Global Optimization Toolbox Research Articles

Inverse design and optimization of a one-dimensional metagrating beam deflector by smart pattern search

This work introduces a fast semi-analytical algorithm for the inverse design and optimization of a one-dimensional beam deflector metagrating, utilizing Smart Pattern Search (SPS), an enhanced pattern search algorithm from MATLAB’s Global Optimization Toolbox. This algorithm demonstrates a significantly shorter processing time compared to machine learning based approaches for the same metagrating structure setup, parameters, and electromagnetic solver while achieving highly competitive efficiencies. At a wavelength of 1100 nm with angles of 60° and 70°, SPS even outperforms these methods. The SPS algorithm needs no state-of-the-art computers and completes the process in less than 27 min, while for counterpart methods at least several hours are needed on an Intel Core i7-3632QM CPU at 2.2 GHz, with 8 GB of DDR3 RAM.

Sizing and energy management of grid-connected hybrid renewable energy systems based on techno-economic predictive technique

This study intends to construct and optimally run a grid-connected hybrid renewable energy system (HRES) powering a residential building. A special techno-economic multi-objective optimization technique is used for sizing the HRES. In addition, an energy management strategy (EMS) is established as a distinct multi-objective optimization problem to minimize degradation and operating costs while improving system performance. A Bi-level mixed integer non-linear programming (BMINLP) is the framework used to formulate the two-optimization problems. Sizing problem is characterized by the higher level, on contrast; the nested EMS problem within the constraints of the size problem is presented on the lower level. For this investigation, the problem is executed via the MATLAB program. The global optimization toolbox is applied via the Multi-Objective Genetic Algorithm (MOGA) to solve the sizing optimization. While the EMS is executed using the "Intlinprg" mixed integer linear programming (MILP) solver. The technical and economic performance parameters such as degradation, renewable energy fraction (REF), operating, maintenance, and investment costs are evaluated in this study. The primary results reveal that the summer week encounters the lowest total cost and the highest REF, at roughly 99484 $ and 60 %, respectively. Furthermore, the investigation shows that the lowest degradation value attained in the same week with approximately 50.

Simulation of power consumption control of receivers at underground iron ore mining enterprises

The article presents the results of developing a concept for controlling the process of power consumption by electrical receivers with a voltage of up to 1000 V at underground mining enterprises in the function of hourly tariffs, which are characterized by variable pricing for the day ahead in current market conditions. The following parameters are considered: limitations on operation duration of a separate electrical unit during the day, the maximum load on underground substation transformers, and the amount of power ordered by the enterprise, the excess of which leads to the application of penalties. To solve the control problem, it is proposed to apply a heuristic optimization method based on a genetic algorithm. System efficiency is studied by determining settings of the evolutionary search algorithm that would ensure the lowest cost of power purchase. In particular, the crossover function (one-point, two-point, or Laplace) and the number of elite individuals in the population are modified. The experiments are carried out on the basis of the Global Optimization Toolbox in the MATLAB software package. Simulation of system efficiency through different settings of the genetic algorithm demonstrates that the minimum power cost can be ensured by using the Laplace crossover method with 10 individuals in a population of 100, of which 10 are elite and pass to the next generation unchanged. This option allows obtaining an average of 2.62 % lower daily power cost than the other parameters studied. The proposed method of power consumption control allows us to identify the achievable potential for reducing the energy component in the final product cost of iron ore mining at underground mining enterprises. It can be recommended for practical implementation at both operating and projected enterprises

Planning of UAV Flight Routes in the Problems of Group Patrolling of the Extended Territories

Currently one of the promising areas of joint use of unmanned aerial vehicles (UAVs) is group air patrolling of large territories. Here the organization of patrolling assumes the solving the planning problem of routes flight of UAV group. The paper considers the problem of optimal planning of flight routes of the same type of UAVs during group patrolling of large territories. The territorial waters or narrow border areas of any State may serve as an example of such territories. It is suggested that the patrolled area has an elongated shape and is divided into a chain of adjacent patrol zones prescribed by a separate UAV. The drone’s flight route passes through adjacent zones. The flight task performed periodically by each drone consists in moving it to a given flight zone, collecting operational data and transmitting this data to a control point (center, station). The optimization aspect of UAV flight route planning is to minimize the maximum time required to complete flight tasks. The considered problem of group patrolling reduced to the multiple traveling salesman problem — one of the classic intractable combinatorial optimization problems. A brief analysis of modern methods for solving the multiple traveling salesman problem is given. Due to the lack of effective exact methods for solving this problem, it is natural to use approximate heuristic and metaheuristic methods focused on solving NP-hard optimization problems, reducing the full search and giving a solution close to the exact one. The multiple traveling salesman problem considered in this paper is reduced to the problem of integer linear programming, for the solution of which a genetic algorithm implemented in MATLAB based on the mathematical package Global Optimization Toolbox is proposed. An illustrative example of patrolling by three UAVs of an extended territory with 11 adjacent zones is considered. Computational experiments confirm the effectiveness of the algorithmic solutions proposed in the work.

Range of application of heat pump systems on various natural refrigerants

GROUNDING: The utilization of heat pumps (variation of vapor compressing machines) for heat transfer between different temperature levels is a promising development trend, considering low cost of heat energy, environmental friendliness of working mediums, economically sufficient solutions and low cost maintenance. Heat pumps are used for heating in building structures where low potential heat sources are wastewater streams, groundwater streams, air, heat of the soil. It is also possible to use low potential heat of heat emissions from industrial plants, that can be cost effectively in terms of production resources usage.
 AIMS: Selection of the refrigerant and its composition in order to provide operational stability for heat pumps at temperature levels from 48 to 95 ̊C with minimum energy consumption for the most widespread thermodynamical cycles.
 MATERIALS AND METHODS: Standard thermodynamic cycles of heat pumps were simulated using Aspen HYSYS software. Further optimization and parameter selection were performed using MATLAB module Global Optimization Toolbox.
 RESULTS: In compliance with demanded design parameters the results of each working medium simulation were obtained. Energy efficient parameters of the common heat pumps thermodynamical cycles were determined.
 CONCLUSIONS: According to exergy analysis of the thermodynamical cycles it has been determined that mixed refrigerants, pentane and ammonia are the most suitable and energy efficient working fluids for heat pumps.

Fuzzy-based prediction of solar PV and wind power generation for microgrid modeling using particle swarm optimization

Regardless of their nature of stochasticity and uncertain nature, wind and solar resources are the most abundant energy resources used in the development of microgrid systems. In microgrid systems and distribution networks, the uncertain nature of both solar and wind resources results in power quality and system stability issues. The randomization behavior of solar and wind energy resources is controlled through the precise development of a power prediction model. Fuzzy-based solar PV and wind prediction models may more efficiently manage this randomness and uncertain character. However, this method has several drawbacks, it has limited performance when the volumes of wind and solar resources historical data are huge in size and it has also many membership functions of the fuzzy input and output variables as well as multiple fuzzy rules available. The hybrid Fuzzy-PSO intelligent prediction approach improves the fuzzy system's limitations and hence increases the prediction model's performance. The Fuzzy-PSO hybrid forecast model is developed using MATLAB programming of the particle swarm optimization (PSO) algorithm with the help of the global optimization toolbox. In this paper, an error correction factor (ECF) is considered a new fuzzy input variable. It depends on the validation and forecasted data values of both wind and solar prediction models to improve the accuracy of the prediction model. The impact of ECF is observed in fuzzy, Fuzzy-PSO, and Fuzzy-GA wind and solar PV power forecasting models. The hybrid Fuzzy-PSO prediction model of wind and solar power generation has a high degree of accuracy compared to the Fuzzy and Fuzzy-GA forecasting models.The rest of this paper is organized as: Section II is about the analysis of solar and wind resources row data. The Fuzzy-PSO prediction model problem formulation is covered in Section III. Section IV, is about the results and discussion of the study. Section V contains the conclusion. The references and abbreviations are presented at the end of the paper.

Trihedral lattice supports geometry optimization according to the stability criterion

The study proposes a technique for optimizing trihedral lattice tower structures from the condition of maximum critical load. Towers with a cross section of elements in the form of round pipes are considered. The load is represented by a horizontal concentrated force at the upper end of the tower, simulating the operation of a wind turbine. A constraint on the constancy of the mass of the structure is introduced. The variable parameters are the width of the tower, which varies in height, the height of the panels, the external diameters of the cross-section of the chords and lattice. The solution of the nonlinear optimization problem is performed in the MATLAB environment using the Optimization Toolbox and Global Optimization Toolbox packages. A tower of constant width is taken as the initial approximation. The calculation of the critical load is performed by the finite element method in a linear formulation by solving the eigenvalue problem. To solve the nonlinear optimization problem, the interior point method, the pattern search method and the genetic algorithm are used. The efficiency of the listed methods is compared. It has been found that the interior point method is the most efficient. The critical load for the optimal tower compared to the tower of constant width with the same mass increased by 2.3 times.

Multi-objective Optimization of Subsonic Glider Wing Using Genetic Algorithm

The widespread adoption of Unmanned Aerial Vehicles (UAVs) can be traced to its flexibility and wide adaptability to various operating conditions and applications, comparably low cost of construction and maintenance and environmental friendliness as they can be easily configured for electric power. The use of electric power also favours its low noise applications such as surveillance. A major issue associated with surveillance, as addressed in this study is the compromise between Range and Endurance operation modes. The Range mode relates to being able to cover longer distances while the Endurance mode relates to spending longer times in the atmosphere for a fixed charge. Trying to balance the interplay of these parameters gave rise to a multi-objective optimization where the objectives are somewhat conflicting. This resulted in a set of Pareto solutions which are a set of design parameters (primarily angle of attack) that satisfy the joint requirements of the performance parameters of Range and Endurance. This study first considered a baseline aerodynamic design using traditional design methods. Design of Experiment techniques were then used to select the most favourable design points. This model was then used to build an input framework for Genetic Optimization algorithm deployed in the Global Optimization Toolbox of MATLAB. The result of this research shows that most of the region associated with medium angle of attack (AOA) setting (7 degrees) jointly satisfies good Range and Endurance performances with an average lift-to-drag ratio of 20 in the flight configuration considered. The implication of this result is that low velocity drag encountered in surveillance that requires a high AOA is largely reduced with the medium setting, albeit stabilized with other structural and aerodynamic settings, namely an aspect ratio of 13 and a taper ratio of 0.6.

A new very simply explicitly invertible approximation for the standard normal cumulative distribution function

<abstract><p>This paper proposes a new very simply explicitly invertible function to approximate the standard normal cumulative distribution function (CDF). The new function was fit to the standard normal CDF using both MATLAB's Global Optimization Toolbox and the BARON software package. The results of three separate fits are presented in this paper. Each fit was performed across the range $ 0 \leq z \leq 7 $ and achieved a maximum absolute error (MAE) superior to the best MAE reported for previously published very simply explicitly invertible approximations of the standard normal CDF. The best MAE reported from this study is 2.73e–05, which is nearly a factor of five better than the best MAE reported for other published very simply explicitly invertible approximations.</p></abstract>

A Comparison Between Two Approaches to Optimize Weights of Connections in Artificial Neural Networks

Artificial neural networks (ANNs) have been used for estimation in numerous areas. Raising the accuracy of ANNs is always one of the important challenges, which is generally defined as a non-linear optimization problem. The aim of this optimization is to find better values for the weights of the connections and biases in ANN because they seriously affect the efficiency. This study uses two approaches to do such optimization in an ANN. For this aim, we create a feed-forward backpropagation ANN using the functions of MATLAB's deep learning toolbox. To improve its accuracy, in the first approach, we use the Levenberg - Marquardt algorithm (LMA) for training, which is available in MATLAB's deep learning toolbox. In the second approach, we optimize the values of weights and biases of ANN with Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), available in MATLAB's global optimization toolbox. Then, we assess the accuracy of estimation for the trained ANNs. In this way, for the first time in the literature, we compare these methods for the optimization of an ANN. The used data sets are also available in MATLAB. Based on the acquired results, in some data sets, training with LMA, and for some others training with PSO cause the best results, however, training with LMA is faster, significantly. Although the used approaches and the obtained conclusions are beneficial for researchers that work in this field, they have some limitations. For instance, since only the functions and data sets from MATLAB are used, it can only serve as an example for researchers.

Control systems design: the method of the generalized criterion composition for multi-criteria optimization

The article deals with optimization issues in design of an automatic control system (ACS). The method of multicriteria optimization is presented, which combines simulation of ACS and optimization procedure based on a genetic algorithm and implemented by the MATLAB / Global Optimization Toolbox. The method of the generalized criterion composition based on the initial particular criteria is also proposed. The use of this generalized criterion makes it possible to reduce the complexity of determining the optimal parameters of the ACS and allows to take into account the constraints when searching for the optimal solution.

Neural Modelling of APS Thermal Spray Process Parameters for Optimizing the Hardness, Porosity and Cavitation Erosion Resistance of Al2O3-13 wt% TiO2 Coatings

The study aims to elaborate a neural model and algorithm for optimizing hardness and porosity of coatings and thus ensure that they have superior cavitation erosion resistance. Al2O3-13 wt% TiO2 ceramic coatings were deposited onto 316L stainless steel by atmospheric plasma spray (ASP). The coatings were prepared with different values of two spray process parameters: the stand-off distance and torch velocity. Microstructure, porosity and microhardness of the coatings were examined. Cavitation erosion tests were conducted in compliance with the ASTM G32 standard. Artificial neural networks (ANN) were employed to elaborate the model, and the multi-objectives genetic algorithm (MOGA) was used to optimize both properties and cavitation erosion resistance of the coatings. Results were analyzed with MATLAB software by Neural Network Toolbox and Global Optimization Toolbox. The fusion of artificial intelligence methods (ANN + MOGA) is essential for future selection of thermal spray process parameters, especially for the design of ceramic coatings with specified functional properties. Selection of these parameters is a multicriteria decision problem. The proposed method made it possible to find a Pareto front, i.e., trade-offs between several conflicting objectives—maximizing the hardness and cavitation erosion resistance of Al2O3-13 wt% TiO2 coatings and, at the same time, minimizing their porosity.

Development of automatic control system: simulation, optimization and analysis of stability

The issues of creating an automatic control system (ACS) as part of the software and hardware complex (SHC) designed to control the technological equipment of the turbine compartment of a nuclear power plant are considered. Multicriteria optimization was carried out using ACS simulation and an optimization method based on a genetic algorithm implemented by the MATLAB / Simulink / Global Optimization Toolbox. The approximation of SHC relay-pulse controllers, which are used in control loops, by linear regulators, is carried out. Based on this, an analysis of the system stability was performed. Resistance margins are determined taking into account the influence of signal discretization in control loops. The studies showed that the optimized ACS has sufficient stability margins and provides the accuracy of maintaining the object parameters in the normal operation of the power unit.

Signal Generation for Switched Reluctance Motors using Parallel Genetic Algorithms

Switched reluctance motors (SRM) are an inherent part in robotics and automation systems where energy and cost efficiency is required. This motor type has no windings and permanent magnets on the rotor which results in a simple and robust structure. However, SRMs require a complex electronic control system to generate a specified number of voltage pulses for each motor phase. This paper presents the signal generation of multiple phases using only one current sensor in an asymmetric half bridge (AHB). In addition to maintain the predetermined phase voltages, sufficient current measurement windows and a minimal current ripple for the individual phases are further optimization criteria for signal generation. The generation of a state vector which controls the individual semiconductor for each motor phase to achieve a required phase voltage and simultaneously fulfill the multi-objective optimization criteria is challenging. Due to the vast number of possible solutions, a genetic algorithm (GA) was used to find state combinations that are suitable for the formulated optimization criteria. The results were discussed and recommendations about the genotype representation and the used genetic operators were given. Interested readers will find detailed information about the software technical implementation using the Global Optimization Toolbox from MATLAB.

Fractional-order Control: Nyquist Constrained Optimization

The adoption of fractional calculus in control systems has enabled the synthesis of new controllers with fractional-order derivatives and integrals. Several optimization-based methods for tuning of linear fractional-order controllers have been explored. However, few have considered the stability of the closed-loop system during optimization. This paper presents a model-driven method for tuning of fractional-order controllers based on a heuristic optimization technique and the experimental use of Nyquist’s stability criterion to enforce closed-loop stability of fractional-order systems. The proposed frequency domain tuning method enables tuning of linear fractional-order controllers with few to medium number of parameters. The method can handle both fractional-order linear and integer-order linear plant models and controllers. To assist the experimental use of Nyquist’s stability criterion, a function for drawing a Logarithmic amplitude polar diagram has been developed. Simulation results of the method applied to a nanopositioning system in atomic force microscopy suggest that the proposed method can be used for optimization of fractional-order controllers while enforcing closed-loop stability. Given that the system can be stabilized with the given controller. Matlab code building on the FOTF toolbox and global optimization toolbox is provided.

The control system simulation technology for optimization and determination of the feasible parameters domain

This paper focuses on the simulation technology for optimization of the automatic control system (ACS) parameters vector to be tuned and to provide a stable operating mode eliminating self-oscillations. A hybrid approach (synthesis of optimal control methods and simulation research) for designing ACS using genetic algorithms is presented, which allows taking into account constraints when searching for the optimal solution. Simulation of the ACS was performed using the software tools MATLAB / Simulink / Global Optimization Toolbox. It is shown that the proposed technology for determining the domain of recommended tuning parameters is effective for computer-aided design of ACS, it allows to significantly improve the quality of control and reduce the time spent on pre-setting developed controllers.

Numerical model for distributors of railway vehicles equipped with composite blocks

The paper describes the main features of a new numerical model of distributor for railway vehicles equipped with type K composite blocks, available in the TrainDy software. The composite brake blocks (CBB) type K guarantee better braking performance and quieter operation than traditional cast iron blocks (P10). Railway wagons with this type of shoes have different braking systems compared to wagons with traditional shoes, since their performance changes, for example, depending on the load carried by the wagon and the type of braking regime. The paper shows a series of tests comparing the numerical results provided by the new module with the experimental data. In this work, the parameters of the numerical model of the distributor are automatically calculated, by using the Mathworks "Global Optimization toolbox" for comparison between numerical and experimental data, provided by Faiveley Transport (Wabtec group) during the revision process of Leaflet UIC 421. The Frechet distance, which allows evaluating the degree of similarity of two curves, is the basis for the comparison. This approach allows identifying, on a rational and numerical basis, the parameters of the distributor, without having to use the support of an expert user.

Multistage extraction and purification of waste Sargassum natans to produce sodium alginate: An optimization approach

Sargassum in the Caribbean region has affected the livelihood of several coastal communities due to the influx of large quantities of the seaweed in recent times. This article seeks to explore how waste Sargassum natans can be utilized to produce sodium alginate. The novelty in this research lies in the optimization process, whereby multistage extraction and precipitation were investigated over commonly used single stage processing, in an effort to maximize both yield and purity. The results showed that a maximum yield of 19% was observed after 1 stage, while the purity was 74% after 4 stages. In addition, optimization of the multistage precipitation process using the Global Optimization Toolbox in MATLAB R2017b provided a novel model which indicated that a compromise between the maximum purity and yield can be obtained at 3 stages; 71–74% and 12–16% respectively. Furthermore, characterization was done using FTIR and NMR, with results comparable to a commercial sodium alginate brand, giving absorption bands at 1610 cm−1 and 1395 cm-1 and an M/G ratio of 0.51 respectively.

Model-Based Optimization of Velocity Strategy for Lightweight Electric Racing Cars

The article presents a method for optimizing driving strategies aimed at minimizing energy consumption while driving. The method was developed for the needs of an electric powered racing vehicle built for the purposes of the Shell Eco-marathon (SEM), the most famous and largest race of energy efficient vehicles. Model-based optimization was used to determine the driving strategy. The numerical model was elaborated in Simulink environment, which includes both the electric vehicle model and the environment, i.e., the race track as well as the vehicle environment and the atmospheric conditions. The vehicle model itself includes vehicle dynamic model, numerical model describing issues concerning resistance of rolling tire, resistance of the propulsion system, aerodynamic phenomena, model of the electric motor, and control system. For the purpose of identifying design and functional features of individual subassemblies and components, numerical and stand tests were carried out. The model itself was tested on the research tracks to tune the model and determine the calculation parameters. The evolutionary algorithms, which are available in the MATLAB Global Optimization Toolbox, were used for optimization. In the race conditions, the model was verified during SEM races in Rotterdam where the race vehicle scored the result consistent with the results of simulation calculations. In the following years, the experience gathered by the team gave us the vice Championship in the SEM 2016 in London.

An Innovative Genetic Algorithms-Based Inexact Non-Linear Programming Problem Solving Method

In this paper, an innovative Genetic Algorithms (GA)-based inexact non-linear programming (GAINLP) problem solving approach has been proposed for solving non-linear programming optimization problems with inexact information (inexact non-linear operation programming). GAINLP was developed based on a GA-based inexact quadratic solving method. The Genetic Algorithm Solver of the Global Optimization Toolbox (GASGOT) developed by MATLABTM was adopted as the implementation environment of this study. GAINLP was applied to a municipality solid waste management case. The results from different scenarios indicated that the proposed GA-based heuristic optimization approach was able to generate a solution for a complicated nonlinear problem, which also involved uncertainty.