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In this work, four orthogonal composite designs (orthogonal-array composite designs (OACDs), orthogonal-array composite minimax-loss (OACM) designs, orthogonal uniform composite designs (OUCDs) and orthogonal uniform composite minimax-loss (OUCM) designs) for second-order models were evaluated in the presence of errors for 3 ≤ k ≤ 7 factors with 1 ≤ nc ≤ 3 center points. The design efficiency (in terms of D- and G-efficiency values) and fraction of design space (FDS) plots were used to evaluate the performance of these designs in the presence of errors. The results showed that in terms of D-efficiency values, OACDs and OUCDs performed poorly for k = 6 and 7 factors in the presence of errors while OACM designs were the best-performing designs. The OUCM designs outperformed all the other designs for G-efficiency values with OACM designs as the next best performing designs. The FDS plots showed that OACM and OUCM designs maintained high G-efficiency values in the presence of errors. [ABSTRACT FROM AUTHOR]

Theanalysisoftrajectorydynamicsandthesolutionofoptimizationproblemsusingcomputermethods are relevant areas of research in dynamic population-migration models. In this paper, four-dimensional dynamic models describing the processes of competition and migration in ecosystems are studied. Firstly, we consider a modification of the “two competitors-two migration areas” model, which takes into account uniform intraspecific and interspecific competition in two populations as well as non-uniform bidirectional migration in both populations. Secondly, we consider a modification of the “two competitors-two migration areas” model, in which intraspecific competition is uniform and interspecific competition and bidirectional migration are non-uniform. For these two types of models, the study is carried out taking into account the variability of parameters. The problems of searching for model parameters based on the implementation of two optimality criteria are solved. The first criterion of optimality is associated with the fulfillment of such a condition for the coexistence of populations, which in mathematical form is the integral maximization of the functions product characterizing the populations densities. The second criterion of optimality involves checking the assumption of the such a four-dimensional positive vector existence, which will be a state of equilibrium. The algorithms developed on the basis of the first and second optimality criteria using the differential evolution method result in optimal sets of parameters for the studied population-migration models. The obtained sets of parameters are used to find positive equilibrium states and analyze trajectory dynamics. Using the method of constructing self-consistent one-step models and an automated stochastization procedure, the transition to the stochastic case is performed. The structural description and the possibility of analyzing two types of populationmigration stochastic models are provided by obtaining Fokker-Planck equations and Langevin equations with corresponding coefficients. Algorithms for generating trajectories of the Wiener process, multipoint distributions and modifications of the Runge-Kutta method are used. A series of computational experiments is carried out using a specialized software package whose capabilities allow for the construction and analysis of dynamic models of high dimension, taking into account the evaluation of the stochastics influence. The trajectory dynamics of two types of population-migration models are investigated, and a comparative analysis of the results is carried out both in the deterministic and stochastic cases. The results can be used in the modeling and optimization of dynamic models in natural science.

In this paper, the prediction variance capabilities of two new second-order designs orthogonal uniform composite designs and orthogonal array composite designs are examined using the variance dispersion graph and the fraction of design space plot in the spherical region. Also, the D- and G-optimality criteria are evaluated for these two response surface designs. The orthogonal array composite designs were shown to have a better prediction variance in terms of the fraction of design space plot and the variance dispersion graphs over the orthogonal uniform composite designs. [ABSTRACT FROM AUTHOR]

Objective. The purpose of the study is to substantiate the design criteria for optimality, taking into account the multi-criteria purpose and functioning of the object.Method. The study was carried out on the basis of multicriteria optimization methods, the hierarchy analysis method, the convolution method, and heuristic methods.Result. The paper describes general problems of multicriteria optimization of mechanical systems. The importance of the problem of substantiating the design criteria for optimality, taking into account the multi-criteria purpose and functioning of the object, and introducing quantitatively measurable goals from a variety of alternative options is indicated. It is noted that the choice and formation of a generalized optimality criterion is the most responsible in solving optimization problems. The need to ensure the correctness of the application of one or another convolution method is indicated. Various approaches to the formation of a generalized optimality criterion are analyzed. Their features, advantages and disadvantages are given. The possibility of correcting parametric constraints in problems of improving optimal solutions is pointed out.Conclusion. When solving multi-criteria problems, it is necessary to pay great attention to both the formulation of the problem and the choice of a system of criteria and the implemented method for solving the problem.

Summary: Structural optimization design aims to identify optimal design variables corresponding to a minimum objective function with constraints on performance requirements. To this end, many optimization frameworks have been proposed to determine optimal structural systems that are subjected to seismic and wind hazards in isolation. However, some modern tall buildings are sensitive to seismic and wind excitation owing to their complex structural systems and geographic regions. Therefore, a proper structural optimization method for such buildings is required to ensure that the expected performance is achieved in a multi‐hazard scenario. This study proposes a multi‐objective serviceability design optimization methodology for buildings in multi‐hazard seismic and wind environments by combining optimality criteria and the nondominated sorting genetic algorithm II (NSGA‐II). Seismic and wind effects can be instantaneously updated due to changes in the structural dynamic properties during the optimal design process. A neural‐network‐based surrogate model with self‐updating is proposed to predict the structural natural frequency so that the overall computation time of the optimization process can be reduced. The proposed method was used to optimize a 50‐story frame‐tube building and was compared against the general genetic algorithm and general NSGA‐II to verify the feasibility and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, we considered interval optimization problems for financial investment and optimality criteria. $ UC $ order relation is derived for the considered maximization interval-valued optimization problems. Further, the real-world example of a maximization problem related to investment is given to illustrate the aforesaid results. Moreover, the necessary and sufficient optimality criteria for interval programming problems are derived. [ABSTRACT FROM AUTHOR]

Most of the scientific and industrial experiments usually involve small number of factors, especially biomedical experiments and computer based experiments. We construct some highly useful designs for small number of factors. Designs are constructed using subsets of regular structure and the subsets based on irregular fractions. We compare the various designs on the basis of their robustness to missing design point under minimax loss criterion. To explore some other useful properties designs are also compared on the basis of common alphabetic optimalities. For the investigation of prediction capability of competing designs, we have constructed fraction of design space plots for the variance of difference of response. We observe that some uncommon designs reveal nicer qualities of a good design. It was interesting to see various choices of designs under different optimality criteria. Suggested designs can be highly useful for the experimenters to choose a plan possessing desirable qualities. [ABSTRACT FROM AUTHOR]

Based on a previous concept that has been successfully applied to the sizing optimization of truss and frame structures, this work extends and improves the strain energy criterion in the topology optimization of 2D continuum structures under a single displacement constraint. To make the proposed methodology transparent to other researchers and at the same time meaningful, the numerical value of the displacement constraint was taken to be equal to that obtained through the well-known Solid Isotropic Material with Penalization (SIMP) method under the same boundary conditions and the same external forces. The proposed method is more efficient than the SIMP method while leading to topologies very close to those obtained by the latter.

Subdata selection methods provide flexible tradeoffs between computational complexity and statistical efficiency in analyzing big data. In this work, we investigate a new algorithm for selecting informative subdata from massive data for a broad class of models, including generalized linear models as special cases. A connection between the proposed method and many widely used optimal design criteria such as A-, D-, and E-optimality criteria is established to provide a comprehensive understanding of the selected subdata. Theoretical justifications are provided for the proposed method, and numerical simulations are conducted to illustrate the superior performance of the selected subdata. [ABSTRACT FROM AUTHOR]

Based on a previous concept that has been successfully applied to the sizing optimization of truss and frame structures, this work extends and improves the strain energy criterion in the topology optimization of 2D continuum structures under a single displacement constraint. To make the proposed methodology transparent to other researchers and at the same time meaningful, the numerical value of the displacement constraint was taken to be equal to that obtained through the well-known Solid Isotropic Material with Penalization (SIMP) method under the same boundary conditions and the same external forces. The proposed method is more efficient than the SIMP method while leading to topologies very close to those obtained by the latter. [ABSTRACT FROM AUTHOR]

The possibility of constructing a multi-position direction finding system for the case of a priori uncertainty, based on the application of the principles of multiplication of single marks of the location of the emitting target (multistructure principle) and their subsequent partition into classes (clustering principle) is considered. The criteria and algorithms for detecting the resulting cluster and for constructing the optimal estimation of target location stable to anomalous measurement errors are presented, taking into account the time costs of their computer realization. Practical recommendations and results of comparative analysis of different algorithms are given. [ABSTRACT FROM AUTHOR]

Predator-prey models are often used in ecology to represent realistic encounters between species. Lotka-Volterra differential equations are famously used by ecologists to model the relationship between a predator and prey. Given ecological data collection is known to be time consuming and difficult, the purpose of this paper is to optimize the process and improve sampling efficiency. The method of sequential optimality is applied to a more complex population model with multiple basins of attraction, the Lotka-Volterra differential equations. In this application, various theoretical scenarios are simulated using varying sample sizes and timeframes to determine optimal designs. The first scenario uses a standard sample size and design window to represent a realistic budget for ecological data collection. The second scenario decreases the budget and extends the design window as a representation of a limited budget. The third scenario represents ample resources available for sampling. The three scenarios are used to then compare the optimal designs and help ecologists evaluate the method of sequential optimality. I, A and D optimal designs are compared in the simulation results. The I-optimality criterion tends to outperform the A and D criteria and is recommended as a primary selection when using the sequential optimality algorithm. This simulation study has further developed sequential optimality by predicting optimal sampling regimes according to the dynamics associated with the Lotka-Volterra differential equations. [ABSTRACT FROM AUTHOR]

Optimal designs provide the best experimental conditions, where the researcher should observe or measure a variable of interest. To find these designs, the assumption of uncorrelation in the model's error term is generally required, this allows to easily obtain the Fisher information matrix used in the optimization process for the search for the designs of interest. This article proposes a methodology to compare exact D-optimal designs when the assumption of uncorrelation of the error term in the model is not fulfilled and four covariance structures are taken into consideration to model it. A simplified expression of the Fisher’s information matrix is found for the general case of correlated observations and is used in the four considered covariance structures. With each covariance structure, the respective optimal design is found, known as the nominal design, and the robustness of the other optimal designs is evaluated by finding their efficiency in relation to the nominal design. It is concluded that the four optimal designs are competitive with respect to the other considered covariance structures, by observing a minimal loss of efficiency of each of these designs and showing that the optimal designs, at least with the considered covariance structures, are robust to the choice of the covariance structure. Additionally, it is shown, via simulation, that, with the optimal designs, under each covariance structure, good estimators are obtained for the model parameters when evaluating the magnitude of the coefficient of variation and the relative mean square error. [ABSTRACT FROM AUTHOR]

Ecologists are interested in modeling the population growth of species in various ecosystems. Specifically, logistic growth arises as a common model for population growth. Studying such growth can assist environmental managers in making better decisions when collecting data. Traditionally, ecological data is recorded on a regular time frequency and is very well-documented. However, sampling can be an expensive process due to available resources, money and time. Limiting sampling makes it challenging to properly track the growth of a population. Thus, this design study proposes an approach to sampling based on the dynamics associated with logistic growth. The proposed method is demonstrated via a simulation study across various theoretical scenarios to evaluate its performance in identifying optimal designs that best estimate the curves. Markov Chain Monte Carlo sampling techniques are implemented to predict the probability of the model parameters using Bayesian inference. The intention of this study is to demonstrate a method that can minimize the amount of time ecologists spend in the field, while maximizing the information provided by the data.

Variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of problems arising in pure and applied sciences. In this paper, we introduce and consider a new class of exponentially general variational inequalities. Some new iterative methods are proposed and analyzed using the auxiliary principle technique. Our results present a significant improvement of previously known results for solving variational inequalities and related optimization problems. Several open problems have been suggested for further research in these areas. [ABSTRACT FROM AUTHOR]

Existing criteria for optimal coke quality used in practice in batch formulation are reviewed. The chemical and petrographic parameters of the optimal batches are presented for various Russian coke plants and for the production of high-quality coke. It is found that the economic indices of blast-furnace operation—such as the coke consumption and productivity—depend more on the mechanical strength M10 of the coke than on M25. A cost–quality criterion is proposed for finding the optimal coke. In contrast to previous criteria, the cost–quality criterion is based on a model for M10, ignoring M25. That simplifies the calculations required to find the optimal batch. [ABSTRACT FROM AUTHOR]

Multi criteria optimization of complicated catalytic reactions based on a kinetic model is relevant for both manufacturing and laboratory processes. However, this is not enough just to calculate all effective trajectories, values of variable parameters and optimality criteria. Information about feasible interval for optimal mode changes is important when applying the calculated modes in practice. This article provides mathematical formulation of the task of the Pareto front parameter analysis and solution algorithm. For benzyl butyl ether catalytic synthesis reaction, the conditions multi criteria optimization task was resolved, and acceptable interval of changing the optimal values of temperature, mole ratio of initial reagents and reaction time was calculated in order to prevent significant change of optimality criteria values. [ABSTRACT FROM AUTHOR]

In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as A -, D -, and E -optimal designs. We also give the one-parameter family of optimality criteria which includes these criteria. We then extend a classical result in the design problem, the Kiefer–Wolfowitz theorem, to a qubit system showing the D -optimal design which is equivalent to a certain type of the A -optimal design. We next compare and analyze several optimal designs based on the efficiency. We explicitly demonstrate that an optimal design for a certain criterion can be highly inefficient for other optimality criteria. [ABSTRACT FROM AUTHOR]

Sigmund's 2001 educational paper with a self-contained 99-line MATLAB code had far-reaching impact to teaching and research of topology optimization. This brief note aims to close the gaps on self-contained content desirable for classroom teaching. The goal is to add clarity to the theoretical foundation, and to enable students' learning of the complete iterative optimization solution with minimum additional effort. [ABSTRACT FROM AUTHOR]

In structural optimization, one of the most fascinating fields is Topological Optimization (TO). In this article, the evolutionary topological optimization methods Smoothing Evolutionary Structural Optimization (SESO) and Sequential Element Rejection and Admission (SERA) are used to minimize the growth of compliance using the Method of Moving Asymptotes (MMA). The effect of changing asymptotes is to control the generation of subproblems, which can both stabilize and accelerate the convergence of the overall process. The three-dimensional topological optimization of two large-scale problems: a) a cantilever beam with distributed load, b) an MBB beam and c) a cantilever with concentrated load is performed. Therefore, to solve computational problems such as cost and excess memory, which occur in these types of problems, the Preconditioned Conjugated Gradient Method (PCG) is used as an iterative solver. The results obtained are compared with the Solid Isotropic Material with Penalization (SIMP) that uses for convergence the Optimality Criteria (OC). [ABSTRACT FROM AUTHOR]

In this study, three variants of strain smoothing technique, viz. the cell-based, edge-based, and node-based smoothed finite element method, are employed for structural topology optimization. The salient features of the strain smoothing technique are: (i) does not require an explicit form of shape functions and (ii) less sensitive to mesh distortion. Within the proposed framework, the structural materials are modelled as the relative material density powered by the power-law approach. An optimum structural topology is estimated from the condition that minimizes the total strain energy of the structures of interest. The efficacy and the robustness of the strain smoothing technique, when applied to topology optimization, are demonstrated with a few standard benchmark problems. A systematic parametric study is done to find suitable and optimal control parameters for the topology optimization, viz. filter size, tuning parameter, and move limit. The relative performance of different strain smoothing techniques for structural topology optimization is also presented. [ABSTRACT FROM AUTHOR]

[Objectives] This paper aims to propose an approach for optimization of the multipurpose ice-going ship characteristics and design particulars,considering methodological interdependence among these values. The ship particulars do not appear to be independent in the systemic sense, and any of the characteristics of the size could be predetermined by the definite approximation.[Methods] The methodological approach means the selecting an independent characteristic which is varied in the next for searching its optimal value on the criteria used. It is taken into account the methodological property of superposition of design characteristics as to find the optimal values of the independent design characteristics,the associated balance proportions with the rest of the ship size characteristics and the associated parametric dependences with the design particulars,that means as well determining in the initial approximation of the rest characteristics of ship size and design particulars. Since in the subsequent design stages the refinement are carried out in the narrow intervals of their variation of the approximate values of rest ship size characteristics and design particulars,which were found approximately at the initial stage,corresponding to definite inaccuracy of their approximate determination at the initial stage. The improvement of the originally found values within the inaccuracy does not exert the noticeable influence on the optimum value of the independent design characteristic,determined at the initial stage, serving as the design constraint in the improving of the values of the rest characteristics,as well as its design particulars, found approximately in determining of optimal value of independent design characteristic.[Results] The property of superposition in finding optimal design characteristics and particulars means the possibility of their independent sequential determination if the characteristics found in the previous design stages and particulars are used as the design constraints in subsequent stages.[Conclusions] Initially the characteristics of ship size are determined with the allowance of design constraints,and then the design particulars are sought,while the design constraints are found for ship characteristics.

In this study, the method of inscribed hyperspheres (IHS) is presented and applied for the optimal design of 2-D steel moment frame structures. The weight of the structures, which is a function of the design variables (cross-sectional areas), is optimized subject to stress, displacement, size limits, and the variables' linkage constraints. The IHS approach is employed to find the acceptable centers. The basic idea of this method is to inscribe the largest possible sphere in a closed space that has been created by the objective function and linearized constraints in each step. The obtained results were presented in discrete and continuous variables and compared to the results reported in the literature. This comparison showed the efficiency of this method. Also, a new mixed method of combining the optimality criteria (OC) method and the IHS method is presented in this study. It was observed that the number of iterations needed to reach the optimal solution using this new method is less than that of the above two methods when used individually, and the problem is converged to the optimal answer with extremely low iterations. [ABSTRACT FROM AUTHOR]

We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a single, differentiable one. Then, the problem is sequentially approximated by using MMA-like expansions and an OC-like scheme is tailored to update the variables. The inspection of the stress stiffness matrix leads to a vectorized implementation for its efficient construction and for the sensitivity analysis of the BLFs. This, coupled with the efficiency improvements already presented by Ferrari and Sigmund (Struct Multidiscip Optim 62:2211–2228, 2020a), cuts all the computational bottlenecks associated with setting up the buckling analysis and allows buckling topology optimization problems of an interesting size to be solved on a laptop. The efficiency and flexibility of the code are demonstrated over a few structural design examples and some ideas are given for possible extensions. [ABSTRACT FROM AUTHOR]

In this work, interval programming problems are considered for financial investment and optimality criteria. An order relation, defined by Ishibuchi and Tanaka for maximization problems, is used to obtain the solution of the problems. A real-life example, related to investment, and its solution are given. Necessary and sufficient optimality criteria including weak and strongly solution for interval programming problems are introduced via basic calculus rule, scalarization, and vectorization. [ABSTRACT FROM AUTHOR]

Measures of the prediction variance performances of three variations of central composite designs when the region is hypercube were examined and compared using the G-efficiency and I-optimality criterion so as to determine the economical design(s) that perform(s) better than the other. The hypercube is the multidimensional cuboidal region with the axial distance, α = 1.0 . The designs are the standard central composite designs (CCD), the small composite design (SCD) and minimum run resolution V (minResV) design. Two prediction variance based optimality criteria, I-optimality and G-efficiency were determined, a plot of variance dispersion graph and fraction of design space are used to give a comprehensive picture of the behavior of the prediction variance throughout the region of interest. Comparing the three designs mentioned above for 3, 4, and 5 factors on cuboidal region, the result showed that CCD performed better than SCD and MinResVdesign considering 2, 3, and 5 center points. [ABSTRACT FROM AUTHOR]

In topology optimization, the bisection method is typically used for computing the Lagrange multiplier associated with a constraint. While this method is simple to implement, it leads to oscillations in the objective and could possibly result in constraint failure if proper scaling is not applied. In this paper, we revisit an alternate and direct method to overcome these limitations. The direct method of Lagrange multiplier computation was popular in the 1970s and 1980s but was later replaced by the simpler bisection method. In this paper, we show that the direct method can be generalized to a variety of linear and nonlinear constraints. Then, through a series of benchmark problems, we demonstrate several advantages of the direct method over the bisection method including (1) fewer and faster update iterations, (2) smoother and robust convergence, and (3) insensitivity to material and force parameters. Finally, to illustrate the implementation of the direct method, drop-in replacements to the bisection method are provided for popular Matlab-based topology optimization codes. [ABSTRACT FROM AUTHOR]

When experiments are designed, it is uncommon to use criteria to determine the treatments and number of replicates that should be conducted to properly estimate the parameters in the model under study. This is mainly due to a lack of knowledge of said criteria and, in many other cases, to the difficulty of interpreting them. Optimal designs try to overcome this difficulty by providing optimal experimental conditions and factor levels whose response should be evaluated in order to improve the quality of the statistical inference at a lower cost. Said designs also use optimality criteria, which are functions of the Fisher-information matrix. One of the most common estimation problems in nonlinear models is specifying local values for the parameters of the model, which is necessary to minimice the optimality criterion (King & Wong, 2000) [1]. This work examines the robustness of optimal designs obtained from logistic models when perturbations in the local values of the parameters are considered. The objective is to provide researchers with a wide range of action to select local values while guaranteeing that the efficiency of the resulting optimal designs is not considerably compromised compared to reference values. For that purpose, based on the data of an example, the efficiency of each resulting design was contrasted with the efficiency of unperturbed values. Furthermore, cD-optimal designs were created to estimate the logit variance. The impact of said perturbations on local cD-optimal designs resulted in an efficiency of approximately 70%, with a range of 0.04 of perturbation above the reference value.

The aim of this article is to develop scientific and methodological recommendations on the integral assessment of potential of an enterprise. The achievement of this goal requires solving the following tasks: analysis of the theoretical bases of enterprise potential; analysis of the components of enterprise potential; analysis of methods for assessment of enterprise potential; development of a multi-criteria model for an integral assessment of enterprise potential based on the program- and goal-oriented approach and the theory of utility. In the work the concept of Management by Objectives is used. Enterprise potential management is represented as a multi-level system consisting of several management objects. To study enterprise potential, the program- and goal- oriented approach is used. Based on graph theory, the “tree of goals” of enterprise potential is built. For the formulation and evaluation of goals, expert methods are used. As a criterion of optimality of achieving a goal, it is proposed to use a multi-criteria utility function. In this study, the system of goal-setting corresponds to the combination principle, i.e., it is advisable to use the additive utility function to assess potential of an enterprise. The proposed approach using the multi-criteria utility function makes it possible to calculate the integral indicator of enterprise potential. This allows a comparison of the potential of an enterprise for several years and a comparison of a number of enterprises, as well as identifying the ways for effective growth and use of the potential of an enterprise.

The game-theoretic approach has a vast potential in solving economic problems. On the other hand, the theory of games itself can be enriched by the studies of real problems of decision-making. Hence, this study is aimed at developing and testing the game-theoretic technique to optimize the management of investment planning. This technique enables to forecast the results and manage the processes of investment planning. The proposed method of optimizing the management of investment planning allows to choose the best development strategy of an enterprise. This technique uses the “game with nature” model, and the Wald criterion, the maximum criterion and the Hurwitz criterion as criteria. The article presents a new algorithm for constructing the proposed econometric method to optimize investment project management. This algorithm combines the methods of matrix games. Furthermore, I show the implementation of this technique in a block diagram. The algorithm includes the formation of initial data, the elements of the payment matrix, as well as the definition of maximin, maximal, compromise and optimal management strategies. The methodology is tested on the example of the passenger transportation enterprise of the Sverdlovsk Railway in Ekaterinburg. The application of the proposed methodology and the corresponding algorithm allowed to obtain an optimal price strategy for transporting passengers for one direction of traffic. This price strategy contributes to an increase in the company’s income with minimal risk from the launch of this direction. The obtained results and conclusions show the effectiveness of using the developed methodology for optimizing the management of investment processes in the enterprise. The results of the research can be used as a basis for the development of an appropriate tool and applied by any economic entity in its investment activities.

Considerable academic research has been conducted on truss design optimization by standard metaheuristic methods; however, the generic nature of these methods becomes inefficient for problems with many decision variables. This may explain the simplicity of the relevant test problems in the academic literature in comparison with real structures. To address this challenge, this study advocates a customized optimization methodology which utilizes problem-specific knowledge. It improves upon a new bilevel truss optimization method to allow for an arbitrary trade-off between the stochastic upper level and the deterministic lower level search. Numerical simulations demonstrate that for large-scale truss design problems, the proposed method can find significantly lighter structures up to 300 times more quickly than the best existing metaheuristic methods. The remarkable findings of this study demonstrate the importance of using engineering knowledge and discourage future research on the development of purely metaheuristic methods for truss optimization. [ABSTRACT FROM AUTHOR]

In this paper, we formulate the active SLAM paradigm in terms of model-free Deep Reinforcement Learning, embedding the traditional utility functions based on the Theory of Optimal Experimental Design in rewards, and therefore relaxing the intensive computations of classical approaches. We validate such formulation in a complex simulation environment, using a state-of-the-art deep Q-learning architecture with laser measurements as network inputs. Trained agents become capable not only to learn a policy to navigate and explore in the absence of an environment model but also to transfer their knowledge to previously unseen maps, which is a key requirement in robotic exploration. [ABSTRACT FROM AUTHOR]

Technological assurance and improvement of the economic efficiency of production are the first-priority issues for the modern manufacturing engineering area. It is possible to achieve a higher value of economic efficiency in multiproduct manufacturing by multicriteria optimization. A set of optimality criteria based on technological and economic indicators was defined with the aim of selecting the optimal manufacturing process. Competitive variants and a system of optimization were developed and investigated. A comparative analysis of the optimality criteria and their influence on the choice of optimal machining processes was carried out. It was determined that the batch of parts made an impact on the selection of the manufacturing process. [ABSTRACT FROM AUTHOR]

We study the sensitivity of some optimality criteria based on progressively type-II right censored order statistics scheme changes and explain how the sensitivity analysis helps to find the optimal censoring schemes. We find that determining an optimal censoring plan among a class of one-step censoring schemes is not always recommended. We consider optimality criteria as the model output of a sensitivity analysis problem and quantify how this model depends on its input factor and censoring scheme, using local and global sensitivity methods. Finally, we propose a simple method to find the optimal scheme among all possible censoring schemes. [ABSTRACT FROM AUTHOR]

Inferential sensing is a cost-effective and reliable approach to replace expensive and impractical hardware sensing, while yielding robust fault detection and isolation (FDI) during system maintenance or operation. Yet, their high computational footprint necessitates the employment of advanced and efficient estimation techniques, along with symbolic mathematics and automatic differentiation. Herein, we attempt to combine model-driven sensor selection methods with inferential sensing to accurately identify faults in the presence of system noise and uncertainty. During sensor selection, we employ criteria from information theory to maximize the estimability of system faults from available system measurements. The most informative sensor set stems from a comparison of all possible sensor suites via information theoretic criteria expressed as functions of the Fisher Information Matrix. Optimal inferential sensors are calculated through a novel fusion of symbolic regression and information theory. For built-in test deployment, we utilize k -Nearest Neighbors classification to assess the capability of each sensor suite for all plausible instantiations of uncertainty and system noise, and evaluate FDI performance benefits from the inclusion of inferential sensor(s). The proposed computational framework is deployed with steady-state and dynamic models of a cross-flow plate-fin heat exchanger, at varying levels of measurement noise and uncertainty. As shown, the augmented system of composite sensors (i.e., inferential and hardware) provides accurate information on system fault(s) and reduces the evidence of uncertainty. Compared to traditional sensor approaches, the proposed techniques are shown to be more precise while simultaneously granting increased insight into details otherwise hidden by noise. Thus, they form a robust and reliable tool when conducting fault diagnosis and possibly toward system safety. • Fault identification from symbolically regressed inferential sensors. • Explainable inferential sensors derived with information-theoretic objective functions. • Inferential sensors are robust to system uncertainty and noise. • Symbolically regressed sensors provide better fault classification. [ABSTRACT FROM AUTHOR]

This work proposes an evaluation – through data simulations – of optimality criteria A and D in mixture designs built from a rotational design, considering a normal model and exploring the edge of zero in parts of simplex components, in addition to the analysis of the use of inverse terms in such components. As a function of the mathematical restrictions imposed on such designs, rotationality is obtained by following a specific algebraic procedure, thus preserving the constant prediction variance in all experimental points. When it comes to mixture problems, a response may show extreme alterations when a part of such components tends to the edge of zero and the models may not be suitable to deal with that. The adequate alternative to deal with such response alterations is to include inverse terms into the models. Given the assessed scenarios, the optimum designs were more robust and more promising than the rotational ones, when evaluating the precision of residual mean squares (RMS) in all such scenarios. When a part of the components tends to the edge of zero, RMS was more precise under the D-optimum designs with inverse terms in the components of the normal lineal model.

In this work, set-valued optimization problems are considered according to an order relation, which is a partial order on the family such that contains nonempty bounded sets of the space. A generalized convexity is defined for set-valued mapping by using the partial order relation. Nonsmooth variational inequality problems are introduced with the aid of M-directionally derivative. Some optimality criteria including the necessary and sufficient optimality conditions are obtained for mentioned optimization problems. [ABSTRACT FROM AUTHOR]

In his pioneering work on Abstract Argumentation, P.M. Dung set a wide scenario by connecting stable models in Logic and Game Theory to simple Abstract Argumentation Frameworks (AAF), which are essentially directed graphs in which arguments are represented as nodes, and the attack relation is represented by arrows. From such abstraction and simplicity, it is possible to capture important properties in many different fields. The Stable Marriage (SM) problem is exactly one of such representable problems. Given two sets of individuals partitioned into men and women, a matching is stable when there does not exist any man-woman match by which both man and woman would be individually better off than they are with the person to which they are currently matched. Stable matchings correspond to stable extensions if an AAF is correctly generated from the given SM problem. In this paper we elaborate on the original formulation by Dung, by also encoding SM problems with ties and incomplete preference lists into AAFs. Moreover, we use Weighted Abstract Argumentation to represent optimality criteria in the optimal extension of SM problems, where some matchings are better than others: criteria may consider only the preference of either men, or women, or a more global view obtained by combining the preferences of both. [ABSTRACT FROM AUTHOR]

• An Optimality Criteria method was proposed for the wind resistant structural optimization of a portal steel frame. • The GLF based, single objective LRC-based and multiple objective universal-based ESWLs were derived for the large-span portal frame. • The effect of different forms of ESWLs, the stiffness of support restraint and semi-rigid connection on the optimized results were analyzed. • The optimized section heights of rafters and columns for minimum structural weight were obtained under wind-induced drift constraint. Large span portal-rigid frames with tapered sections in low-rise metal building system are often used in industrial and commercial buildings. The drift of such portal-rigid frames induced by the wind load needs to be smaller than a prescribed limit, and at the same time the frames should be as light as possible for cost-effectiveness. To this end, structural optimization of such portal-rigid frames subjected to the wind-induced drift constraint is required. However, little research for optimization of the large span portal-rigid frame with tapered sections has been reported. This paper proposed a procedure for structural optimization of such portal-rigid frames by adopting the Optimality Criteria (OC) method. Based on an aerodynamic database of the measured wind pressure from a wind tunnel test, several forms of the Equivalent Static Wind Load (ESWL) acting on a large-span portal-rigid frame were evaluated by the Gust Loading Factor (GLF), Load Response Correlation (LRC) and Proper Orthogonal Decomposition (POD) method. The method of virtual-work was utilized to construct the wind-induced drift or displacement. An effective iteration algorithm was derived for the minimum weight optimization of the frame while all wind-induced drift constraints were satisfied. The wind resistant structural optimization for the large-span rigid frame with taped section were conducted when it was bore by different forms of ESWL (GLF based, single objective and multiple objective ESWLs), and their optimized results were multi-compared in the form of the optimized total weight and the height of the optimized structural members. The effects of the connection stiffness at semi-rigid joints and the stiffness of support restraints on the optimized results are also investigated. Finally the global optimality property of the proposed OC method adopted for the optimized case in this paper was also discussed and verified. Optimized results show that the OC optimization procedure proposed in this paper is very effective for the optimization design of large-span portal-rigid steel frames with tapered sections under wind-induced drift constraints. [ABSTRACT FROM AUTHOR]

In probabilistic robust optimization problems we generally take as objective function the weighted sum of the expected value and the standard deviation of the performance. Unfortunately, it has been observed that if the weight given to the standard deviation is too high, then the designs obtained may have no physical meaning at all. If this occurs we say that the design obtained is not consistent from the physical point of view. In this work we present a probabilistic robust optimization approach aimed to preserve physical consistency of the problem being addressed. The objective function is written as the p -norm of a vector composed of the expected value and the weighted standard deviation. We then demonstrate that the standard approach is a particular case of this p -norm approach with p = 1. In the proposed approach we take p = 2 and prove that physical consistency is ensured provided the standard deviation is not given more weight than the expected value. A similar proof is not available for the standard approach. This makes statement of the robust optimization problem much easier with the proposed approach. The proposed approach can be adapted into existing computational routines, since the same statistical moments and sensitivities are required. The theoretical results are illustrated in the context of compliance-based topology optimization. In the numerical examples we show that the concept of physical consistency may have a significant impact on the designs obtained. • A discussion on physical consistency of robust optimization is presented. • An approach that is always consistent is proposed. • Theoretical results are illustrated in the context of compliance-based topology optimization. [ABSTRACT FROM AUTHOR]

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This study developed a new framework by correlating the clinical measurements in vivo with numerical modeling in silico at different time points for quantifying the magnitudes and directions of oral muscle forces. The human masticatory system has received significant attention in the areas of biomechanics due to its sophisticated co-activation of a group of masticatory muscles which contribute to the fundamental oral functions. However, determination of each muscular force remains fairly challenging in vivo ; the conventional data available may be inapplicable to patients who experience major oral interventions such as maxillofacial reconstruction, in which the resultant unsymmetrical anatomical structure invokes a more complex stomatognathic functioning system. Therefore, this study aimed to (1) establish an inverse identification procedure by incorporating the sequential Kriging optimization (SKO) algorithm, coupled with the patient-specific finite element analysis (FEA) in silico and occlusal force measurements at different time points over a course of rehabilitation in vivo ; and (2) evaluate muscular functionality for a patient with mandibular reconstruction using a fibula free flap (FFF) procedure. The results from this study proved the hypothesis that the proposed method is of certain statistical advantage of utilizing occlusal force measurements, compared to the traditionally adopted optimality criteria approaches that are basically driven by minimizing the energy consumption of muscle systems engaged. Therefore, it is speculated that mastication may not be optimally controlled, in particular for maxillofacially reconstructed patients. For the abnormal muscular system in the patient with orofacial reconstruction, the study shows that in general, the magnitude of muscle forces fluctuates over the 28-month rehabilitation period regardless of the decreasing trend of the maximum muscular capacity. Such finding implies that the reduction of the masticatory muscle activities on the resection side might lead to non-physiological oral biomechanical responses, which can change the muscular activities for stabilizing the reconstructed mandible. [ABSTRACT FROM AUTHOR]

Step‐stress accelerated degradation testing (SSADT) has become a common approach to predicting lifetime for highly reliable products that are unlikely to fail in a reasonable time under use conditions or even elevated stress conditions. In literature, the planning of SSADT has been widely investigated for stochastic degradation processes, such as Wiener processes and gamma processes. In this paper, we model the optimal SSADT planning problem from a Bayesian perspective and optimize test plans by determining both stress levels and the allocation of inspections. Large‐sample approximation is used to derive the asymptotic Bayesian utility functions under 3 planning criteria. A revisited LED lamp example is presented to illustrate our method. The comparison with optimal plans from previous studies demonstrates the necessity of considering the stress levels and inspection allocations simultaneously. [ABSTRACT FROM AUTHOR]

This work proposes an evaluation - through data simulations - of optimality criteria A and D in mixture designs built from a rotational design, considering a normal model and exploring the edge of zero in parts of simplex components, in addition to the analysis of the use of inverse terms in such components. As a function of the mathematical restrictions imposed on such designs, rotationality is obtained by following a specific algebraic procedure, thus preserving the constant prediction variance in all experimental points. When it comes to mixture problems, a response may show extreme alterations when a part of such components tends to the edge of zero and the models may not be suitable to deal with that. The adequate alternative to deal with such response alterations is to include inverse terms into the models. Given the assessed scenarios, the optimum designs were more robust and more promising than the rotational ones, when evaluating the precision of residual mean squares (RMS) in all such scenarios. When a part of the components tends to the edge of zero, RMS was more precise under the D-optimum designs with inverse terms in the components of the normal lineal model. [ABSTRACT FROM AUTHOR]

SAP2000 is well-known commercial software for analysis and design of structural systems that is equipped with an open application programming interface (OAPI). In this work, a code written in C# able to solve three-dimensional topology optimization problems is presented, where a topology optimization framework was integrated into SAP2000 taking advantage of its OAPI feature. The code is partially based on the 99 and 88 line codes written by Sigmund (Struct Multidiscip Optim 21(2):120-127, 2001) and Andreassen et al. (Struct Multidiscip Optim 43(1):1-16, 2011). The code solves the problem of minimum compliance while through OAPI it takes advantage of all modelling capabilities of SAP2000. The paper covers the theoretical aspects of topology optimization incorporated in the code and provides detailed description of their numerical implementations. Special effort was made to the latter one, describing in detail all numerical aspects of the code, in order to facilitate the reader to understand the code, and therefore being able to further enhance its capabilities. The complete code can be downloaded from GitHub (https://github.com/nikoslagaros/TOCP). [ABSTRACT FROM AUTHOR]

The popularity of precast concrete in construction is rising due to its capacity for improving building efficiency and quality in comparison to cast-in-situ concrete. While researchers have focused on enhancing constructability factors like logistics and sequencing, the need for developing standardization in this area remains evident. This paper describes a framework for studying the relationship between construction cost and standardization by optimizing precast component dimensions and rebar designs. The framework involves using Building Information Modeling techniques to extract semantic information from architectural plans, followed by a gradient-based Optimality Criteria method to optimize the sizing variables of precast components. Finally, a hybrid approach called NSGA-II-GD, which combines the Non-dominated Sorting Genetic Algorithm II and Great Deluge Algorithm, is used to optimize the rebar layout design of each precast component. The Results demonstrate that an optimal point exists between construction cost and standardization, particularly for components subjected to similar stresses. Additionally, the NSGA-II-GD algorithm improves the searching efficiency in terms of convergence, computational time, and searching space. • Develop a BIM-based framework for structural design optimization of precast elements. • Formulate the design optimization of construction cost and constructability of precast elements. • Integrate the Optimality Criteria method with NSGA-II-GD for element sizing and rebar detailing optimization. • Integrate NSGA-II with the Great Deluge Algorithm for rebar detailing optimization. • Show that the proposed method can identify the best trade-off for the precast building design. [ABSTRACT FROM AUTHOR]

The article shows that the estimation (forecasting) of the values of random variables, according to the minimum variance estimation error is not always effective, and sometimes not even possible. The authors give examples to prove it. The estimation is described with a functional. The task of the estimation is treated as a search for an optimal solution and is illustrated with formation of the optimal playing strategy.