Hooke-Jeeves Method Research Articles

Оптимальный выбор начальных условий задачи Коши и его применение для расчета начального состава реакционной смеси

The article is devoted to the development of a numerical algorithm for optimal selection of initial conditions of the Cauchy problem and its application to the problem of optimal selection of initial concentrations of substances in a chemical reaction. In general form, the problem of determining the optimal composition of the reaction mixture is formulated based on the kinetic model of the reaction. A step-by-step algorithm has been developed to solve the problem using the penalty method and the Hooke-Jeeves method. The advantage of the algorithm is that it takes into account the physical and chemical features of the problem. Based on the formulated algorithm, a software package has been developed for the catalytic reaction of the synthesis of N-(adamantyl)acetamide. With its help, the optimal concentrations of the reaction reagents were calculated, at which the highest concentration of the target product is achieved.

The effectiveness of the Hooke-Jeeves method in the experiment under error conditions is assessed

The effectiveness of the Hooke-Jeeves method in the experiment under error conditions is assessed

A MEMETIC ALGORITHM APPLIED TO INDUCTION MACHINE PARAMETERS IDENTIFICATION BASED ON AN OUTPUT ERROR

Based on an output error, several evolutionary methods have been applied to identify the parameters of an Induction Machine (IM). The main drawback of these methods is their premature convergence in many situations. To overcome this issue and achieve a more accurate solution, this paper proposes a Memetic Algorithm (MA), which combines a Genetic Algorithm (GA) and a local search method. This approach uses the Hooke-Jeeves (HJ) method for the local search as a mutation operator.GA has proven good ability in global search. The HJ method has a good ability to refine the local search and achieve the optimal accuracy solution. The proposed MA, which maintains a tradeoff between exploration and exploitation strategies, is applied to minimize the related objective function to obtain the electrical and mechanical machine parameters. The validation of the method is confirmed by an experiment carried out on an (0.4 kW) IM with parameters estimated using the measured data. Using the estimated parameters, the computed transient and steady-state currents agree well with the measured data.

OPTIMAL DESIGN OF OXYGEN PRODUCTION SYSTEM BY PATTREN SEARCH METHODS

Optimal design of Oxygen production system along with production rate, pressure in storage tank, compressor power and storage tank volume constraints were formulated in this study. In formulated optimization Oxygen production system the constraints were handled by using the exterior penalty functions. The derivative free methods were used for the optimization of this formulated problem. The methods were basically designed for unconstrained optimization problems. The optimum results of the Oxygen production optimization model were obtained by using MATLAB programming environment which demonstrated the effectiveness and applicability of the model. It was observed that the results of Nelder-Mead method were better than Hooke-Jeeves method. Nelder-Mead method was more efficient with respect to its function value and its number of function evaluations.

Оптимизация величины неравномерного воздушного зазора синхронной машины с постоянными магнитами на роторе

The article proposes an approach to determining the uneven air gap of a synchronous machine with prismatic magnets on the rotor, in which the distribution of the normal component of magnetic induction along the inner circumference of the stator core has a shape close to sinusoidal. The calculation of the magnetic field of an electric machine model with the specified geometric dimensions and properties of the element materials is performed in the FEMM program. To solve the optimization problem, the Hook-Jeeves method is used, restrictions are taken into account by the method of penalty functions. As a result of modeling the magnetic field of an electric machine with a calculated optimal uneven air gap, a distribution curve of the normal component of magnetic induction along the inner circumference of the stator is obtained, the average deviation of which from the sinusoidal curve is 4,8 %.

Modeling of effective elastic-plastic properties of layered composites with a periodic structure in the framework of the anisotropic flow theory

The article is devoted to the development of a method for constructing theoretical strain diagrams. The method is based on the use of a model of effective constitutive relations for approximating the deformation diagrams of layered composites obtained using the asymptotic averaging method. To find the elastic constants of the model of a transversally isotropic composite, the method of minimizing the deviation of the approximation deformation diagrams from the diagrams obtained by the asymptotic homogenization (AH) method is used for a series of standard problems of deformation at small deformations. Minimization problems were solved using the Hooke-Jeeves method. The results of numerical simulation by the proposed method for layered composites are presented, which showed good approximation accuracy, which is achieved due to the proposed method for separating the coupled problems of micro- and macroscopic deformation.

Aircraft parameter estimation using a novel hybrid Luus–Jaakola/Hooke–Jeeves neural-network based optimization technique

The neural network–based aircraft parameter estimation techniques have gained prominence in the last decade. Neuro–Gauss–Newton (NGN) technique is a widely used neural network–based algorithm. Although the NGN technique is useful for aircraft parameter estimation, it has some limitations. The present study is motivated by the limitations of the NGN method in estimating aircraft parameters, and hence, a new hybrid Luus–Jaakola/Hooke–Jeeves (LJ/HJ) method is proposed. The hybrid LJ/HJ method is based on two direct search methods: the Luus–Jaakola (LJ) method and the Hooke–Jeeves (HJ) method. In the hybrid LJ/HJ method, a global search of the minima of the error cost function is performed using the Luus–Jaakola method in the first phase. After that, the final solution is obtained using the Hooke–Jeeves method. The parameters estimated by the hybrid LJ/HJ method are compared with those estimated using the NGN method. The results obtained from the hybrid method are accurate, and unlike gradient-based optimization methods, the convergence issues are not observed during the estimation of parameters.

Biaxial tensile test and meso damage numerical simulation of HTPB propellant

Aiming at the shortcomings of the current research on the mechanical properties of solid propellants under complex stress conditions, an effective cross-shaped test piece configuration and variable-scale biaxial tensile test method are designed in this paper, and the meso-simulation model of propellant is constructed by Micro-CT test and random filling algorithm. Then, based on the Hook-Jeeves method and the cohesive force model, the mechanical performance parameters of each mesoscopic component were obtained, and finally the damage evolution process of the propellant was numerically simulated. The results show that the stress–strain curve of the propellant under biaxial loading is similar to that of uniaxial stretching, and has obvious rate dependence and stress state dependence. The mechanical properties of the propellant under biaxial tensile loading are significantly lower than those in uniaxial stretching, and the maximum elongation is only 45–85% of that in uniaxial stretching. The fracture process of propellant can be divided into initial linear stage, damage evolution stage and fracture stage. The dewetting phenomenon generally occurs at the interface between the large-sized AP particles and the matrix. With the loading of the load, the pores formed by the dewetting and matrix tearing continue to converge into cracks and expand in the direction perpendicular to the resultant force, and finally fracture. The propellant dehumidifies more easily under high strain rate loading, but the degree of dewetting is lower when the same strain is reached.

Combination of quadratic ranking selection real-coded genetic algorithm with the Hooke-Jeeves optimization method for solar photovoltaic parameter estimation

Estimating accurate parameters for Photovoltaic cell (PVC) models plays a very important role in evaluation, simulation, control and maximum power point tracking (MPPT) of solar PV systems. Indeed, parameter extraction for solar cells and modules from experimental data is a challenging problem. These parameters must be evaluated from a set of nonlinear equations that cannot be solved analytically. Therefore, an optimization approach is essential to estimate these parameters by minimizing the difference between the calculated current from the PV model and the measured current. In this paper, a real-coded genetic algorithm (GA) based on quadratic ranking selection combined with the Hooke-Jeeves (HJ) method is proposed for this parameter extraction. It is well known that GA has proven good capacities in global search while on the other hand, the HJ has high-performance capacities in local search. As a hybrid technique, the HGAHJ has the feature of combining the capabilities of global and local searching. The proposed algorithm is developed and then applied for the parameter estimation for the single and double diode solar cell models. In addition, a comparative study with the GA and particle swarm optimization (PSO) algorithms is presented to demonstrate the effectiveness of the proposed approach using measured data of two commercial solar panels, which are Kyocera KC200GT and RTC France. Results reveal the superior capabilities of the suggested HGAHJ algorithm as a global optimization technique.

Computational Methods for Parameter Identification in 2D Fractional System with Riemann-Liouville Derivative.

In recent times, many different types of systems have been based on fractional derivatives. Thanks to this type of derivatives, it is possible to model certain phenomena in a more precise and desirable way. This article presents a system consisting of a two-dimensional fractional differential equation with the Riemann–Liouville derivative with a numerical algorithm for its solution. The presented algorithm uses the alternating direction implicit method (ADIM). Further, the algorithm for solving the inverse problem consisting of the determination of unknown parameters of the model is also described. For this purpose, the objective function was minimized using the ant algorithm and the Hooke–Jeeves method. Inverse problems with fractional derivatives are important in many engineering applications, such as modeling the phenomenon of anomalous diffusion, designing electrical circuits with a supercapacitor, and application of fractional-order control theory. This paper presents a numerical example illustrating the effectiveness and accuracy of the described methods. The introduction of the example made possible a comparison of the methods of searching for the minimum of the objective function. The presented algorithms can be used as a tool for parameter training in artificial neural networks.

Research on the capacity configuration of the “flywheel + lithium battery” hybrid energy storage system that assists the wind farm to perform a frequency modulation

Abstract In order to reduce the adverse impact of wind power fluctuations on the primary frequency modulation of the grid, based on the operation data and frequency modulation performance of the wind farm power generation equipment, the analysis is carried out, and combined with the characteristics of the “flywheel + lithium battery” hybrid energy storage system, a random time delay hybrid system is constructed. Using wavelet packet to decompose wind power grid-connected power, decoupling lithium battery energy storage and flywheel energy storage components. In order to achieve the goal of maximizing the net present value (NPV), the minimum average annual energy storage cost is taken as the objective function, and the pattern search method based on the Hooke-Jeeves method in the direct search method is used to solve the problem. The simulation results show that the research can ensure the frequency modulation performance of the wind farm-energy storage hybrid system, and at the same time determine the wind farm supporting energy storage capacity based on economic optimization, and the configuration of flywheel energy storage and lithium batteries in the hybrid energy storage system to improve the overall economic benefits of the system.

On some general scheme of constructing iterative methods for searching the Nash equilibrium in concave games

The subject of the paper is finite-dimensional concave games id est noncooperative $n$-person games with objective functionals concave with respect to `their own' variables. For such games we investigate the problem of designing iterative algorithms for searching the Nash equilibrium with convergence guaranteed without requirements concerning objective functionals such as smoothness and as convexity in `strange' variables or another similar hypotheses (in the sense of weak convexity, quasiconvexity and so on). In fact, we prove some assertion analogous to the theorem on convergence of $M$-Fej\'{er iterative process for the case when an operator acts in a finite-dimensional compact and nearness to an objective set is measured with the help of arbitrary continuous function. Then, on the base of this assertion we generalize and develop the approach suggested by the author formerly to searching the Nash equilibrium in concave games. The last one can be regarded as "a cross between" the relaxation algorithm and the Hooke-Jeeves method of configurations (but taking into account a specific character of the the residual function being minimized). Moreover, we present results of numerical experiments with their discussion.

Software Methodology for Estimating the Efficiency of the Hardware Composition of Deep Packet Inspection System Using the Modernized Hooke ‒ Jeeves Method

Deep packet inspection systems on communication networks are used to identify the application generating a specific traffic flow. The issues related to modeling and design of deep packet inspection systems remain poorly understood. In this paper, a software technique for evaluating the effectiveness of the hardware composition of the servers of the deep packet inspection system is presented, using a mathematical model of such a system and software search methods. The description of the program search by the maximum element method and the Hook - Jeeves method is given. A modernization of the Hook-Jeeves method for a monotonically decreasing function is proposed. Comparison of the methods by the number of search steps is performed.

Application of Optimization Algorithms for Identification of Reference Points in a Monitoring Network.

Geodetic measurements are commonly used in displacement analysis to determine the absolute values of displacements of points of interest. In order to properly determine the displacement values, it is necessary to correctly identify a subgroup of mutually stable points constituting a reference system. The complexity of this task depends on the spatial size of the network, the timespan of measurements and geological conditions affecting the type of changes in the location of points. As a consequence of the abovementioned factors, the task of stable identification in a longer timespan for a subgroup of points may produce equivocal results. In particular, it is likely that alternative subgroups of reference points meeting the mutual stability criteria will be selected, sometimes without common reference points. The proposed method of reference system identification utilises optimisation algorithms. Two such algorithms were tested, i.e., simulated annealing (SA) and Hooke-Jeeves (HJ) method. Two numerical examples were used to test the proposed method. Although in the first example both methods delivered a positive result, the second example showed the superiority of the SA method over the HJ. The proposed method can be considered a tool supporting the person analysing and making calculations in reaching the ultimate decision on reference points.

АЛГОРИТМЫ ПАРАМЕТРИЧЕСКОГО СИНТЕЗА, ПРИМЕНЯЕМЫЕ ПРИ ПРОЕКТИРОВАНИИ ГИБКИХ ПРОИЗВОДСТВЕННЫХ СИСТЕМ НА ОСНОВЕ КОМПЬЮТЕРНОГО МОДЕЛИРОВАНИЯ

The article discusses an approach to the automation of parametric synthesis of production equipment of highly automated production systems. Three optimization methods are considered: the coordinate descent method based on the golden ratio, the Hook-Jeeves method, and the genetic algorithm. With the help of the considered methods, a computational experiment was carried out aimed at finding the design parameters of a flexible manufacturing system that are optimal according to the criterion of equipment loading. The design parameters were assessed on the basis of a computer model of the production equipment operation process. The analysis of the experimental results showed that the highest efficiency of determining the global optimum was obtained using the genetic algorithm, but its operation takes the longest time. It has been suggested that it is possible to reduce the search time by studying the effect of the mutation value, which does not allow the genetic algorithm to get stuck in the local optimum, but worsens the convergence of the solution.

Solving the Turbine Balancing Problem Using a Metropolis Algorithm Hybridized with the Hooke-Jeeves Method

Solving the Turbine Balancing Problem Using a Metropolis Algorithm Hybridized with the Hooke-Jeeves Method

Numerical Solution of the Vibration Suppression Problem for a Moving Web

Mechanical processes occurring in paper production are modeled. In a papermaking machine, paper moves in the form of a thin sheet. The characteristic thickness of a sheet varies from 0.1 mm (office paper) to 1 mm (cardboard). Every papermaking machine contains open segments where a paper web passes without mechanical support in its motion from one roller to another. On such segments, the web may lose stability, performing transverse vibrations, and, as a result, might tear. The possibility of reducing these vibrations with the help of various control actuators is explored. The transverse vibrations of a moving web with nonzero bending stiffness are modeled by a fourth-order inhomogeneous partial differential equation. The action of control actuators is modeled a function on the right-hand side of the equation. The vibration amplitude is assumed to be identical across the moving web. The vibration suppression problem is reduced to the minimization of a multivariable function. The solution of the problem splits into two stages: the solution of an initial-boundary value problem with a given control and the minimization of a multivariable function. A numerical method is proposed for solving the initial-boundary value problem. The fourth-order differential equation is reduced to a system of two second-order differential ones. The latter are simplified by changing the sought functions. The resulting equations are approximated by a finite-difference scheme, which is proved to be absolutely stable. This scheme is solved using block Gaussian elimination. The multivariable function is minimized by applying the Hooke–Jeeves method. Examples of computations are given for actuators of three types, namely, point actuators, actuators acting on a web segment, and actuators acting along the entire web.

Методы моделирования кинетики радиофармацевтических препаратов с изотопами йода в задачах ядерной медицины

The paper considers modeling methods and develops a unified approach to the construction of mathematical models of the kinetics of radiopharmaceuticals with iodine isotopes in the human body during diagnostic and therapeutic procedures of nuclear medicine. Based on this approach, three- and four-compartment pharmacokinetic models were developed and corresponding calculation programs were created in the C++ programming language for processing and evaluating the results of radionuclide diagnostics and therapy. Various methods for identifying model parameters based on quantitative data from radionuclide studies of the functional state of vital organs are proposed. The results of pharmacokinetic modeling for radionuclide diagnostics of the liver, kidney, and thyroid using iodine-containing radiopharmaceuticals are presented and analyzed. Using clinical and diagnostic data, individual pharmacokinetic parameters of transport of different radiopharmaceuticals in the body (transport constants, half-life periods, maximum activity in the organ and the time of its achievement) were determined. It is shown that the pharmacokinetic characteristics for each patient are strictly individual and cannot be described by averaged kinetic parameters. Within the framework of three pharmacokinetic models, “Activity-time” relationships were obtained and analyzed for different organs and tissues, including for tissues in which the activity of a radiopharmaceutical is impossible or difficult to measure by clinical methods. Also discussed are the features and the results of simulation and dosimetric planning of radioiodine therapy of the thyroid gland. It is shown that the values of absorbed radiation doses are very sensitive to the kinetic parameters of the compartment model. Therefore, special attention should be paid to obtaining accurate quantitative data from ultrasound and thyroid radiometry and identifying simulation parameters based on them. The work is based on the principles and methods of pharmacokinetics. For the numerical solution of systems of differential equations of the pharmacokinetic models we used Runge-Kutta methods and Rosenbrock method. The Hooke-Jeeves method was used to find the minimum of a function of several variables when identifying modeling parameters.

Ascent guidance law for a horizontal take-off vehicle with a multi-combined cycle engine

This paper researches the ascent guidance law for the vehicle with a multi-combined cycle propulsion. The guidance law comprises two parts, namely, the off-line optimal trajectories generation and online guidance. With respect to the off-line part, disturbances are discretized and incorporated into the trajectory optimization problem; subsequently, a set of trajectories is calculated to constitute a database. To quickly obtain a database that comprises a large number of trajectories, a novel ascent profile is proposed with respect to height and velocity. Based on this profile, only inequity constraints exist in the optimization model, and the original optimization problem is converted to a parameter searching problem. The optimal trajectories are calculated using a hybrid optimization method that comprises a particle swarm optimization (PSO) method and the Hooke-Jeeves (HJ) method. With respect to online guidance, the profile is updated using a radial basis function neural network (RBFNN) based on the current flight states and the database. Simulation validates the efficiency of the proposed optimization method by comparing the method with the pseudospectral method; the robustness of the guidance law is also validated using Monte Carlo simulation.

Estimation of the Seabed Parameters in a Nonuniform Waveguide Using the Matched-Field Method

We estimate geoacoustic parameters of a layered bottom in a shallow waveguide, which is nonuniform along the path, using the data of the full-scale experiment and the matched-field method. On the basis of the available a priori geological and geophysical data, a waveguide consisting of two sedimentary layers and the underlying half-space is used as the reference geoacoustic model. When seeking the geoacoustic parameters corresponding to the global minimum of the objective function, the hybrid algorithm, which is a combination of the fast simulated annealing method and the Hook–Jeeves method of direct search, is used.