Mathematical Optimization Model Research Articles

Optimization design and analysis of internal gear transmission with double contact points

Internal gear transmission with double contact points is consist of the pinion having circular-arc tooth profile and the internal gear having parabola tooth profile. To further improve load capacity and reduce total volume of internal gear drive with double contact points, a multi-objective and multi-parameter optimization mathematical model is established based on genetic algorithm. Through the comparison analysis, contact stress of tooth surfaces after optimization design is reduced by 21.9% and the volume of gear after optimization design is reduced by 3.93%. Furthermore, contact characteristics of tooth surfaces are discussed considering the parameters optimization of contact angles and pressure angles. Based on Hertz contact theory, theoretical calculations of contact stresses under different contact angles and pressure angles are provided. And finite element method is used to analyze the contact conditions of tooth surfaces to verify theoretical calculation results. Research results show that contact angle of the internal gear pair with double contact points should less than 12.5° and pressure angle of the internal gear pair with double contact points should be 20°–30°.

Hybrid Machine Learning-Mathematical Programming Approach for Optimizing Gas Production and Water Management in Shale Gas Fields

This paper presents a novel mathematical programming approach that simultaneously incorporates a mixed-integer nonlinear programming formulation with machine learning models to determine the operating conditions, gas production, and optimal water management for the completion phase in shale gas fields. The dataset for the development of an artificial neural network model has been collected from the Eagle Ford Texas formation. The total cumulative gas production and flowback water generated in shale gas wells are selected as output variables. The mathematical optimization model considers machine learning models for each well, mass balances, treatment, storage, reuse, and disposal options as well as well location selection and associated costs and revenues from the sale of the shale gas produced. A case study has been used to illustrate the benefits of the proposed approach. The compromise solution offers a water consumption per produced energy of 6.71 L/GJ in addition to the fact that 27% of the total fracture water required can be obtained by reusing the flowback water with attractive economic indicators.

Restoration Strategy of Distributed Power Supply in Distribution Network Based on Genetic Algorithm

Nowadays, the penetration of distributed power in distribution network increases the complexity of power supply restoration. For the recovery of the traditional method in the field of distributed power supply system restore deficiency, the improving measures are put forward based on the many kinds of operation constraints, proposes the mathematical model of multi-objective optimization. In addition to conventional constraints in the mathematical model, will also be the network structure and branch power flow constraints into consideration. In view of the model, using the rough set theory, a multi-objective optimization problem into a single objective problem, and on this basis, considering the characteristic of radial network and the characteristics of the different load, by using genetic algorithm to reconstruct network, finally through the corresponding example recovery strategy is feasible and efficient.

Optimization of holes routing in hydraulic manifold blocks based on simulated annealing algorithm

The design of the hydraulic manifold block is time-consuming, laborious, and prone to make mistakes due to the vertical intersection and dense complexity of its internal oil passage network. The mathematical optimization model of this problem is given based on the comprehensive analysis of the structural characteristics and design rules of the internal orifices of the hydraulic manifold block. Using the integrated circuit layout algorithm for reference, an optimization design method of a multi-wire mesh channel network based on routing sequence optimization is proposed and verified by an example. The research results show that the optimization of the connection order between multiple wire networks at both ends and the routing order between multiple wire networks in a single-wire network can not only achieve the optimal design of the connectivity of the single-wire network but also ensure the optimal connectivity result of the entire hole network. At the same time, as the bottom core algorithm of the integrated block layout optimization design, it can provide a powerful technical guarantee for improving the integrated block design level, quality, and automation.

Resource Allocation Optimization Algorithm of Power 5G Network Slice Based on NFV and SDN

To realize 5G network slicing, the virtual resource scheduling and allocation method based on NFV and SDN is designed. The scheme comprehensively considers 5G communication technology and network slice structure, and establishes the optimal mathematical model of network slice operation economy. Then the network functions and resources are virtualized by NFV and SDN, the greedy algorithm is adopted to solve the mapping problem of network slices, and the specific implementation algorithm is provided. The simulation results show that the allocation algorithm can customize the management of network slice resources, achieve flexible control and sharing of network traffic and resources, and significantly promote the construction, optimization and promotion of 5G mobile communication network architecture.

Optimal calculation of the operation strategy of a distributed heating system combining wind, solar and electrical energy

In this paper, a distributed combined heating system is proposed, composed of an electrically driven air source heat pump (two-stage compression type), solar collector, wind turbine heater, and thermal storage device. A multi-objective optimization mathematical model is established, aiming to minimize the operating cost and carbon dioxide emission during a certain time. The multi-objective planning problem is used to guide solutions to building heating problems in Northern China. Subsequently, for a specific example, the NSGA2 algorithm is used to solve the calculation. Based on the compromise solution of the two optimization objectives, the optimal operation strategy is determined: the amount of heat generated or stored by each device on a typical day. The optimal operating strategy is as follows. In the low heat load period (9:00-16:00), which coincides with the sunny period, the heat production of the solar collectors and the wind turbine heaters exceeds the heat load, and the storage device stores surplus heat. During peak hours (0:00-9:00, 16:00-24:00), the solar collectors are not activated because the solar irradiance is nearly zero. And at this point, the heat production by the wind turbine heaters fluctuates greatly, and the air source heat pump turns out to be the main heating equipment and the heat storage device to release heat when necessary.

Utopia for Norwegian helicopter emergency medical services: Estimating the number of bases needed to radically bring down response times, and lives needed to be saved for cost effectiveness.

Helicopter Emergency Medical Services (HEMS) throughout Europe are generally on scene within 10-15 minutes. In Norway, however, with its 13 HEMS bases, only 75% of the population can currently be reached within half an hour. We estimate the number of HEMS bases needed to reach the full Norwegian population within 10-15 minutes, and discuss implications regarding cost effectiveness. Using geographic location and population characteristics from Norway's 428 municipalities as input to the Maximal Covering Location Problem-a mathematical location optimization model-we estimate the number of HEMS bases required along with accompanying personnel and healthcare costs. We estimate the minimum number of lives that would have to be saved to achieve a net social benefit of zero. To reach 99% or 100% of the Norwegian population by HEMS within 15 minutes 78 or 104 bases are needed, respectively. The incremental need for personnel going from 20 to 15 minutes for 99/100% of the population is 602/728, with an accompanying incremental cost of 228/276 million EURO per year. A yearly total of 280/339 additional lives would have to be saved to obtain a net social benefit of zero. Then, the HEMS-system as a whole would be cost effective although the least efficient bases still would not be. Reducing Norwegian HEMS response times to 10-15 minutes requires a drastic increase in the number of HEMS bases needed. Choice of ethical philosophy (utilitarianism or egalitarianism) determines when the expansion might be considered cost effective.

TÍNH TOÁN THIẾT KẾ VÀ TỐI ƯU HÓA KẾT CẤU KHUNG MÁY IN 3D BÊ TÔNG KÍCH THƯỚC LỚN DẠNG CỔNG TRỤC

This article presents the structural analysis and design optimization of the frame of a large-scale 3D concrete printer for construction. A finite element model of the frame of the 3D printer with various operating conditions was established using NX Nastran and Ansys APDL software. The script code for automated calculation of the deflection and natural frequency of the structure was built in the integrated Matlab-Ansys APDL language. The influence of different design parameters on the behavior of the structure is clearly evaluated with the aid of script code. Then, the optimal mathematical model of the X and Z axis structure is built with the criteria of the minimum mass, four constraints, and six variables as design parameters. The problem is solved by the genetic algorithm. Based on the optimal set of parameters and the standard box steel size table, a reasonable design option was selected, with the mass reduced by 70.6 % compared to the design option based on early experience.

Mathematical Modeling for Distribution Optimization of Senior High School Telephone Booths

Due to the policy of the Ministry of Education, many senior high schools in China have constructed some telephone booths. However, the survey found that the distribution of telephone booths in senior high school is irrational. Previous studies focused on the humanized design of telephone booths and the 0-1 planning optimization of charging pile location, but there were few studies on optimizing the distribution of phone booths in campus. It is necessary to optimize the distribution of telephone booths in senior high schools to facilitate students' life and save students' time. In this paper, Qingdao No. 2 Middle School in Shandong Province is taken as an example. Firstly, according to the previous research on 0-1 programming model, the number of people and demand in the distribution area of telephone booths in the campus are scored, and the scoring matrix is formed. Then 0-1 programming modeling was carried out and solved with Matlab. Finally, the optimal construction point to be built is obtained.

Optimisation Models for Pathway Activity Inference in Cancer.

With advances in high-throughput technologies, there has been an enormous increase in data related to profiling the activity of molecules in disease. While such data provide more comprehensive information on cellular actions, their large volume and complexity pose difficulty in accurate classification of disease phenotypes. Therefore, novel modelling methods that can improve accuracy while offering interpretable means of analysis are required. Biological pathways can be used to incorporate a priori knowledge of biological interactions to decrease data dimensionality and increase the biological interpretability of machine learning models. A mathematical optimisation model is proposed for pathway activity inference towards precise disease phenotype prediction and is applied to RNA-Seq datasets. The model is based on mixed-integer linear programming (MILP) mathematical optimisation principles and infers pathway activity as the linear combination of pathway member gene expression, multiplying expression values with model-determined gene weights that are optimised to maximise discrimination of phenotype classes and minimise incorrect sample allocation. The model is evaluated on the transcriptome of breast and colorectal cancer, and exhibits solution results of good optimality as well as good prediction performance on related cancer subtypes. Two baseline pathway activity inference methods and three advanced methods are used for comparison. Sample prediction accuracy, robustness against noise expression data, and survival analysis suggest competitive prediction performance of our model while providing interpretability and insight on key pathways and genes. Overall, our work demonstrates that the flexible nature of mathematical programming lends itself well to developing efficient computational strategies for pathway activity inference and disease subtype prediction.

Small tradeoffs between social equity and conservation outcomes in a freshwater payment for ecosystem services scheme.

Conservation programs around the world aim to balance social equity, economic efficiency, and conservation outcomes. Tradeoffs among these three objectives necessarily exist but have been quantified in only a handful of systems. Here, we use a multi-objective mathematical optimization model in a large, water-limited river basin to quantify these tradeoffs in a freshwater payment for ecosystem services (PES) program aimed at establishing environmental flows (e-flows). Across a range of budgetary and future climate scenarios, we find that tradeoffs between social equity and conservation outcomes are small. We also show that payment schemes in which incentives are allocated to a single water use sector are much less cost-effective than schemes in which incentives are allocated among multiple sectors. Thus, allocating payments equally among agricultural, municipal, and industrial sectors can be both more equitable and more cost-effective. Overall, our results illustrate how some carefully designed conservation programs may be able to achieve a triple bottom line of social equity, economic efficiency, and conservation effectiveness.

Aspect and orientation-based sentiment analysis of customer feedback using mathematical optimization models

Aspect and orientation-based sentiment analysis of customer feedback using mathematical optimization models

Multi-objective Optimization Design of Solar UAV Overall Parameters

Based on the design background of solar UAV, this paper introduces the characteristics of this kind of UAV, such as high flying height, large wingspan, large structural deformation and low wing load. The mathematical model of multi-objective optimization for this type of UAV is established, and the multi-objective genetic algorithm is used to optimize the design. The optimization results of the aircraft design are obtained by computer. Finally, the summary parameters and basic design drawings of this kind of aircraft are given. The results show that multi-objective optimization can be used in the design of solar UAV, and the optimal combination of the overall parameters of this kind of UAV can be obtained to avoid design defects and improve design efficiency. After the optimization design, the overall performance of the aircraft has been improved. This method has a certain reference value for the design of new aircraft.

Using applied program packages in determining optimum cutting modes

Purpose. Comparison of the functionality of application program packages when determining optimal cutting modes during mechanical processing. Creation of a mathematical model with technological limitations when boring a shaft in one pass and carrying out calculations. The methods. Research methods were based on the principles of optimization of cutting processes, the theory of cutting and cutting tools, standard methods of determining correction factors were used when creating technological limitations. The smallest machine processing time is chosen as the objective function. Using the functionality of the mathematical package Mathcad and the "Turning optimization" program. Findings. The created mathematical model of turning optimization sufficiently fully describes the machining process. The difference between calculations by two methods is no more than 10%. The functionality of the application programs is enough to determine the optimal parameters of the cutting modes - the number of revolutions of the machine spindle and feed. In addition, when using the Mathcad package, it is possible to add or remove technological constraints. Without a suitable database of correction factors, the search and calculation process is complicated. On the other hand, the "Turning optimization" program works in automatic mode, you only need to enter the initial data. But it is impossible to change the technological limitations, the insufficient number of standard materials of cutting tools and parts. The originality. A mathematical model of optimization of cutting modes when boring a shaft to a pass with corresponding technological limitations was created and investigated. A comparison of application program packages was carried out when determining the optimal cutting modes. Advantages and disadvantages of application programs are defined. Practical implementation. The proposed mathematical model of optimization of cutting modes during turning allows to determine the optimal parameters of the number of revolutions and feed of the machine. Its use will greatly facilitate calculations carried out by designer-technologists when designing technological routes for processing parts and calculating cutting modes. This will significantly reduce production preparation time, especially when using CNC machines.

Simultaneous Wireless Information and Power Transfer in mmWave Networks Under User-Centric Base Station Clustering

User-centric base station (BS) deployment has been designed for the fifth-generation (5G) dense millimeter wave (mmWave) networks for alleviating the inter-cell interference and improving the cell-edge user experience. However, the system power consumption increases sharply with the network density. In this paper, we investigate a user-centric simultaneous wireless information and power transfer (SWIPT) mmWave system employing a time-switching protocol at users to allow both energy harvesting (EH) and data decoding. To enable user-centric BS cooperation, adaptive BS clustering model is used to determine the user’s serving cluster based on its channel condition. Considering both linear and non-linear EH models, we analyze the joint coverage, namely, the probability that the user harvests enough energy in a given time slot and receives the required data from its serving cluster. The random serving clusters and the correlation between the amount of harvested energy and received data rate make the joint coverage analysis more challenging. A tractable tight approximation of the joint coverage probability is thus derived for ultra-dense networks. A mathematical optimization model for the time switching coefficient is also developed to maximize the system joint rate and energy coverage performance. All mathematical expressions are validated by Monte-Carlo simulations. Our results show that the proposed analytical framework is accurate and efficient for the design and deployment of SWIPT-enabled user-centric mmWave networks.

Selecting an Optimal Scenario for Addressing Supplier Selection Problem by Considering Sustainable Scheduling: A Hybrid Approach

The iron and steel industry is a pillar industry of the national economy in many countries and is also a source of high energy consumption and pollution gas emissions. In addition to the economic aspect, there have been increasing concerns over how to minimise the negative environmental impact and enhance the awareness of social responsibility for iron and steel enterprises. Therefore, this study proposes an intelligent scheduling system for addressing the supplier selection problem by considering sustainable scheduling (SS) (ISS-AFLCSS) to achieve maximised benefits of logistics costs, carbon emission and fatigued driving for the Chengsteel Company. In the ISS-AFLCSS, first, a multiobjective mathematical optimisation model is formulated. Second, this study proposed a hybrid approach using an improved genetic algorithm (GA) to optimise multiple objectives of scenarios and adopting the technique for order preference by similarity to an ideal solution (TOPSIS) method with the analytic hierarchy process (AHP) to precisely optimise and select a best-ideal scenario. The results confirm that the proposed ISS-AFLCSS can provide accurate guidance in practicing SS for managers of enterprises.

METHODOLOGICAL APPROACH TO THE MATHEMATICAL MODELS CONSTRUCTION OF BIOOBJECT PROBLEMS

This article reveals a technique for the mathematical modeling of biotechnological systems that contain sources of laser action. Calculation and optimization mathematical models for finding rational values of the technical parameters of the emitters are the basis for this. The authors researched the main aspects of the theory of analysis and synthesis of complex systems that contain concentrated, moving sources of physical fields. To ensure the viability of embryo cells, it is necessary to carefully monitor the level of embryo heating not only at the points closest to the laser dissection site but also at the end of the laser action. It should also be noted that at the end of the short-term effect of laser radiation, the flow of heat from the border of the embryo dissection passes to other parts of it. The non-stationary process of thermal distribution will occur until a stationary mode is established, which is necessary to maintain the viability of the embryo. Due to the peculiarities of the microbiological object, the authors perform mathematical modeling of a non-stationary, nonlinear, multidimensional biotechnological system, which contains a discrete, moving source of laser action. It is quite difficult to implement applied optimization mathematical models that are used to optimize the modeled system. Therefore, it is advisable to obtain approximate solutions to boundary value problems with averaged values of thermophysical parameters of laser emitters without considering the three-layer structure of the embryo. To increase the level of viability of germ cells, the authors propose to implement an applied optimization mathematical model for minimizing the deviation of the temperature of laser action from its acceptable value. This will make it possible to obtain rational technical parameters of the emitters, which are close to reality and satisfy the needs of the technical use of laser emitters.

Multi-objective optimization and dynamic response predictions of an articulated offshore wind turbine

In this manuscript, a compliant articulated offshore wind turbine (AOWT) is proposed to operate in the transitional water depth area and a three-objective optimization mathematical model is established to optimize the main dimensions of the articulated foundation. The relative optimal solutions (pareto solutions) are obtained by the third generation non-dominated sorting genetic algorithm (NSGA-Ⅲ). The corresponding main dimensions are determined through the fuzzy comprehensive evaluation. In order to verify the robust dynamic performances of the optimized AOWT, the time domain simulations are carried out to numerically predict the AOWT responses under both rated operational and extreme survival sea scenarios. According to the results, the optimized AOWT is significantly improved in terms of construction cost, structural stability, motion performance and power generation stability, and fully satisfies the operating requirements under different sea scenarios. From the impact of different load factors on response results, the second-order load induces larger oscillations but has little effect on the mean positions of the AOWT. Both turbulent wind and second-order difference frequency second order force induce greater dynamic responses in the low-frequency region.

A Novel Mathematical Model That Predicts the Protection Time of SARS-CoV-2 Antibodies.

Infectious diseases such as SARS-CoV-2 pose a considerable threat to public health. Constructing a reliable mathematical model helps us quantitatively explain the kinetic characteristics of antibody-virus interactions. A novel and robust model is developed to integrate antibody dynamics with virus dynamics based on a comprehensive understanding of immunology principles. This model explicitly formulizes the pernicious effect of the antibody, together with a positive feedback stimulation of the virus-antibody complex on the antibody regeneration. Besides providing quantitative insights into antibody and virus dynamics, it demonstrates good adaptivity in recapturing the virus-antibody interaction. It is proposed that the environmental antigenic substances help maintain the memory cell level and the corresponding neutralizing antibodies secreted by those memory cells. A broader application is also visualized in predicting the antibody protection time caused by a natural infection. Suitable binding antibodies and the presence of massive environmental antigenic substances would prolong the protection time against breakthrough infection. The model also displays excellent fitness and provides good explanations for antibody selection, antibody interference, and self-reinfection. It helps elucidate how our immune system efficiently develops neutralizing antibodies with good binding kinetics. It provides a reasonable explanation for the lower SARS-CoV-2 mortality in the population that was vaccinated with other vaccines. It is inferred that the best strategy for prolonging the vaccine protection time is not repeated inoculation but a directed induction of fast-binding antibodies. Eventually, this model will inform the future construction of an optimal mathematical model and help us fight against those infectious diseases.

Cable Force Optimization of Cable-Stayed Bridge Based on Multiobjective Particle Swarm Optimization Algorithm with Mutation Operation and the Influence Matrix

To compensate the incapability of traditional cable force adjustment methods to automatically optimize cable forces, this paper proposes Midas/Civil and MATLAB as a structure calculator and a cable force optimizer, and external memory as a data transfer. Initial solutions from conventional methods can be optimized by internalizing the influence matrix into the multiobjective particle swarm optimization algorithm with mutation operation and constructing the mathematical model of cable force optimization, and then, a series of Pareto frontier solution sets are obtained. For the first time, fuzzy set theory is introduced for selecting Pareto presolution set for the optimization of cable-stayed bridges, to solve the final reasonable dead load state of bridges. By using this method, the peak vertical displacement of a main girder of the optimized cable-stayed bridge decreased from −11 mm to −6 mm, with a reduction of 45%. Before and after optimization, the difference of peak negative bending moment at the top of the pier was 34.8%, indicating that the main beam was more evenly stressed and the alignment was more reasonable.