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Many optimization mathematical models, associated with the technical-economic processes of real-world problems, have elements of uncertainty in their structure, which places them in stochastic optimization programming. Their diversity and complexity, due to the large uncertainty space, require special methods of solving, because there is no general solution method. Within this context, in this paper we consider the category of optimization models that can contain random variable type coefficients and/or imposed probability levels on the constraints. The purpose of the paper is to propose a methodology dedicated to these studied models. Applying the methodology leads to developing a deterministic linear programming model, associated with the initial stochastic model. In fact, the proposed methodology reduces the stochastic formulation to a deterministic formulation. The methodology is illustrated with a numerical case study based on a manufacturing problem. Solving the obtained deterministic model is carried out in the version assisted by a specialized software product (WinQSB Version 2.0). It allows for the performing of a sensitivity analysis of the optimal solution, and/or a parametric analysis relative to certain model coefficients, both also presented in the paper. The main result of the study in this paper is the proposed methodology, which is applicable on a large scale, for any mathematical model of stochastic optimization of the mentioned type, regardless of complexity, dimensions and the domain of the process to which it is associated. The numerical results obtained when applying this methodology indicate its efficiency and effectiveness in finding the solution for the studied models. The approach to this issue in the present paper is determined by the wide range of stochastic optimization problems in the various studied real-life processes and by the imperative need to adopt the best decisions in conditions of uncertainty. [ABSTRACT FROM AUTHOR]

This paper explores the concept of Generalized Roughness in LA-Semigroups and its applications in various mathematical disciplines. We highlight the fundamental properties and structures of Generalized Roughness, examining its relationships with Fuzzy Lie Algebras, Order Theory, Lattice Structures, Algebraic Structures, and Categorical Perspectives. Moreover, we investigate the potential of mathematical modeling, optimization techniques, data analysis, and machine learning in the context of Generalized Roughness. Our findings reveal important results in Generalized Roughness, such as the preservation of roughness under the fuzzy equivalence relation and the composition of roughness sets. We demonstrate the significance of Generalized Roughness in the context of order theory and lattice structures, presenting key propositions and a theorem that elucidate its properties and relationships. Furthermore, we explore the applications of Generalized Roughness in mathematical modeling and optimization, highlighting the optimization of roughness measures, parameter estimation, and decision-making processes related to LA-Semigroup operations. We showcase how mathematical techniques can enhance understanding and utilization of LA-Semigroups in practical scenarios. Lastly, we delve into the role of data analysis and machine learning in uncovering patterns, relationships, and predictive models in Generalized Roughness. By leveraging these techniques, we provide examples and insights into how data analysis and machine learning can contribute to enhancing our understanding of LA-Semigroup behavior and supporting decision-making processes. [ABSTRACT FROM AUTHOR]

The most commonly used model of solar cells is the single-diode model, with five unknown parameters. First, this paper proposes three variants of the single-diode model, which imply the voltage dependence of the series resistance, parallel resistance, and both resistors. Second, analytical relationships between the current and the voltage expressed were derived using the Lambert W function for each proposed model. Third, the paper presents a hybrid algorithm, Chaotic Snake Optimization (Chaotic SO), combining chaotic sequences with the snake optimization algorithm. The application of the proposed models and algorithm was justified on two well-known solar photovoltaic (PV) cells—RTC France solar cell and Photowatt-PWP201 module. The results showed that the root-mean-square-error (RMSE) values calculated by applying the proposed equivalent circuit with voltage dependence of both resistors are reduced by 20% for the RTC France solar cell and 40% for the Photowatt-PWP201 module compared to the standard single-diode equivalent circuit. Finally, an experimental investigation was conducted into the applicability of the proposed models to a solar laboratory module, and the results obtained proved the relevance and effectiveness of the proposed models. [ABSTRACT FROM AUTHOR]

There are a sufficient number of works devoted to modeling crushing machines. Nevertheless, the fact that there are a large number of working conditions, and the ongoing development of science and technology, require continuous improvement and specification of the models intended for crushing processes and those of the devices concerned. However, there are few studies related to single-roll gyratory crushers. Such crushers are promising for use in mines to crush rocks laid in the developed space. Mathematical modeling and optimization of the design parameters of the working chamber and the executive body (roll) of a single-roll gyratory shaft crusher, designed for crushing strong rocks, was performed in this paper. A differential equation was derived. As a result of its solution, the rational shape of the working chamber cheek of the single-roll gyratory crusher was established, representing a logarithmic spiral arc. Analytical expressions were derived to determine the rational rotation speed and productivity of the crusher under consideration. Expressions for calculating the kinematic load components acting on the roll were formulated. They are the periodic functions of the shaft rotation angle. The Fourier series expansion showed that the loads contained harmonics of the first, second, third and fourth orders. Using the concept of fuzzy sets, a multi-criteria optimization of the design parameters of the working chamber was performed, including the values of the eccentricity and the central angle of the beginning of the cheek profile. The variation coefficients of the kinematic components of the loads acting on the working body reduced, due to the optimal choice of the working chamber profile and the angular coordinates of the installation of the fixed cheeks. The torque reduced 1.67 times, while the radial load decreased 1.2 times. [ABSTRACT FROM AUTHOR]

Investments in the development of the district heating system require a thorough analysis of the technical, economic, and legal aspects. Regarding the technical and economic context, a mathematical model of the district heating system has been proposed. It optimizes both the technical and economic aspects of the function and development of a district heating system. To deal with non-linearities, the developed linear programming model is divided into three phases: flow, thermal, and pressure. Therein, non-linear dependencies are calculated between the linear optimization phases. This paper presents the main assumptions and equations that were used to calculate the parameters of the heating system, along with the optimal level of heat production, the flow rate of the heating medium in the heat nodes and edges of the network graph, the heat, power, and temperature losses at each edge, and the purchase costs of heat and its transmission. The operation of the model was tested on a real-world district heating system. The case study results confirm that the model is effective and can be used in decision support. The economic results of the model, before the calibration process, were 3.6% different from historical values. After the calibration process, they were very similar to the real data—all percentage deviations were within 1%. [ABSTRACT FROM AUTHOR]

This paper proposes an impedance-accelerated inverse-time over-current protection optimization scheme based on the improved quantum genetic algorithm. First, the speed of remote backup protection is improved by increasing the optimization level of backup protection. Second, to ensure the coordination of protection when the distributed generation is connected to the distribution network, a mathematical model for the optimization of inverse time protection parameters is established. The mathematical model takes the minimum total action time of the optimized main and backup protection as the objective function, and the selectivity and sensitivity requirements of the protection as the constraints. In addition, the genetic algorithm is improved from four aspects: coding method, population initialization, quantum revolving gate, and variational evolution. The theoretical analysis and simulation results show that the proposed scheme can effectively improve the selectivity and operation speed of the protection. [ABSTRACT FROM AUTHOR]

The Riemannian manifold optimization algorithms have been widely used in machine learning, computer vision, data mining, and other technical fields. Most of these algorithms are based on the geodesic or the retracement operator and use the classical methods (i.e., the steepest descent method, the conjugate gradient method, the Newton method, etc.) to solve engineering optimization problems. However, they lack the ability to solve non-differentiable mathematical models and ensure global convergence for non-convex manifolds. Considering this issue, this paper proposes a quantum-behaved particle swarm optimization (QPSO) algorithm on Riemannian manifolds named RQPSO. In this algorithm, the quantum-behaved particles are randomly distributed on the manifold surface and iteratively updated during the whole search process. Then, the vector transfer operator is used to translate the guiding vectors, which are not in the same Euclidean space, to the tangent space of the particles. Through the searching of these guiding vectors, we can achieve the retracement and update of points and finally obtain the optimized result. The proposed RQPSO algorithm does not depend on the expression form of a problem and could deal with various engineering technical problems, including both differentiable and non-differentiable ones. To verify the performance of RQPSO experimentally, we compare it with some traditional algorithms on three common matrix manifold optimization problems. The experimental results show that RQPSO has better performance than its competitors in terms of calculation speed and optimization efficiency. [ABSTRACT FROM AUTHOR]

Optimal operation of the active distribution networks (ADN) is essential to keep its safety, reliability and economy. With the integration of multiple controllable resources, the distribution networks are facing more challenges in which the optimization strategy is the key. This paper establishes the optimal operation model of the ADN considering a diversity of controllable resources including energy storage devices, distributed generators, voltage regulators and switchable capacitor banks. The objective functions contain reducing the power losses and improving the voltage profiles. To solve the optimization problem, the Kriging model based Improved Surrogate Optimization-Mixed-Integer (ISO-MI) algorithm is proposed in this paper. The Kriging model is applied to approximate the complicated distribution networks, which speeds up the solving process. Finally, the accuracy of the Kriging model is validated and the efficiency among the proposed method, genetic algorithm (GA) and particle swarm optimization (PSO) is compared in an unbalanced IEEE-123 nodes test feeder. The results demonstrate that the proposed method has better performance than GA and PSO. [ABSTRACT FROM AUTHOR]

When faults and disturbances occur in power systems, backup power resources respond to maintain the system's frequency, and the frequency recovery effect is related to the primary frequency regulation of the reserve capacity provided by and the response speeds of the system's generating units and interruptible loads. The relationships between a system's frequency and the frequency regulation capacity of the generating units and the interruptible loads are different. In this paper, an index for the frequency recovery effect is proposed based on the static frequency adjustment coefficient of the interruptible load and the adjustment coefficients of the generating units, and an optimization model of an interruptible load participating in primary frequency regulation is built with the objective of minimizing the cost of the primary frequency regulation reserve that uses the system's frequency recovery effect as a constraint. The simulation results verify the validity of the model. [ABSTRACT FROM AUTHOR]

Power system electromagnetic transient (EMT) simulation has been used to study the electromagnetic behavior of power system components. It generally comprises detailed models of the study area and an equivalent circuit which represents an external part of the study area. However, a detailed description of an external system that includes transmission or distribution system models is required to study the interaction among power system components because the number of high power converter based devices in a power grid have been increasing. Since detailed models of the system components are necessary to simulate a series of events such as cascading faults the computational burden of power system simulation has increased. Therefore a more effective and practical framework has been sought to handle this computational challenge. This paper proposes a co-simulation framework including a delay compensation algorithm to compensate the time delayed signals due to network segmentation and a fast and flexible simulation environment composed of non-real time power system EMT simulation on a general purpose computer with a multi core central processing unit (CPU), which is currently very popular owing to its performance. The proposed methods are applied to an AC/DC power system model. [ABSTRACT FROM AUTHOR]

In this paper, we propose a generalized explicit algorithm for approximating the common solution of generalized split feasibility problem and the fixed point of demigeneralized mapping in uniformly smooth and 2-uniformly convex real Banach spaces. The generalized split feasibility problem is a general mathematical problem in the sense that it unifies several mathematical models arising in (symmetry and non-symmetry) optimization theory and also finds many applications in applied science. We designed the algorithm in such a way that the convergence analysis does not need a prior estimate of the operator norm. More so, we establish the strong convergence of our algorithm and present some computational examples to illustrate the performance of the proposed method. In addition, we give an application of our result for solving the image restoration problem and compare with other algorithms in the literature. This result improves and generalizes many important related results in the contemporary literature. [ABSTRACT FROM AUTHOR]

Fused filament fabrication (FFF) is a layer-by-layer additive manufacturing (AM) process for producing parts. For industries to gain a competitive advantage, reducing product development cycle time is a basic goal. As a result, industries' attention has turned away from traditional product development processes toward rapid prototyping techniques. Because different process parameters employed in this method significantly impact the quality of FFF manufactured parts, it is essential to optimize FFF process parameters to enhance component quality. The paper presents optimization of fused filament fabrication process parameters to improve the shape deviation such as cylindricity and circularity of 3D printed parts with the Taguchi optimization method. The effect of thickness, infill pattern, number of walls, and layer height was investigated as variable parameters for experiments on cylindricity and circularity. The MarkForged® used Nylon White (PA6) to create the parts. ANOVA and the S/N ratio are also used to evaluate and optimize the influence of chosen factors. As a result, it was concluded that the hexagonal infill pattern, the thickness of 5 mm, wall layer of 2, and a layer height of 1.125 mm were known to be the optimal process parameters for circularity and cylindricity in experiments. Then a linear regression model was created to observe the relationship between the control variables with cylindricity and circularity. The results were confirmed by a confirmation test. [ABSTRACT FROM AUTHOR]

Numerous optimization problems have been defined in different disciplines of science that must be optimized using effective techniques. Optimization algorithms are an effective and widely used method of solving optimization problems that are able to provide suitable solutions for optimization problems. In this paper, a new nature-based optimization algorithm called Snow Leopard Optimization Algorithm (SLOA) is designed that mimics the natural behaviors of snow leopards. SLOA is simulated in four phases including travel routes, hunting, reproduction, and mortality. The different phases of the proposed algorithm are described and then the mathematical modeling of the SLOA is presented in order to implement it on different optimization problems. A standard set of objective functions, including twenty-three functions, is used to evaluate the ability of the proposed algorithm to optimize and provide appropriate solutions for optimization problems. Also, the optimization results obtained from the proposed SLOA are compared with eight other well-known optimization algorithms. The optimization results show that the proposed SLOA has a high ability to solve various optimization problems. Also, the analysis and comparison of the optimization results obtained from the SLOA with the other eight algorithms shows that the SLOA is able to provide more appropriate quasi-optimal solutions and closer to the global optimal, and with better performance, it is much more competitive than similar algorithms. [ABSTRACT FROM AUTHOR]

According to the authors of this paper, the mathematical point of view allows us to see what sometimes cannot be seen from the designer's point of view. The aim of this study was to estimate the influence of the most important parameters (volume of heat storage tanks, daily consumption of domestic hot water, optical efficiency, heat loss coefficient, and total area of a solar collector) on the thermal power output of solar domestic hot water (SDHW) system in European climatic conditions. Three deterministic mathematical models of these relationships for Madrid, Budapest, and Helsinki were created. The database for the development of these models was carried out using computer simulations made in the TRNSYS software environment. The SDHW system located at the Bialystok University of Technology (Poland) was the source of the measurement results used to validate the simulation model. The mathematical optimization procedure showed that the maximum annual useful energy output that can be obtained from 1 m2 of gross collector area is 1303 kWh in the case of Madrid, 918.5 kWh for Budapest, and 768 kWh for Helsinki weather conditions. [ABSTRACT FROM AUTHOR]

Dissolved gas analysis (DGA) is widely used to detect the incipient fault of power transformers. However, the accuracy is greatly limited by selection of DGA features and performance of fault diagnostic model. This paper proposed a fault diagnostic method integrating feature selection and diagnostic model optimization. Firstly, this paper set up three feature sets with eight basic DGA gases, 28 DGA gas ratios and 36 hybrid DGA features, respectively. Then, to eliminate the interference of weak-relevant and irrelevant features, the genetic-algorithm-SVM-feature-screen (GA-SVM-FS) model was built to screen out the optimal hybrid DGA features subset (OHFS) from three feature sets. Next, using the OHFS as the input, the support vector machine (SVM) multi-classifier optimized by ISGOSVM (SVM classifier optimized by improved social group optimization) was built to diagnose fault types of transformers. Finally, the performance of OHFS and ISGOSVM diagnostic model was tested and compared with traditional DGA features and diagnostic models, respectively. The results show that the OHFS screened out is comprised of 14 features, including 12 gas ratios and two gases. The accuracy of OHFS is 3–30% higher than traditional DGA features, and the accuracy of ISGOSVM can increase by 3% to 14% compared with the SGOSVM (SVM classifier optimized by social group optimization), GASVM (SVM classifier optimized by genetic algorithm optimization), PSOSVM (SVM classifier optimized by particle swarm optimization), and SVM diagnostic models. The proposed approach integrating the OHFS with ISGOSVM achieves the highest accuracy of fault diagnose (92.86%). [ABSTRACT FROM AUTHOR]

Battery systems bring technical and economic advantages to electrical distribution systems (EDSs), as they conveniently store the surplus of cheap renewable generation for use at a more convenient time and contribute to peak shaving. Due to the high cost of batteries, technical and economic studies are needed to evaluate their correct allocation within the EDS. To contribute to this analysis, this paper proposes a stochastic mathematical model for the optimal battery allocation (OBA), which can be guided by the optimization of two different economic metrics: net present value (NPV) and internal rate of return (IRR). The effects of the OBA in the EDS are evaluated considering the stochastic variation of photovoltaic generation and load. Tests with the 33-node IEEE test system indicate that OBA results in voltage profile improvement (~1% at peak time), peak reduction (31.17%), increased photovoltaic hosting capacity (18.8%), and cost reduction (3.06%). Furthermore, it was found that the IRR metric leads to a different solution compared to the traditional NPV optimization due to its inherent consideration of the relation between cash flow and investment. Thus, both NPV and IRR-based allocation alternatives can be used by the decision maker to improve economic and technical operation of the EDS. [ABSTRACT FROM AUTHOR]

The vanadium-titanium black ceramic (VTBC) coating on all-ceramic solar collectors has both high absorptance (0.94) and high emissivity (90%). However, the thermal conductivity of ceramic is very low (1.256 W/mK). To improve the heat collection efficiency of VTBC solar collectors, this paper establishes a mathematical model based on the energy-conservation relationships under steady-state conditions and creates a corresponding computer program. Key parameters for VTBC solar collectors include the heat-removal factor, effective transmittance-absorptance product for the absorber, total heat loss coefficient, etc. Then, via experimental testing, this study proposes a reference model for domestic VTBC solar collectors in a cold location (η = 0.89 − 2.20Tm*). Last, this work analyzes the influences of fin design and transparent cover design on VTBC solar collectors individually, using the created computer program. Results show that the most effective optimization method is to increase the transmittance of the transparent cover. By increasing the transmittance from 0.93 to 0.96, this study creates an optimized VTBC solar collector theoretical model (η = 0.92 − 2.20Tm*). [ABSTRACT FROM AUTHOR]

This paper proposes an optimal scheduling model under production and maintenance constraints for a real case of a discrete event system. The intent was to use the rich mathematical theory and algorithms of optimization in the study of this important class of systems. The current study detailed firstly a new approach for mapping a simulation event relationship graph into a mixed-integer program, with a flexible workshop real case. Several other potential applications of the mathematical model are examined, thanks to the model constraints flexibility characteristics, including a general case of a manufacturing system for optimal resource scheduling, an application on the case of hospital beds' management. The model extension could be also interesting for other applications like museum systems or the case of big data in complex and social networks. [ABSTRACT FROM AUTHOR]

In this paper, we consider a job-shop scheduling problem with mixed blocking constraints. Contrary to most previous studies, where no blocking or only one type of blocking constraint was used among successive operations, we assume that, generally, we may address several different blocking constraints in the same scheduling problem depending on the intermediate storage among machines, the characteristics of the machines, the technical constraints, and even the jobs. Our objective was to schedule a set of jobs to minimize the makespan. Thus, we propose, for the first time, a mathematical model of the job-shop problem taking into account the general case of mixed blocking constraints, and the results were obtained using Mosel Xpress software. Then, after explaining why and how groups of jobs have to be processed, a blocking constraint conflict-free warranted evaluation function is proposed and tested with the particle swarm optimization and genetic algorithm methods. The results prove that we obtained a near-optimal solution to this problem in a very short time. [ABSTRACT FROM AUTHOR]

Visual-inertial odometry (VIO) has recently received much attention for efficient and accurate ego-motion estimation of unmanned aerial vehicle systems (UAVs). Recent studies have shown that optimization-based algorithms achieve typically high accuracy when given enough amount of information, but occasionally suffer from divergence when solving highly non-linear problems. Further, their performance significantly depends on the accuracy of the initialization of inertial measurement unit (IMU) parameters. In this paper, we propose a novel VIO algorithm of estimating the motional state of UAVs with high accuracy. The main technical contributions are the fusion of visual information and pre-integrated inertial measurements in a joint optimization framework and the stable initialization of scale and gravity using relative pose constraints. To account for the ambiguity and uncertainty of VIO initialization, a local scale parameter is adopted in the online optimization. Quantitative comparisons with the state-of-the-art algorithms on the European Robotics Challenge (EuRoC) dataset verify the efficacy and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Concerns have been increasing regarding the environmental sustainability of disassembly activities that take place in various recovery operations at end of life stage of products, and subsequently, disassembly activities have been gaining increased exposure. The disassembly line is a good choice for automated disassembly of end-of-life products. Although interest in addressing energy saving in manufacturing is rising, the study of incorporating energy consumption reduction and disassembly efficiency improvement into disassembly line balancing is still limited. The analysis, design, and balanced decision-making for disassembly lines are urgently needed in order to make the disassembly line as energy-saving as possible. In this paper, an energy-saving optimization method, which was used in scheduling workstation selection and the disassembly sequence for the disassembly line, is proposed. Energy consumption of each stage of the disassembling process was analyzed and modeled. Then, a mathematical model of the disassembly line balancing problem with energy saving considerations was formulated and the objective of energy consumption was integrated into the objectives of cost and working load in order to balance a disassembly line. Optimal solutions for the disassembly line balancing problem with an energy saving consideration were obtained by using an artificial bee colony algorithm, which was a feasible way of minimizing workstations, and ensuring similar working load, as well as minimizing energy consumption. Finally, a case study of disassembly line balancing for a typical driving system is presented to illustrate the proposed method. [ABSTRACT FROM AUTHOR]