BPSO are very competitive in comparison with existing algorithms as they can find the optimal workflow memory configuration. [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]

We investigate how well different investment strategies can give pre‐retirees more certainty about their income in retirement, whilst allowing them to benefit from taking investment risk. Under an expected utility‐maximizing framework, we find that a loss aversion utility function gives a high degree of certainty about its desired wealth target and is robust to different market models. Imposing terminal wealth constraints does not improve the certainty of achieving the desired target enough to counterbalance the increased chance of obtaining a lower income. The power utility function is not robust to different market models and becomes too risk‐averse with wealth constraints. [ABSTRACT FROM AUTHOR]

Artificial neural networks are generally employed in the numerical solution of differential equation problems. In this article, we propose an approach that deals with the combination of the feed‐forward neural network method and the optimization technique in solving the partial differential equation arising from the valuation of barrier options. The methodology entails transforming the extended Black–Scholes partial differential equations (PDE), which defines a barrier option, into a constrained optimization problem, and then proposing a trial solution that reduces the differential equation problem to an unconstrained one. This trial function consists of the adjustable and non‐adjustable neural network parameters. We design it to be differentiable, analytic, and satisfy the initial and boundary conditions of the corresponding option pricing PDE. We compare the corresponding option values to the Monte‐Carlo simulated values, Crank–Nicolson finite‐difference values and the exact Black–Scholes prices. Numerical results presented in this research show that neural networks can sufficiently solve PDE‐related problems with sufficient precision and accuracy. Furthermore, they can be applied in the fast and accurate valuation of financial derivatives without closed analytic forms. [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 apply an iterative weighting scheme for additive light field synthesis. Unlike previous work optimizing additive light field evenly over viewpoints, we constrain the optimization to deliver a reconstructed light field of high image quality for viewpoints of large weight. [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]

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 feed mass and the filter‐press mass per cabinet (FMP) are uncertain variables in the thickening‐dewatering (TD) process. These uncertain variables must be considered for the optimization; otherwise, the energy economic index (EEI) and the safety risks will increase. Therefore, in this paper, a two‐layer chance‐constrained optimization model for the TD process with uncertain variables is proposed. The optimization model is a sample average approximate‐expected value model (SAA‐EVM), and scenarios are generated by Monte‐Carlo simulation. To reduce the computational time, the optimization model is divided into a two‐layer chance‐constrained optimization model. The computational time is reduced by reducing the dimensions of the decision variables. Simulation results show that this two‐layer chance‐constrained optimization model can reduce the EEI and safety risks and improve the stability of the process, while the computational time meets the requirements of mineral processing plants. [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]

The paper presents a new advanced computational method for ultimate and nominal strength analysis of composite steel‐concrete cross‐sections with arbitrary shape subjected to elevated temperatures. The capacity diagrams are evaluated for a given bending‐moments ratio, generating plane and smooth distribution points on interaction diagrams. The ultimate (maximum) strength capacity is formulated as a problem of constrained mathematical optimization of the total bending moment, whereas the proposed approach evaluates the nominal strength capacity by means of enforcing the nonlinear equilibrium equations in conjunction with a total strain field tangent at the ultimate strain surface. Both methods are unified within the same strain‐driven algorithm used to solve the resulted nonlinear coupled equations. This algorithm coupled with a bracketing approach by means of combining Bisection and Newton method represents the main computational framework to ensure global convergence of the developed methods. An adaptive effective plastic centroid has been introduced ensuring that the origin of the reference axes is within the iso‐load contour circumventing in this way any potential convergence issues. The computational examples prove the effectiveness and the reliability of the proposed method. [ABSTRACT FROM AUTHOR]

This study proposes an extremum‐seeking controller design for unknown static maps subject to a combination of saturated and discrete actuators with unknown characteristics but with measurable final control elements. The proposed design techniques incorporate a filter for each uncertain actuator that enables the design of a constrained extremum‐seeking control that operates at a slow time‐scale. The stability analysis demonstrates that the closed‐loop system has a practically asymptotically stable equilibrium at the unknown constrained optimum of the optimization problem. A simulation is presented that demonstrates the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

Decision support methodologies provide notations for expressing and communicating the priorities that inform a decision. Although a substantial literature has explored the theoretical merits of such notations and methodologies, much less work has investigated their usability in practice, which is of vital importance for their widespread adoption by users. In this paper, we explore the usability of two well‐known preference elicitation techniques, pairwise comparisons and constrained optimization. The techniques were explored through two contrasting crowd worker experiments, a preliminary one evaluating recognition, that is, the ability to identify the most suitable formulation for a given task, and the other synthesis, that is, the ability to construct formulations for a given task. The tasks are based on a case study involving source selection, a well‐known problem in the data integration domain. The results of the empirical evaluation show that, overall, pairwise comparisons resulted in significantly higher performance than constrained optimization, yet there is negligible difference between the usability appraisals for each technique. Furthermore, we observed that the technique that participants perform better with is not necessarily the one that they consider more usable. [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]

Purpose: The orientation distribution function (ODF), which is obtained from the radial integral of the probability density function weighted by rn$$ {r}^n $$ (r$$ r $$ is the radial length), has been used to estimate fiber orientations of white matter tissues. Currently, there is no general expression of the ODF that is suitable for any n value in the HARDI methods. Theory and methods: A novel methodology is proposed to calculate the ODF for any n>−1$$ n>-1 $$ through the Taylor series expansion and a generalized expression for −1

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]

The purpose of this article is twofold. We first develop the first‐order necessary optimality conditions for a general constrained fractional optimal control problem using calculus of variation. These conditions are of the form of fractional ordinary differential equations which reduce to the conventional Euler–Lagrange equations when the dynamical system becomes a first‐order one. Then, we prove, via the optimality conditions established, that a popular penalty method used for conventional constrained optimal control and optimization is an "exact" penalty method for the fractional control problem by showing that an optimal solution to the penalized problem satisfies the optimality conditions of the original one when the penalty parameter is sufficiently large. An example is also provided to verify the necessary optimality conditions. [ABSTRACT FROM AUTHOR]

Environmental concerns motivate the researchers to consider the pollutants emission as an important objective in the cogeneration‐based unit commitment problem (CBUCP). Hence, single objective CBUCP has been extended as a multi‐objective optimization problem (MOP). In the MO CBUC problem (MO‐CBUCP), in which operating costs are optimized along with pollutants. The CBUCP is a nonlinear, mixed‐integer, and highly constrained optimization problem. The nature‐inspired binary and continuous particle swarm optimization (BPSO‐PSO) approach have been applied to deal with binary (ON/OFF) and real variables of the CBUCP, respectively. To attain a global best solution with the minimum CPU burden, an enhanced optimization approach (EOA) based on the combination of conventional and global optimization techniques is also applied. The enhanced successive approximation approach (SAA) is applied to deal with binary variables of the UC problem and global search is employed to search continuous variables. In the MOP, a fuzzy membership approach unifies the different objectives of MO‐CBUCP. The decision‐making method decides the best‐satisfied non‐dominated solution among Pareto optimal solutions. The MO‐CBUCP test system has been undertaken and results reveal that the 'EOA' technique is superior as compared to the BPSO‐PSO approach. It has been examined from results that cogeneration unit has a significant impact on operating cost and pollutants emission of the cogeneration system. [ABSTRACT FROM AUTHOR]

In this study, a multi‐objective and constrained optimization problem is discussed. The SAHRESOpt (multi‐objective and constrained optimization algorithm for SA‐HRES) which includes size optimization and minimization of the loss of power supply probability was developed based on non‐dominated sorting genetic algorithm‐II (NSGA‐II). Additionally, a power management strategy was designed to ensure that the power flow between the system elements minimizes the unmet load and/or the excess energy. In this context, with the aim of obtaining uninterrupted hydrogen energy in the system, a reformer was used transforming methane gas produced by an anaerobic reactor into hydrogen. Thus, a stand‐alone hybrid renewable energy system (SA‐HRES) that does not generate CO2 emissions was designed. Furthermore, within the scope of size optimization, both the types of system elements and the numbers of them were optimized. Then, the positive effects of reformer existence on both of the objective functions, and also the effects of considering the waste energy percentage as a constraint are presented. Also, Pareto solutions of SAHRESOpt and NSGA‐II are compared. Finally, a case study including photovoltaic panels, wind turbines, fuel cells, electrolyzers, hydrogen tanks, and a reformer is presented to prove the effectiveness of the presented algorithm and validate the results. [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]

Summary: The portfolio optimization problem with cardinality constraint is usually solved by exact algorithms, heuristic algorithms, or combinations of them. We decompose the cardinality constraint mean‐variance model, and determine the assets and proportions by double roulette wheel selection (DRWS) and quadratic programming (QP), respectively. Then the accuracy of the solution is improved by a local search after we obtain the preliminary solution by combining DRWS and QP. Experimental results show that the proposed algorithm achieves better accuracy and more efficiency than the algorithms in the literature. Therefore, we can see that the algorithm designed according to the characteristics of specific problems can improve the computational efficiency, but the algorithm needs to be adjusted for different problems. [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]

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]

We present a constrained model‐based optimization and predictive control framework to maximize the production efficiency of batch fermentations based on the core idea of manipulating adenosine triphosphate (ATP) wasting. In many bioprocesses, enforced ATP wasting —rerouting ATP use towards an energetically possibly suboptimal path— allows increasing the metabolic flux towards the product, thereby enhancing product yields and specific productivities. However, this often comes at the expense of lower biomass yields and reduced volumetric productivities. To maximize the overall efficiency, we formulate ATP wasting as a model‐based optimal control problem. This allows for balancing trade‐offs between different objectives such as product yield and volumetric productivity for batch fermentations. Unlike static metabolic control, one obtains a higher degree of flexibility, adaptability, and competitiveness. This can be advantageous towards achieving a sustainable and economically efficient biotechnology industry. To compensate for model‐plant mismatch, disturbances, and uncertainties, we propose not only solving the optimal control problem once. Instead, we exploit the concept of moving horizon model predictive control combined with constraint‐based dynamic modeling to capture the fermentation dynamics. The approach is underlined considering the industrially relevant bioproduction of lactate by Escherichia coli. We discuss practical challenges for the described control strategy and provide an outlook towards future developments. [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]

With the advent of fifth generation (5G) systems and the Internet‐of‐Things (IoT), the number of interconnected wireless devices is increasing significantly. Protocols that allow these deceives to interconnect peer‐to‐peer through wireless links are becoming of interest. The major challenge is the inevitable interference among the simultaneously activated wireless links. Given a set of wireless links, this article addresses the non‐deterministic polynomial‐time (NP) hard problem of selecting the maximum subset of links that can be simultaneously activated at their respective signal‐to‐interference‐plus‐noise‐ratio (SINR) targets. The contribution of this article is two‐fold. First, we introduce a new genetic algorithm (GA) constraint‐handling mechanism, and prove analytically that finding optimal link schedules is guaranteed. Second, we develop a novel parallelized GA to solve the problem. Through serial algorithm analysis, we utilize data decomposition as well as exploratory decomposition in order to achieve significant running time speedup, which scales well with problem size. Our numerical results for openMP parallelization illustrate 6.5× and 5.4× reduction in computation time as compared to the serial versions of the GA and hybrid genetic algorithm (HGA), respectively. Moreover, the parallelization of the GA and HGA result in a speedup of 10.4× and 5.4×, respectively, using master‐slave multithreading. [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]

Purpose: Slice‐wise shimming can improve field homogeneity, but suffers from large noise propagation in the shim calculation. Here, we propose a robust shim current optimization for higher‐order dynamic shim updating, based on Tikhonov regularization with a variable regularization parameter, λ. Theory and Methods: λ was selected for each slice separately in a fully automatic procedure based on a combination of boundary constraints and an L‐curve search algorithm. Shimming performance was evaluated for second order slice‐wise shimming of the brain at 7T, by simulation on a database of field maps from 143 subjects, and by direct measurements in 8 subjects. Results: Simulations yielded on average 36% reduction in the shim current norm for just 0.4 Hz increase in residual field SD as compared to unconstrained unregularized optimization. In vivo results yielded on average 34.0 Hz residual field SD as compared to 34.3 Hz with a constrained unregularized optimization, while simultaneously reducing the shim current norm to 2.8 A from 3.9 A. The proposed regularization also reduced the average step in the shim current between slices. Conclusion: Slice‐wise variable Tikhonov regularization yielded reduced current norm and current steps to a negligible cost in field inhomogeneity. The method holds promise to increase the robustness, and thereby the utility, of higher‐order shim updating. [ABSTRACT FROM AUTHOR]

At the harmonic level, compliance constants are the inverse force constant matrix elements. In the present work, conversion of anharmonic force constants to compliance constants has been revisited and several new variants of the existing equations have been suggested. The reverse conversion of anharmonic compliance constants to force constants is addressed. The change in the internal coordinate (Ri) for constrained optimization is written as a monotonic polynomial function of the change in another chosen constrained internal coordinate (Rk) and the expansion coefficients extracted "directly" are the interaction coordinates (ICs). New expressions for computing the cubic and quartic anharmonic ICs using compliance constants are presented and the obtained numerical values are compared with the ICs extracted by the "direct" method. The work also highlights an effective way of extracting the diagonal harmonic and anharmonic compliance and force/relaxed force constants characterizing the bond in diatomic molecules and pseudo diatomic fragments in a molecule. The ability to compute the mentioned numerical values is likely to open up new possibilities for useful chemical applications. [ABSTRACT FROM AUTHOR]

Summary: This article presents an advanced hybrid algorithm (haDEPSO) for nonlinear constrained function optimization problem. It consists of the advised advanced differential evolution, that is, aDE (wherein a novel mutation, crossover, and selection strategy is introduced, to avoid premature convergence) and particle swarm optimization, namely, aPSO (in which novel gradually varying parameters is utilized, to escape stagnation). The proposed haDEPSO achieve better results as aDE and aPSO provides diverse convergence characteristic to the solution space. Moreover, in haDEPSO distinct population is merged with other in a predefined way, to balance between exploration and exploitation. Efficiency of the proposed hybrid haDEPSO along with its integrating component aDE and aPSO are inspected on IEEE CEC'2006 constrained benchmark functions and IEEE CEC'2011 real world problems. According to the comparison results, the proposed methods achieved better results than traditional DE and PSO with their hybrids as well as over many state‐of‐the‐art algorithms. [ABSTRACT FROM AUTHOR]

In this work, two improvements are proposed for a class of interval‐based state estimators applied to discrete‐time uncertain linear systems subject to additive bounded process and measurement uncertainties. First, we propose to compute the observer gain as a solution of an off‐line constrained nonlinear optimization problem, where the cost function depends on the estimation error width and the constraints ensure the invariance of the estimation error set. Second, to obtain tighter state enclosures, we propose to apply zonotope set computation instead of interval analysis to design a new set‐valued state estimation algorithm. Through simulations, we highlight the interest of the proposed technical improvements. [ABSTRACT FROM AUTHOR]

As an extension of the conventional set‐point control problem, the dynamic region‐based tracking control scheme with obstacle avoidance is proposed for a class of uncertain strict‐feedback non‐linear systems. A novel adaptive tracking controller is designed by a fusion of artificial potential field, recursive backstepping approach, neural networks, dynamic surface control technique, calculus method, and Lyapunov stability theory. In the proposed control scheme, the objective region cannot be required to have a regular shape or a fixed size for the passibility of the system in constrained space. The region tracking error is transformed into a new virtual error variable for recursively designing a dynamic surface controller, and the dimension of neural network inputs can be greatly reduced, especially for high‐order systems. The Lyapunov theorem is used to confirm the stability and uniform boundedness of all closed‐loop signals. Simulation results are provided to demonstrate the effectiveness of the proposed controller. [ABSTRACT FROM AUTHOR]

This article presents an adaptive multi-surrogate constrained optimization method (AMSCOM) that can automatically determine the appropriate metamodel for each black-box function in the constrained optimization problem (COP) and concurrently find the optimum. In AMSCOM, each black-box function is approximated initially by several different types of candidate surrogates. Then, as optimization progresses, the poorly performing candidate surrogates of each black-box function are gradually eliminated until the appropriate surrogate is found. Meanwhile, as more than one candidate surrogate exists for each unknown function in the optimization process, multiple approximate optimization problems (AOPs) can be constructed, and new samples can be obtained by solving these AOPs. Additionally, we employ the genetic operator and the local-linear approximation-Voronoi method to generate new samples. To verify the effectiveness and investigate several properties of AMSCOM, the proposed method is tested on 12 benchmark COPs and compared with several single surrogate-based methods. Furthermore, AMSCOM is compared with several published surrogate-based constrained optimization methods, and the results further prove the superior performance of AMSCOM. The proposed method is then employed to optimize the shaft-clinching process of wheel-hub-bearing units, and a desirable result is achieved. [ABSTRACT FROM AUTHOR]

Policymakers face difficult choices over which health interventions to publicly finance. We developed an approach to health benefits package design that accommodates explicit tradeoffs between improvements in health and provision of financial risk protection (FRP). We designed a mathematical optimization model to balance gains in health and FRP across candidate interventions when publicly financed. The optimal subset of interventions selected for inclusion was determined with bi‐criterion integer programming conditional on a budget constraint. The optimal set of interventions to publicly finance in a health benefits package varied according to whether the objective for optimization was population health benefits or FRP. When both objectives were considered jointly, the resulting optimal essential benefits package depended on the weights placed on the two objectives. In the Sustainable Development Goals era, smart spending toward universal health coverage is essential. Mathematical optimization provides a quantitative framework for policymakers to design health policies and select interventions that jointly prioritize multiple objectives with explicit financial constraints. [ABSTRACT FROM AUTHOR]

Considering structural strength and castability in topology optimization is very attractive from the perspective of theory and application. This article introduces stress considerations into casting‐oriented topology optimization to explore structural optimization methods that simultaneously consider the above two vital design indicators. Two stress‐related topology optimization formulations for castable design are proposed and assessed systematically, namely, a compliance minimization with stress and casting constraints and a stress minimization with casting constraint. An effective optimization algorithm is developed to overcome various numerical difficulties caused by stress and castability issues in the solution. Particularly, a nonuniform threshold scheme along with the corresponding implementation algorithm is proposed to improve the casting constraint on irregular structures without appreciably increased computational effort. Benchmark examples are presented to discuss the numerical characteristics of the achieved designs and demonstrate the effectiveness of the introduced algorithms. This research illustrates the necessity and feasibility of stress considerations in casting‐oriented topology optimization. The results show that it is more appropriate to treat stress as a constraint rather than an optimization objective in the casting‐constrained topology optimization. The proposed formulations and algorithms allow designers to effectively achieve high‐performance castable designs with required structural strength requirements. [ABSTRACT FROM AUTHOR]

This article develops a concurrent topology optimization approach for designing two‐scale hierarchical structures under stress constraints without specifying the topology of the unit cell as a priori. Compared with traditional stress‐constrained topology optimization, the number of stress constraints involved in concurrent topology optimization is much larger and the sensitivity analysis for stress constraints is computationally more expensive. To address these challenges, a novel hierarchical aggregation strategy is proposed to handle the large number of stress constraints and an adjoint method is developed for efficient sensitivity analysis. Several numerical examples are presented to demonstrate the effectiveness of the proposed method. It is also found that the structures obtained by traditional topology optimization usually perform better than the two‐scale structures obtained by concurrent topology optimization when only concentrated loads are considered, while the latter may exhibit better performance in the case that distributed loads are involved. [ABSTRACT FROM AUTHOR]