Simplex Method Research Articles

Influence of Fixed Ring Gear Structural Compliance on the Quasi-Static and Dynamic Response of Epicyclic Gear Sets

Abstract The structural compliance of annular ring gear can significantly influence the quasi-static and dynamic performance of an epicyclic gear set. As powertrain components are continually being optimized to their design limits, this influence becomes prominent and can no longer be ignored. The current paper will study the impact of ring gear compliance on the dynamic response of epicyclic gear sets, in fixed ring kinematic configuration. To achieve this objective the current study will incorporate a finite element based ring gear formulation into the three-dimensional planetary load distribution model of Ryali and Talbot [1]. The proposed model employs a modified simplex algorithm to iteratively solve for the elastic gear mesh contacts in conjunction with a numerical integration scheme, which enables it to inherently capture the influence of several component and system level design variations. The developed formulation is used to conduct parametric studies involving different planetary gear designs, ring gear fixtures (bolted vs. splined), and operating conditions (quasi-static, dynamic). In the case of a splined ring gear fixture, an external splined tooth contact model is developed, which will be used to validate the model against the quasi-static experiments of Ligata et al. [2]. The discussed results demonstrate the fidelity of the developed model, thus making it an excellent tool for the design and analysis of planetary gears with thin annular ring gears.

Influence of the radius of Monson’s sphere and excursive occlusal contacts on masticatory function of dentate subjects

ObjectiveTo determine the influence of the radius of Monson’s sphere, the number of posterior laterotrusive, mediotrusive, and protrusive contacts, and the chewing rate on food comminution. DesignSixty healthy dentate subjects, aged 21.22 ± 2.30 years, were selected. The three-dimensional coordinates of the cusp tips of the lower canine, premolar, and molar teeth were identified from the subjects’ digital models. Monson’s sphere was designed using the simplex method for function minimisation by adjusting the coordinates on its surface. The contacts were verified using 12 µm metal strips in jaw excursions at 0.5, 1.0, 2.0, and 3.0 mm. The masticatory performance and efficiency, swallowing threshold, and chewing rate were assessed through particle size fractionation. Data were analysed with multiple linear regression (α = 0.05). ResultsThe sphere’s radius, laterotrusive and protrusive contacts at 0.5 mm, and chewing rate were found to be negative predictor variables for masticatory performance until 20 chewing cycles (R2 = 0.429). For 40 cycles, the radius and total contacts (0.5 mm) were also explanatory factors (R2 = 0.223). Only the radius (R2 = 0.176) and the chewing rate (R2 = 0.082) were found to be significant for 60 cycles and swallowing threshold, respectively. Masticatory efficiency was influenced by masticatory performance until 40 and 60 cycles, as well as the radius and total contacts at 2.0 and 3.0 mm (R2 = 0.958). ConclusionA larger radius of Monson’s sphere and a greater number of posterior excursive contacts were found to be related to better masticatory function.

Hybrid beluga whale optimization algorithm with multi-strategy for functions and engineering optimization problems

Beluga Whale Optimization (BWO) is a new metaheuristic algorithm that simulates the social behaviors of beluga whales swimming, foraging, and whale falling. Compared with other optimization algorithms, BWO shows certain advantages in solving unimodal and multimodal optimization problems. However, the convergence speed and optimization performance of BWO still have some performance deficiencies when solving complex multidimensional problems. Therefore, this paper proposes a hybrid BWO method called HBWO combining Quasi-oppositional based learning (QOBL), adaptive and spiral predation strategy, and Nelder-Mead simplex search method (NM). Firstly, in the initialization phase, the QOBL strategy is introduced. This strategy reconstructs the initial spatial position of the population by pairwise comparisons to obtain a more prosperous and higher quality initial population. Subsequently, an adaptive and spiral predation strategy is designed in the exploration and exploitation phases. The strategy first learns the optimal individual positions in some dimensions through adaptive learning to avoid the loss of local optimality. At the same time, a spiral movement method motivated by a cosine factor is introduced to maintain some balance between exploration and exploitation. Finally, the NM simplex search method is added. It corrects individual positions through multiple scaling methods to improve the optimal search speed more accurately and efficiently. The performance of HBWO is verified utilizing the CEC2017 and CEC2019 test functions. Meanwhile, the superiority of HBWO is verified by utilizing six engineering design examples. The experimental results show that HBWO has higher feasibility and effectiveness in solving practical problems than BWO and other optimization methods.

СРАВНЕНИЕ МЕТОДОВ РЕШЕНИЯ ТРАНСПОРТНОЙ ЗАДАЧИ

Mathematical programming is a mathematical discipline that studies various extremal problems and develops algorithms for solving them. Among the problems are those of mathematical integer programming. Integer programming is indispensable for solving mathematical programming problems in which some or all of the variables take on integer values. The problems include the transport problem. The paper considers the transport problem and three linear programming methods for solving it: the method of potentials, the method of differential rents and the simplex method. The paper analyzes and assesses the effectiveness of the three algorithms for optimizing transport problems. Several linear optimization algorithms have been studied and presented. The paper contains the basic concepts, formulas, and algorithms of the methods used. The method of potentials, the method of differential rents and the simplex method are considered. The results of solving the problem using these methods are presented and compared. All calculations were performed using Excel.

Aircraft fleet optimization by the simplex method

The transport system efficiency and the quality of its operation is organically connected with the improvement of air transportation technical means on the basis of modern science and technology. One of the directions of further aviation transport system development is the creation of methodological basis for optimal aircraft operation. Therefore, the increase in aircraft efficiency is one of the important tasks, as its improvement is associated with savings in material and financial resources, which affects the fleet structure and the process of passenger traffic. The article is intended to substantiate the method of optimizing the use of airline aircraft by means of mathematical apparatus. It has been found that the mathematical model structure is required to form an optimal aircraft fleet. A variant of aircraft fleet formation has been proposed taking into account the mathematical model, built on the basis of linear programming, namely, using the simplex method. It has been determined that the choice of optimal aircraft options is greatly influenced by the value of the parametric series. To obtain a reliable result, the aircraft loading must be 100%, otherwise the error grows due to coefficients at unknown target function. The proposed method of determining the optimal fleet with different types of aircraft and air traffic routes, taking into account the conditions of their usage, allows to recommend airlines to use aircraft with the highest efficiency.

Time‑Resolved Spectroscopy Based on Monte Carlo Model and Nelder‑Mead Simplex Algorithm

Time‑Resolved Spectroscopy Based on Monte Carlo Model and Nelder‑Mead Simplex Algorithm

Neutrosophic Treatment of the Modified Simplex Algorithm to find the Optimal Solution for Linear Models

Science is the basis for managing the affairs of life and human activities, and living without knowledge is a form of wandering and a kind of loss. Using scientific methods helps us understand the foundations of choice, decision-making, and adopting the right solutions when solutions abound and options are numerous. Operational research is considered the best that scientific development has provided because its methods depend on the application of scientific methods in solving complex issues and the optimal use of available resources in various fields, private and governmental work in peace and war, in politics and economics, in planning and implementation, and in various aspects of life. Its basic essence is to use the data provided for the issue under study to build a mathematical model that is the optimal solution. It is the basis on which decision makers rely in managing institutions and companies, and when operations research methods meet with the neutrosophic teacher, we get ideal solutions that take into account all the circumstances and fluctuations that may occur in the work environment over time. One of the most important operations research methods is the linear programming method. Which prompted us to reformulate the linear models, the graphical method, and the simplex method, which are used to obtain the optimal solution for linear models using the concepts of neutrosophic science. In this research, and as a continuation of what we presented previously, we will reformulate the modified simplex algorithm that was presented to address the difficulty that we were facing when applying the direct simplex algorithm. It is the large number of calculations required to be performed in each step of the solution, which requires a lot of time and effort.

A Hybrid TLBO and Simplex Algorithm to Extract the Optimal Parameters of Photovoltaic Models

This work aims to improve photovoltaic (PV) system performance by extracting parameters for solar models, on extracting parameters for solar models to enhance the performance of photovoltaic (PV) systems. This paper proposes a hybrid method for figuring out the unknown electrical characteristics of single and dual diode models, integrating Teaching Learning Based Optimization (TLBO) with a simplex algorithm. The primary objective is to achieve optimal parameter extraction for the PV system. To overcome the challenge of local optima, a deterministic algorithm is employed in the hybrid method, leveraging the simplex algorithm’s faster convergence towards optimal parameters. Comparative analysis with other algorithms like Particle Swarm Optimization (PSO) and Genetic Algorithm (GA), known for handling similar problems, reveals the superior and robust performance of the proposed hybrid approach. The results obtained from the developed method are validated against data from a commercial silicon R.T.C. France solar cell and simulation outcomes under various conditions, further confirming the results’ effectiveness and reliability.

A steepest feasible direction method for linear programming. Derivation and embedding in the simplex method

A feasible direction method for linear programming has been proposed. The method is embedded in the framework of the simplex method, even though it works with non-edge feasible directions. The direction used is the steepest in the space of all variables or an approximation thereof, and it is found by solving a strictly convex quadratic program in the space of the nonbasic variables. Further, this program guarantees the feasibility of the direction even in the case of degeneracy. To remain within the simplex framework, the direction is represented by an auxiliary, or external, nonbasic column, which is a nonnegative linear combination of original nonbasic columns. We have made an experimental evaluation of the suggested method on both nondegenerate and highly degenerate problem instances. The overall results are very promising for continued research along this line, especially concerning various computational strategies that can be applied when the method is implemented.

ВПЛИВ ФУНКЦІЙ МЕТОДИКИ НА ЯКІСТЬ ВИРІШЕННЯ ЕКСПЕРТНОГО ЗАВДАННЯ

The publication considers forensic expertise as an integrated system with interconnected elements, one of which is methodological support. The interrelation of the main structural elements in organizing expert research is provided. The impact of methodological functions on the quality resolution of expert tasks through the application of methodology in the process of expert cognition is substantiated. It is suggested that when developing an expert methodology, an additional consideration should be given to the optimization function of the expert's conclusion, which implies the ability to concisely describe the methodology in the research part of the expert's conclusion for a full understanding by investigators, prosecutors, judges, and other participants in the judicial process of the specificity of research in a certain field of knowledge and to evaluate the expert's conclusion in terms of reliability. The development of society constantly increases the requirements for the quality and speed of conducting forensic examinations and research. This requires regular updating of methodologies. Especially, this concerns specialized methodologies for conducting examinations of intellectual property objects, which are unique and multifaceted. The role and significance of a specific methodology in the process of expert cognition can be determined through an analysis of its functions, the main ones being: decisive (or guiding), systematizing, prognostic, pragmatic, managerial, evaluative, substantiating, and cognitive. It is noted that expert research as a cognitive process has two levels of cognition: the first level is empirical; the second level is theoretical. The result of expert cognition should be the solution of an expert task – establishing facts with evidentiary value. General expert knowledge is decisive in conducting qualitative forensic expertise – a dynamic category that is constantly improving through transformation and growth, integrated into the process of expert cognition through the competence of the forensic expert. It is proposed that in organizing the work of a forensic expert to optimize time and labor costs in conducting expert research, the simplex method be used as an algorithm for solving optimization problems. This method involves making directed movements along reference plans to find the optimal solution. The idea of applying the method for expert research lies in finding an expert's action plan according to a certain rule, which is checked against the optimality criterion – time and quality. If the optimality criterion is met, the task is considered solved. In case of non-compliance, a new iteration takes place, using the minimally calculated step, which needs to be recorded in the form of tables.

РОЗВ’ЯЗАННЯ МУЛЬТИМОДАЛЬНОЇ ТРАНСПОРТНОЇ ЗАДАЧІ З УРАХУВАННЯМ ОБМЕЖЕНЬ ЛОГІСТИЧНИХ ПОКАЗНИКІВ

The implementation of military transportation by all types of transport involves planning, management, deployment of transport communications, distribution and preparation of types of transport, organization of the transportation of troops and military property, evacuation of the wounded and sick, damaged weapons and military equipment, and trophy property. As a result of these actions, the issue of timely delivery of material and technical means with the lowest costs should be resolved. The solution to the multimodal (three-index biplanar) transportation problem is presented to find the rational distribution and delivery of material and technical means. The proposed solution considers the limitations of logistics indicators, such as delivery time, the available carrying capacity of different types of vehicles, the total cost of transportation in the operational movement of storage points and consumers, changes in supply routes, and delivery vehicle types. Introducing an additional constraint into the three-index biplanar transport problem turns it into a linear programming problem of general form. The three-index transportation problem with extra logistical constraints is given a mathematical formulation. A form of input data presentation in the extended transport tables of transportation costs and time spent on cargo transportation is given. An easy way to solve this kind of problem using the simplex method is demonstrated in the Microsoft Excel spreadsheet processor "Solver" add-on. The article presents the results of solving a multimodal transportation problem with logistical constraints in Microsoft Excel using the example of the delivery of material and technical means by three types of transport (road, rail, and river), with time and cost constraints. The example uses conditional input data for the simulation of the delivery of cargo from three Ukrainian cities (storage points) to the other three (consumption points).

A Study of Systems of Neutrosophic Linear Equations

Operations research methods are among the modern scientific methods that have occupied a prominent place among the mathematical methods used in planning and managing various economic and military activities. They have been able to help specialists in developing ideal plans in terms of costs, production, storage, or investment of human energies. One of its most important methods is the method Linear programming, which was built based on the sets of linear equations that represent the constraints for any linear model. Based on the methods for solving the systems of linear equations, researchers were able to prepare algorithms for solving linear models, such as the direct Simplex algorithm and its modifications. After the emergence of neutrosophic science, we found that research methods had to be reformulated. Operations using the concepts of this science, and as a basis and foundation for neutrosophic linear programming. In this research, we will reformulate the systems of linear equations and some methods for solving them using the concepts of neutrosophic to be a basis for any study presented in the field of neutrosophic linear programming.

Multi-objective optimal decision for orderly power utilization based on improved ε-constraint method in active distribution networks.

With the increasing demand for electricity load in China, orderly power utilization are important measures to alleviate electricity shortages during peak periods. This article establishes a multi-objective optimization model for orderly power utilization in active distribution networks is established, with the optimization objectives of minimizing the total operation cost, minimizing the cost for users, and minimizing the load fluctuation of the system. This model contains a large number of integer variables and nonlinear constraints, which is difficult to solve. To reduce computation time, convex relaxation techniques are adopted to transform the original model into a mixed-integer second-order cone programming (MISOCP) model, which has lower computational complexity. Furthermore, The improved ε-constraint method is proposed to solve the model, which can directly and quickly find the compromise optimal solution of the multi-objective problem. By using simplex search algorithm, the proposed method dose not need to traverse all grid points, which can significantly reduce computation time. Finally, case study on the the IEEE-33 bus distribution network demonstrate the effectiveness of the proposed method.

ENHANCING CONVERGENCE AND ACCURACY IN SOLVING SYSTEM OF NONLINEAR INTEGRAL EQUATIONS USING MULTILAYER NEURAL NETWORKS

Abstract. This paper presents a novel approach for solving nonlinear integral equations of Fredholm and Volterra types using a multi-layer neural network (MLNN) trained through unrestricted optimization. The learning process involves minimizing the integral equation error function using the Nelder-Mead simplex method (NMSM), enabling efficient convergence in both Fredholm and Volterra equations. Our method ensures high accuracy despite potentially time-consuming computations for complex problems, maintaining convergence and approximation precision. Furthermore, the proposed approach demonstrates robustness against high-dimensional and variant equations. Numerical experiments employing the NMSM showcase its superior performance compared to existing methods. This research offers a promising avenue for solving a system of nonlinear integral equations efficiently and accurately, with broad applicability across diverse domains.

The effect of modulation and pathloss coefficient on Estx optimum and ESB minimum wireless sensor networks

Hardware devices in the Wireless Sensor Network (WSN) have several limitations, one of which is in terms of energy. Energy is needed so that activities running on the WSN keep running. WSN consists of many sensor nodes. Each sensor node has limited energy. In this study, the energy efficiency and bandwidth of the WSN were carried out using the Nelder Mead Simplex method, which uses the principle of differentiation of derivatives to simple forms. Nelder Mead Simplex has been widely used to manage energy efficiency in WSNs. The energy efficiency of this WSN is enhanced by the addition of the PSM-PC hybrid technique. The fuzzy algorithm is flexible in its use. Besides that, fuzzy logic can also save bandwidth by adjusting the waiting time in doing one data transmission from the sensor node to the cluster head. The analysis carried out aims to compare the optimization of energy savings in WSN with the Nelder Mead Simplex method. The research results we get are by using 2-QAM modulation with an Energy Bit used of 4.106×10-6J and an Energy transmitter of 7.1316×10-8J with the same parameter conditions, namely a distance of 125m, a path loss coefficient of 2, the number of bits 100 bits are used.

DETERMINATION OF THE UPPER LIMIT OF THE LOAD-LOADING CAPACITY OF BENDING REINFORCED METAL-COMPOSITE RING PLATES IN CONTACT WITH A LIQUID INCOMPRESSIBLE MEDIUM 1. PROBLEM FORMULATION AND CALCULATION METHOD

The problem of determining the load-bearing capacity of a bendable reinforced annular plate resting on an incompressible liquid base is considered. The internal opening of the structure is closed with a continuous, absolutely rigid insert. The connection between the insert and the plate can be rigid or hinged. The structure is supported on the outer edge, and it is possible to move the support in the vertical direction, for example in the case of a movable jamming. In the limiting state, liquid flow from one front surface of the plate to another surface is not allowed. The materials of the components of the composition are isotropic and rigid-plastic, having the same yield limits in tension and compression. Plastic flow in the phases of the composition is associated with piecewise linear yield criteria (such as the Tresk's or Ishlinsky - Ivlev's yield conditions). The limit state of such a composite plate is described within the framework of the classical theory of transverse bending. Reinforcement structures have axial and radial symmetry. Two reinforcement options are considered: laying two families of fibers along radially symmetrical spiral trajectories and reinforcement in the radial and circumferential directions. The rein-forcing fibers are assumed to be continuous and have constant cross sections along their length, which gives rise to significant heterogeneity of the structures under consideration in the radial direction. The plastic flow of a metal-composition is calculated using a structural model that takes into account the presence of a plane stress state in all substructural elements. Structural formulas have been written that make it possible to determine the coordinates of corner points on piecewise linear yield curves of the compositions under consideration, taking into account their dependence on non-uniform reinforcement parameters: angles and densities. An extremal principle has been formulated that makes it possible to obtain an upper (kinematic) estimate of the maximum load for this type of structure. The formulated problem is discretized along the polar radius. Nodal values of the sagging speed and mechanical energy dissipation were used as unknown grid functions. A numerical algorithm for solving the formulated discretized problem has been developed, based on the application of the simplex method of linear programming theory.

The Application and Practical Exploration of the Simplex Method in Linear Programming Problems

The Application and Practical Exploration of the Simplex Method in Linear Programming Problems

Positronium imaging in J-PET with an iterative activity reconstruction and a multistage fitting algorithm

Positronium imaging is a new technique complementary to positron emission tomography (PET) based on the histogramming of time delay between the emission of a de-excitation photon, and a consequent electron-positron annihilation, to estimate the mean lifetime of orthopositronium (o-Ps), which depends on the local size of the voids, concentration of oxygen and bioactive molecules. We improve the resolution and reduce noise in positronium imaging by building time-delay spectra from the PET activity reconstructed by a 3-photon time-of-flight maximum likelihood expectation maximisation. The method was tested on the data measured for four human-tissue samples injected by <sup>22</sup>Na and put in the Jagiellonian PET “Big barrel” scanner. Due to an ill-posed problem of fitting time-delay histograms, a multistage optimisation procedure was explored along with inferential analysis of the solution space. Run in parallel for multiple sets of initial guesses, we compared the second-order Levenberg- Marquardt algorithm (LMA) and the direct search Nelder-Mead simplex (NMS) method. The LMA proved to be faster and more precise, but the NMS was more stable with a higher convergence rate. The estimated mean o-Ps lifetimes in the 1.9 ns – 2.6 ns range were consistent with the reference results, while other fitting parameters allowed differentiation between the two patients who provided the tissue samples.

Geopolymer Made from Kaolin, Diatomite, and Rice Husk Ash for Ceiling Thermal Insulation

In this study, geopolymers made of metakaolin (MK), diatomite (D), and rice husk ash (RHA) were developed for ceiling thermal insulation in houses to provide protection against cold temperatures. The influence of the constituent mixing ratio and the temperature of curing on the heat conductivity and compressive strength of the geopolymer was investigated. Specimens were formed according to a 10-level mix design with three replicates and subjected to curing at 40 °C and 80 °C. Heat conductivity and compressive strength were determined in accordance with established standards. The simplex lattice method was used to obtain the response surfaces, contour plots, and tracking curves. The geopolymers under study displayed a reduction in heat conductivity and an increase in compressive strength when the curing temperature was raised. The optimal mixing ratio to achieve a balance between the compressive strength and thermal conductivity of the geopolymers investigated was 0.50 MK and 0.50 RHA. Diatomite’s thermal insulation contribution is neutralized when crystals from the geopolymer gel fill the pore volume. The mixture’s optimal results were achieved when cured at 80 °C, demonstrating a thermal conductivity of 0.10 W/m·K and a compressive strength of 5.37 MPa.

An integrated approach to predicting the results of the identification of deposits in conditions of different tectonic confinement of objects

In this paper, for the objects of the Volga-Ural oil and gas province, confined to terrigenous and carbonate reservoirs, a study was conducted aimed at reducing risks and uncertainties when using geological and statistical models. Discriminant analysis revealed a number of inconsistencies in the grouping of objects according to the criterion of tectonic confinement, within which the migration of objects and their significant dispersion relative to the centroids of the groups were revealed. In order to level out the factors of nonlinearity and heterogeneity of processes occurring in disordered oil and gas systems, the boundaries of their stability are formed using four models using algorithms for solving the dual problem by the simplex method. Based on the data obtained, some features of the influence of parameters characterizing the geological and physical properties of productive formations and the fluids saturating them on the integrity and correctness of ideas about the degree of belonging of objects to certain grouping zones are determined. The results obtained make it possible, within the framework of proactive resource management, to create optimal or refine existing algorithms for finding the most suitable analog objects for use at newly discovered sites of the best engineering solutions and practices in the field of field development. Keywords: geological and statistical modeling; oil deposits; tectonic confinement of objects; geological complexes; development of oil fields; asset management of subsoil users.