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This study explores a Robust, Risk-aware, Resilient, and Sustainable Closed-Loop Supply Chain Network Design (3RSCLSCND) to tackle demand fluctuation like COVID-19 pandemic. A two-stage robust stochastic multiobjective programming model serves to express the proposed problems in formulae. The objective functions include minimising costs, CO2 emissions, energy consumption, and maximising employment by applying Conditional Value at Risk (CVaR) to achieve reliability through risk reduction. The Entropic Value at Risk (EVaR) and Minimax method are used to compare with the proposed model. We utilise the Lp-Metric method to solve the multiobjective problem. Since this model is complex, the Lagrange relaxation and Fix-and-Optimise algorithm are applied to find lower and upper bounds in large-scale, respectively. The results confirm the superior power of the model offered in estimating costs, energy consumption, environmental pollution, and employment level. This model and algorithms are applicable for other CLSC problems. [ABSTRACT FROM AUTHOR]

In this work, we provide discrete optimality conditions of the optimal control problems of stochastic differential equations. Euler and Runge–Kutta methods are used for discretization. A Lagrange multiplier method for a discrete-time stochastic optimal control problem is formulated. The discrete adjoint process p n is obtained in terms of conditional expectations E [ p n + 1 ] and E [ p n + 1 Δ W ] for both methods. To estimate these nested conditional expectations at each time step via simulation, we use a very powerful new approach, least-squares Monte-Carlo method, developed by Longstaff–Schwartz. This is the first time to solve a stochastic optimal control problem by calculating the nested conditional expectations numerically with the help of a least-squares Monte-Carlo method. Some examples are studied to test and demonstrate the efficiency of the Lagrange multiplier combined with the least-squares Monte-Carlo method. [ABSTRACT FROM AUTHOR]

Neuroscience is a combination of different scientific disciplines which investigate the nervous system for understanding of the biological basis. Recently, applications to the diagnosis of neurodegenerative diseases like Parkinson's disease have become very promising by considering different statistical regression models. However, well-known statistical regression models may give misleading results for the diagnosis of the neurodegenerative diseases when experimental data contain outlier observations that lie an abnormal distance from the other observation. The main achievements of this study consist of a novel mathematics-supported approach beside statistical regression models to identify and treat the outlier observations without direct elimination for a great and emerging challenge in humankind, such as neurodegenerative diseases. By this approach, a new method named as CMTMSOM is proposed with the contributions of the powerful convex and continuous optimization techniques referred to as conic quadratic programing. This method, based on the mean-shift outlier regression model, is developed by combining robustness of M-estimation and stability of Tikhonov regularization. We apply our method and other parametric models on Parkinson telemonitoring dataset which is a real-world dataset in Neuroscience. Then, we compare these methods by using well-known method-free performance measures. The results indicate that the CMTMSOM method performs better than current parametric models. [ABSTRACT FROM AUTHOR]

We have Derringer and Suich's desirability functions in mind, especially, the two-sided ones in our analysis throughout this study. We propose and develop a finite partitioning procedure of the individual desirability functions over their compact and connected interval which leads to the definition of generalized desirability functions. We call the negative logarithm of an individual desirability function having a max-type structure and including a finite number of nondifferentiable points as a generalized individual desirability function. By introducing continuous selection functions into desirability functions and, especially, employing piecewise max-type functions, it is possible to describe some structural and topological properties of these generalized functions. Our aim with this generalization is to show the mechanism that gives rise to a variation and extension in the structure of functions used in classical desirability approaches. [ABSTRACT FROM AUTHOR]

This paper aims to develop a robust multi-item EPQ formulation considering rework process and imperfect items. The mathematical model consists of two objective functions targeting minimization of total inventory costs and the total required warehouse space, respectively. Since, in real-world applications, parameters of the mathematical formulation are due to uncertainty, in this paper, Basic Chance Constraint Programming and Robust Fuzzy Chance Constraint Programming models are developed to handle uncertainties in both objective function and constraints. By solving examples, the superiority of the RFCCP over the BCCP model is showed and its ability to provide risk-averse solutions is ensured. Due to the nonlinearity of the RFCCP model and to provide the decision maker with the Pareto front, two algorithms, namely, Multi-Objective Grey Wolf Optimizer and Multi-Objective Water Cycle Algorithm, are used to optimize the decision variables. The performance of the algorithms is evaluated within different large-size test problems, using diversity, Spacing, number of non-dominated solutions and CPU-time. In the end, to investigate significant differences and to determine the best algorithm ANOVA test is implemented. In the end, we also offer new research directions, e.g. in terms of further ways of uncertainty modelling and risk management. [ABSTRACT FROM AUTHOR]

Networked materials and micro-architectured systems gain increasingly importance in multi-scale physics and engineering sciences. Typically, computational intractable microscopic models have to be applied to capture the physical processes and numerous transmission conditions at singularities, interfaces and borders. The topology of the periodic microstructure governs the effective behaviour of such networked systems. A mathematical concept for the analysis of microscopic models on extremely large periodic networks is developed. We consider microscopic models for diffusion–advection–reaction systems in variational form on periodic manifolds. The global characteristics are identified by a homogenization approach for singularly perturbed networks with a periodic topology. We prove that the solutions of the variational models on varying networks converge to a two-scale limit function. In addition, the corresponding tangential gradients converge to a two-scale limit function for vanishing lengths of branches. We identify the variational homogenized model. Complex network models, previously considered as completely intractable, can now be solved by standard PDE-solvers in nearly no time. Furthermore, the homogenized coefficients provide an effective characterization of the global behaviour of the variational system. [ABSTRACT FROM AUTHOR]

The goal in inverse electrocardiography (ECG) is to reconstruct cardiac electrical sources from body surface measurements and a mathematical model of torso-heart geometry that relates the sources to the measurements. This problem is ill-posed due to attenuation and smoothing that occur inside the thorax, and small errors in the measurements yield large reconstruction errors. To overcome this, ill-posedness, traditional regularization methods such as Tikhonov regularization and truncated singular value decomposition and statistical approaches such as Bayesian Maximum A Posteriori estimation and Kalman filter have been applied. Statistical methods have yielded accurate inverse solutions; however, they require knowledge of a good a priori probability density function, or state transition definition. Minimum relative entropy (MRE) is an approach for inferring probability density function from a set of constraints and prior information, and may be an alternative to those statistical methods since it operates with more simple prior information definitions. However, success of the MRE method also depends on good choice of prior parameters in the form of upper and lower bound values, expected uncertainty in the model and the prior mean. In this paper, we explore the effects of each of these parameters on the solution of inverse ECG problem and discuss the limitations of the method. Our results show that the prior expected value is the most influential of the three MRE parameters. [ABSTRACT FROM AUTHOR]

Desirability functions (DFs) are commonly used in optimization of design parameters with multiple quality characteristic to obtain a good compromise among predicted response models obtained from experimental designs. Besides discussing multi-objective approaches for optimization of DFs, we present a brief review of literature about most commonly used Derringer and Suich type of DFs and others as well as their capabilities and limitations. Optimization of DFs of Derringer and Suich is a challenging problem. Although they have an advantageous shape over other DFs, their nonsmooth nature is a drawback. Commercially available software products used by quality engineers usually do optimization of these functions by derivative free search methods on the design domain (such as Design-Expert), which involves the risk of not finding the global optimum in a reasonable time. Use of gradient-based methods (as in MINITAB) after smoothing nondifferentiable points is also proposed as well as different metaheuristics and interactive multi-objective approaches, which have their own drawbacks. In this study, by utilizing a reformulation on DFs, it is shown that the nonsmooth optimization problem becomes a nonconvex mixed-integer nonlinear problem. Then, a continuous relaxation of this problem can be solved with nonconvex and global optimization approaches supported by widely available software programs. We demonstrate our findings on two well-known examples from the quality engineering literature and their extensions. [ABSTRACT FROM AUTHOR]

Desirability functions are increasingly used in multi-criteria decision-making which we support by modern optimization. It is necessary to formulate desirability functions to obtain a generalized version with a piecewise max type-structure for optimizing them in different areas of mathematics, operational research, management science and engineering by nonsmooth optimization approaches. This optimization problem needs to be robustified as regression models employed by the desirability functions are typically built under lack of knowledge about the underlying model. In this paper, we contribute to the theory of desirability functions by our robustification approach. We present how generalized semi-infinite programming and disjunctive optimization can be used for this purpose. We show our findings on a numerical example. The robustification of the optimization problem eventually aims at variance reduction in the optimal solutions. [ABSTRACT FROM AUTHOR]

In our study, we integrate the data uncertainty of real-world models into our regulatory systems and robustify them. We newly introduce and analyse robust time-discrete target–environment regulatory systems under polyhedral uncertainty through robust optimization. Robust optimization has reached a great importance as a modelling framework for immunizing against parametric uncertainties and the integration of uncertain data is of considerable importance for the model’s reliability of a highly interconnected system. Then, we present a numerical example to demonstrate the efficiency of our new robust regression method for regulatory networks. The results indicate that our approach can successfully approximate the target–environment interaction, based on the expression values of all targets and environmental factors. [ABSTRACT FROM AUTHOR]

Spatial technologies offer high flexibility to handle substantial amount of spatial data and wide range of modelling capabilities. Remotely sensed data are the most significant data source used in spatial technologies. However, it is often associated with uncertainties due to atmospheric effects (i.e. absorption and scattering by atmospheric gases and aerosols). Methods based on rigorous treatment of radiative transfer models still have some drawbacks in the inversion of top of atmospheric reflectance values to surface reflectance values on large numbers of satellite images. In this paper, our aim is to represent a more flexible (adaptive) approach for the regional atmospheric correction by employing nonparametric regression splines within the frame of inverse problems and modern techniques of continuous optimization. To achieve this objective, atmospheric correction models obtained through conic multivariate adaptive regression splines, which is an alternative method to multivariate adaptive regression splines by constructing a penalized residual sum of squares as a Tikhonov regularization problem, are applied on a set of satellite images in order to convert the top of atmospheric reflectance values into surface reflectance values. The results are compared with the ones obtained by both multivariate adaptive regression splines and a radiative transfer-based method. [ABSTRACT FROM PUBLISHER]

No equipment (system) can be perfectly reliable in spite of the utmost care and best efforts on the part of the designer, decision-maker and manufacturer. The two sides of maintenance arecorrectiveandpreventivemaintenance. It is generally assumed that a preventive maintenance action is less costly than a repair maintenance action. We examine this proposition in detail on the basis of a failure-time model that relates conformance quality to reliability. Illustratively, we present reliability in the context of contracts with asymmetric information. The model shows how to overcome information rents through price distortions and quantity rationing. The paper ends with a conclusion and an outlook to future studies. [ABSTRACT FROM PUBLISHER]

Ground Motion Prediction Equations (GMPEs) are empirical relationships which are used for determining the peak ground response at a particular distance from an earthquake source. They relate the peak ground responses as a function of earthquake source type, distance from the source, local site conditions where the data are recorded and finally the depth and magnitude of the earthquake. In this article, a new prediction algorithm, called Conic Multivariate Adaptive Regression Splines (CMARS), is employed on an available dataset for deriving a new GMPE. CMARS is based on a special continuous optimization technique, conic quadratic programming. These convex optimization problems are very well-structured, resembling linear programs and, hence, permitting the use of interior point methods. The CMARS method is performed on the strong ground motion database of Turkey. Results are compared with three other GMPEs. CMARS is found to be effective for ground motion prediction purposes. [ABSTRACT FROM AUTHOR]

Regression analysis is a widely used statistical method for modelling relationships between variables. Multivariate adaptive regression splines (MARS) especially is very useful for high-dimensional problems and fitting nonlinear multivariate functions. A special advantage of MARS lies in its ability to estimate contributions of some basis functions so that both additive and interactive effects of the predictors are allowed to determine the response variable. The MARS method consists of two parts: forward and backward algorithms. Through these algorithms, it seeks to achieve two objectives: a good fit to the data, but a simple model. In this article, we use a penalized residual sum of squares for MARS as a Tikhonov regularization problem, and treat this with continuous optimization technique, in particular, the framework of conic quadratic programming. We call this new approach to MARS as CMARS, and consider it as becoming an important complementary and model-based alternative to the backward stepwise algorithm. The performance of CMARS is also evaluated using different data sets with different features, and the results are discussed. [ABSTRACT FROM AUTHOR]

Nowadays, the importance of financial crises and defaults of countries are becoming clear due to the globalization in the economic area and investments. Generalized partial linear model (GPLM) is a combination of two different regression models connecting with the mean of the dependent variable with the help of a link function. It is adequate to high-dimensional, non-normal data sets having the flexibility to reflect all anomalies effectively. The nonlinear patterns are also easily explained by the nonparametric component of the model. In this study, we introduce a newly developed conic GPLM (CGPLM) to predict default probabilities of 45 emerging markets using the contribution of a continuous model CMARS and a discrete model logistic regression. We present its application results on a data set with 13 macroeconomic variables in 25 years’ time. To predict debt crises, CGPLM gives better results than a single CMARS and a single logistic regression. In fact, we have 91.81% and 89.31% accuracy rates, computed according to the correctness of the model output, for training and validation sample, respectively. This improvement in prediction of crises can contribute to new prospects and developments in financial mathematics to make more accurate previsions for investments and to take measures due to coming risks. [ABSTRACT FROM PUBLISHER]

Human facial soft tissue is modelled by a dynamic volume spline and the parameters of this model are estimated from the actual human facial skin properties by the optimization-based inverse solution. In the literature, various compressive force-displacement experiments are conducted and the parameters of the proposed models are estimated from the actual force and the corresponding displacement values measured during the experiments. Different from the common techniques in the literature, the displacement is measured in this study not only for the point of force contact with the surface but also for the region around the contact point. This is done by 3D reconstructing the shape of the compressed surface from the multiple camera views. This data is very suitable for estimating the parameters of the dynamic volume spline model by using an optimization-based inverse solution. The inverse solution is tested for various simulations starting from various initial conditions. Also, the inverse solution is applied to the real data collected during the experiments. When the model is used with the estimated parameter values, it behaves in a very similar way to the actual tissue characteristic which is obtained during the force-displacement experiment. Finally, the estimated parameters are used to model and animate the human face for various forehead expressions. [ABSTRACT FROM AUTHOR]

Soft tissue models are of many types, but each type has its own problems in terms of realistic appearance and computational efficiency. In this study, we propose a hybrid model based on dynamic volume splines which combine the advantages of these models. To simulate a realistic appearance, biomechanical properties of the real tissue are obtained by force-displacement experiments and used to tune the parameters of the model. Unlike the usual types described in the literature, a new experiment is proposed where displacement is measured not only for the point of force application but also for the region around the applied force. In our study, multiple camera views were used to enable 3D reconstruction of the surface. The differences arising between the surfaces obtained before and after the application of force were then used in optimization-based inverse solution methods, and the estimated parameters were found to be consistent with the biomechanical tissue properties described in the literature. [ABSTRACT FROM AUTHOR]

A centrally important research area of computational biology, biotechnology – and life sciences at all – is devoted to modelling, prediction and dynamics of gene-expression patterns. However, this enterprise cannot be investigated in a satisfying way without the role of the environment, including the societies, members of the international community of nations. For a representation of the past, present and predicted future states, we also acknowledge the existence of uncertainties in modern technology and decision making, and the negotiations in solving societal problems and in international collaboration. We survey and closer explain recent advances in understanding the mathematical foundations and interdisciplinary implications of the newly introduced gene-environment networks; the main basis of our article is (Weber, Alparslan-Gök and Söyler [to appear]). We integrate the important theme of environmental protection by joint international projects into the context of networks and their dynamics. As an example of environmental protection, we study CO2 emissions, their implications for global warming by green-house effect, the reduction of both and the joint implementation requested for this purpose by Kyoto protocol. Given data from DNA microarray experiments and environmental records, we extract nonlinear ordinary differential equations which contain parameters that have to be determined. This is done by modern approximation and optimization. After this, time-discretized dynamical systems are studied by a combinatorial algorithm which detects the region of parametric stability. Finally, we analyze the ‘landscape’ of gene-environment networks. Its structure and stability have a very important meaning for the understanding of life and social system and of the conductibility of common enterprises, for example, in the environmental sector. To represent the interactions between the project participants, we imply modern collaborative game theory, where the players may be individuals or companies or, in particular, nations. This pioneering work is practically motivated and theoretically elaborated; it is devoted to support improvements in the living conditions of people all over the world, especially, in health care, medicine, education, environmental protection and public awareness. The authors invite the interested readers to future research. [ABSTRACT FROM AUTHOR]

This article contributes to a further introduction of continuous optimization in the field of computational biology which is one of the most challenging and emerging areas of science, in addition to foundations presented and the state-of-the-art displayed in [C.A. Floudas and P.M. Pardalos, eds., Optimization in Computational Chemistry and Molecular Biology: Local and Global Approaches, Kluwer Academic Publishers, Boston, 2000]. Based on a summary of earlier works by the coauthors and their colleagues, it refines the model on gene-environment patterns by a problem from generalized semi-infinite programming (GSIP), and characterizes the condition of its structural stability. Furthermore, our paper tries to detect and understand structural frontiers of our methods applied to the recently introduced gene-environment networks and tries to overcome them. Computational biology is interdisciplinary, but it also looks for its mathematical foundations. From data got by DNA microarray experiments, non-linear ordinary differential equations are extracted by the optimization of least-squares errors; then we derive corresponding time-discretized dynamical systems. Using a combinatorial algorithm with polyhedra sequences we can detect the regions of parametric stability, contributing to a testing the goodness of data fitting of the model. To represent and interpret the dynamics, certain matrices, genetic networks and, more generally, gene-environment networks serve. Here, we consider n genes in possible dependence with m special environmental factors and a cumulative one. These networks are subject of discrete mathematical questions, but very large structures, such that we need to simplify them. This is undertaken in a careful optimization with constraints, aiming at a balanced connectedness, incorporates any type of a priori knowledge or request and should be done carefully enough to be robust against disturbation by the environment. In this way, we take into account attacks on the network, knockout phenomena and catastrophies, but also changes in lifestyle and effects of education as far as they can approximately be quantified. We characterize the structural stability of the GSIP problem against perturbations like changes between data series or due to outliers. We give explanations on the numerics and the use of splines. This study is an attempt to demonstrate some beauty and applicabilty of continuous optimization which might together one day give a support in health care, food engineering, biomedicine and -technology, including elements of bioenergy and biomaterials. [ABSTRACT FROM AUTHOR]

The article discusses various reports published within the issue including one by Ralf Korn and Serkan Zeytun on optimal investment problems, one by J.H. Maruhn on static hedging, and one by Martin Rainer on stochastic models.

In inverse problem of electrocardiography (ECG), electrical activity of the heart is estimated from body surface potential measurements. This electrical activity provides useful information about the state of the heart, thus it may help clinicians diagnose and treat heart diseases before they cause serious health problems. For practical application of the method, having fewer number of electrodes for data acquisition is an advantage. Additionally, inverse problem of ECG is ill-posed due to attenuation and smoothing within the body. Therefore, the solution of ECG inverse problem has to be regularized. In this study, we constrain ourselves to two Lanczos-bidiagonalization-based inverse solution methods, namely, Lanczos least-squares QR (L-LSQR) factorization and Lanczos truncated total least-squares (L-TTLS). Tikhonov regularization is also implemented as a base for comparison for these methods. We use body surface measurements simulated using epicardial potentials measured from the surface of canine hearts. In these experiments, the hearts are stimulated from the ventricles at various sites, mimicking ectopic beats. Torso potentials are obtained from these epicardial measurements by multiplying them with the forward transfer matrix and adding Gaussian distributed noise. We solve the inverse problem using different number of leads on the body surface (771, 192, 64, and 32 leads), and assess the performances of these regularization methods for the reduced lead-sets. These reduced lead-sets are selected from the primary 771-lead configuration by using two main approaches. The first approach is manually selecting appropriate leads, and the second one uses the inverse problem approach to select leads sequentially. The results show that the L-TTLS method is more successful in reconstructing epicardial potentials than the L-LSQR method. The L-TTLS method is faster than the Tikhonov regularization, since it benefits from bidiagonal form of the forward matrix. Reducing the number of electrodes to 64 has a small effect on the solutions, but with 32 leads, inverse solutions get less precise, and the difference between the results of Tikhonov regularization and L-TTLS method becomes less significant. [ABSTRACT FROM AUTHOR]