Parameter Optimization Problem Research Articles

Application of improved gradient projection method to parametric optimization of steel lattice portal frame

The paper has proposed a mathematical model for parametric optimization problem of the steel lattice portal frame. The design variable vector includes geometrical parameters of the structure (node coordinates), as well as cross-sectional dimensions of the structural members. The system of constraints covers load-carrying capacities constraints formulated for all design sections of structural members of the steel structure subjected to all ultimate load case combinations. The displacements constraints formulated for the specified nodes of the steel structure subjected to all serviceability load case combinations have been also included into the system of constraints. Additional requirements in the form of constraints on lower and upper values of the design variables, constraints on permissible minimal thicknesses, constraints on permissible maximum diameter-to-thickness ratio for the structural members with circle hollow sections, as well as the conditions for designing gusset-less welded joints between structural members with circle hollow sections have been also considered in the scope of the mathematical model. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the formulated parametric optimization problem. New optimal layouts of the steel lattice portal frame by the criterion of the minimum weight, as well as minimum costs on manufacturing and erection have been presented.

Parametric approach for approximate efficiency of robust multiobjective fractional programming problems

In this paper, a methodology is developed to solve an uncertain multiobjective fractional programming problem in the face of data uncertainty in the objective and constraint functions. We use the robust optimization approach (worst‐case approach) for finding ɛ‐efficient solutions of the associated robust multiobjective fractional programming problem defined as a robust (worst‐case) counterpart. For the robust multiobjective fractional programming problem constructed in the robust approach, In fact, in the parametric Dinkelbach approach. We define for the given multiobjective fractional programming problem its corresponding parametric robust vector optimization problem. Then, we establish both necessary and sufficient optimality conditions for a feasible solution to be an ‐efficient solution (an approximate efficient solution) of the parametric robust vector optimization problem. Also we prove the relationship between ɛ‐efficiency of the robust multiobjective fractional programming problem (and thus ɛ‐efficiency of the considered uncertain multiobjective fractional programming problem) and ‐efficiency of its corresponding parametric robust vector optimization problem constructed in the Dinkelbach approach. In order to prove this result, we also use a scalarization method. Thus, the equivalence between an approximate efficient solution of the parametric robust vector optimization problem and an approximate minimizer of its associated scalar optimization problem constructed in the used scalarization method is also established.

Optimal numbers of the redundant members for introducing initial pre-stressing forces into steel bar structures

The paper considers parametric optimization problems for the steel bar structures formulated as nonlinear programming ones with variable unknown cross-sectional sizes of the structural members, as well as initial prestressing forces introduced into the specified redundant members of the structure. The system of constraints covers load-bearing capacity constraints for all the design sections of the structural members subjected to all the design load combinations at ultimate limit state, as well as displacement constraints for the specified nodes of the bar system, subjected to all design load combinations at serviceability limit state. The method of the objective function gradient projection onto the active constraints surface with simultaneous correction of the constraints violations has been used to solve the parametric optimization problem. A numerical technique to determine the optimal number of the redundant members to introduce the initial prestressing forces has been offered for high-order statically indeterminate bar structures. It reduces the dimension for the design variable vector of unknown initial prestressing forces for considered optimization problems.

Sparse PLS-Based Method for Overlapping Metabolite Set Enrichment Analysis.

Metabolite set enrichment analysis (MSEA) has gained increasing research interest for identification of perturbed metabolic pathways in metabolomics. The method incorporates predefined metabolic pathways information in the analysis where metabolite sets are typically assumed to be mutually exclusive to each other. However, metabolic pathways are known to contain common metabolites and intermediates. This situation, along with limitations in metabolite detection or coverage leads to overlapping, incomplete metabolite sets in pathway analysis. For overlapping metabolite sets, MSEA tends to result in high false positives due to improper weights allocated to the overlapping metabolites. Here, we proposed an extended partial least squares (PLS) model with a new sparse scheme for overlapping metabolite set enrichment analysis, named overlapping group PLS (ogPLS) analysis. The weight vector of the ogPLS model was decomposed into pathway-specific subvectors, and then a group lasso penalty was imposed on these subvectors to achieve a proper weight allocation for the overlapping metabolites. Two strategies were adopted in the proposed ogPLS model to identify the perturbed metabolic pathways. The first strategy involves debiasing regularization, which was used to reduce inequalities amongst the predefined metabolic pathways. The second strategy is stable selection, which was used to rank pathways while avoiding the nuisance problems of model parameter optimization. Both simulated and real-world metabolomic datasets were used to evaluate the proposed method and compare with two other MSEA methods including Global-test and the multiblock PLS (MB-PLS)-based pathway importance in projection (PIP) methods. Using a simulated dataset with known perturbed pathways, the average true discovery rate for the ogPLS method was found to be higher than the Global-test and the MB-PLS-based PIP methods. Analysis with a real-world metabolomics dataset also indicated that the developed method was less prone to select pathways with highly overlapped detected metabolite sets. Compared with the two other methods, the proposed method features higher accuracy, lower false-positive rate, and is more robust when applied to overlapping metabolite set analysis. The developed ogPLS method may serve as an alternative MSEA method to facilitate biological interpretation of metabolomics data for overlapping metabolite sets.

A SWITCHING GAIN CONTROLLER IN DRSIGNING OPTIMUM CONSTRAINT CONTROL PROBLEMS BASED ON GENETIC ALGORITHM

This paper introduces an iterative approach for the design of an optimum switching gain controller for a linear time invariant single input/single output (SISO) systems. The controller parameters are determined at different switching instants so as to improve the dynamic characteristics of a closed loop system and satisfy a set of inequalities. The approach is based on solving a constrained parameter optimization problem. Optimization is carried out based on the genetic algorithm (GA) in order to find the optimum number of switching, optimum switching instants and optimum controller parameters vector. All that in the sense of minimizing a certain time based objective function and satisfying a set of parametric and operating constraints. Constraints imposed on the controlled system may be in the form of design specifications and/or performance requirements. The technique is applicable for any controller structure, and gives a set of an optimum parameter values switched at optimum switching instants. Parameter values are function of the system states at these instants. Different systems are examined to show the applicability of the presented approach. 
 

Application of the mini-batch adaptive method of random search (MAMRS) in problems of optimal in mean control of the trajectory pencils

The article discusses the application of one of the new methods of constrained optimization to solve the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems emanating from a given set of initial states. The structure of a feedback system is proposed, which contains a model of a control object, a measurement system model, a state observer that generates an estimate of the state vector from incoming measurements, and a regulator. The quality of control is assessed by the value of the average value of the functional determined on individual trajectories. Unknown control laws for the object model and the state observer are found in the form of expansions in terms of orthonormal systems of basic functions defined on the set of admissible states of the dynamic system. The problem of controlling a pencil of trajectories is reduced to the problem of parametric optimization, which is solved using a mini-batch adaptive random search method. A step-by-step algorithm for solving the problem is proposed, which is demonstrated by solving the problem of tracking various coordinates of a dynamical system according to the measurement results. The influence of the mini-batch size on the achieved tracking accuracy is investigated.

Application of the modified self-organizing migration algorithm MSOMA in optimal open-loop control problems

The article discusses the application of the metaheuristic algorithm of global constrained optimization for solving the problem of finding the optimal open-loop control for nonlinear continuous deterministic dynamical systems. The quality of control is assessed by the value of the functional defined on individual trajectories. The optimal control problem is reduced to a parametric optimization problem, which is solved using the MSOMA algorithm, which belongs to the evolutionary group. The MSOMA algorithm is a new algorithm based on the SOMA self-organizing migration algorithm. A step-by-step algorithm for piecewise-constant, piecewise-linear, quadratic spline and cubic spline methods of control laws approximation is proposed. The effectiveness of proposed method is demonstrated by the example of solving the problem of optimal control of a chemical process in a mixing reactor and a singular problem of optimal control. The influence of the parameters of the MSOMA algorithm on the quality of the obtained result is investigated. Comparison of the operation of the algorithm with a known solution, as well as with a solution using the original SOMA method is carried out.

Influence of Steering Angle Profiles on the Orbit Transfer Trajectory

This paper considers a planar orbit transfer trajectory design problem using finite thrust modeling. In this problem, the steering angles associated with the thrust direction are calculated from the predetermined profile format, and the unknown parameters in the profile are directly optimized. Three profile formats that were implemented in previous lunar exploration missions are considered. In addition, a steering angle profile defined in the rotating frame and the optimal steering angle profile are newly studied to compare the performances. To this end, the direct parameter optimization problem and the indirect optimization problem are formulated, and the characteristics of the steering angle profile and its influence on the transfer trajectory are analyzed.

Pruning Multilayered ELM Using Cholesky Factorization and Givens Rotation Transformation

Extreme learning machine is originally proposed for the learning of the single hidden layer feedforward neural network to overcome the challenges faced by the backpropagation (BP) learning algorithm and its variants. Recent studies show that ELM can be extended to the multilayered feedforward neural network in which the hidden node could be a subnetwork of nodes or a combination of other hidden nodes. Although the ELM algorithm with multiple hidden layers shows stronger nonlinear expression ability and stability in both theoretical and experimental results than the ELM algorithm with the single hidden layer, with the deepening of the network structure, the problem of parameter optimization is also highlighted, which usually requires more time for model selection and increases the computational complexity. This paper uses Cholesky factorization strategy and Givens rotation transformation to choose the hidden nodes of MELM and obtains the number of nodes more suitable for the network. First, the initial network has a large number of hidden nodes and then uses the idea of ridge regression to prune the nodes. Finally, a complete neural network can be obtained. Therefore, the ELM algorithm eliminates the need to manually set nodes and achieves complete automation. By using information from the previous generation’s connection weight matrix, it can be evitable to re-calculate the weight matrix in the network simplification process. As in the matrix factorization methods, the Cholesky factorization factor is calculated by Givens rotation transform to achieve the fast decreasing update of the current connection weight matrix, thus ensuring the numerical stability and high efficiency of the pruning process. Empirical studies on several commonly used classification benchmark problems and the real datasets collected from coal industry show that compared with the traditional ELM algorithm, the pruning multilayered ELM algorithm proposed in this paper can find the optimal number of hidden nodes automatically and has better generalization performance.

Global Optimization: A Distributed Compensation Algorithm and its Convergence Analysis

This paper introduces a distributed compensation approach for the global optimization with separable objective functions and coupled constraints. By employing compensation variables, the global optimization problem can be solved without the information exchange of coupled constraints. The convergence analysis of the proposed algorithm is presented with the convergence condition through which a diminishing step-size with an upper bound can be determined. The convergence rate can be achieved at O(lnT/√T). Moreover, the equilibrium of this algorithm is proved to converge at the optimal solution of the global optimization problem. The effectiveness and the practicability of the proposed algorithm is demonstrated by the parameter optimization problem in smart building.

A new model for early diagnosis of alzheimer's disease based on BAT-SVM classifier

Magnetic Resonance Images (MRI) of the Brain is a significant tool to diagnosis Alzheimer's disease due to its ability to measure regional changes in the brain that reflect disease progression to detect early stages of the disease. In this paper, we propose a new model that adopts Bat for parameter optimization problem of Support vector machine (SVM) to diagnose Alzheimer’s disease via MRI biomedical image. The proposed model uses MRI for biomedical image classification to diagnose three classes; normal controls (NC), mild cognitive impairment (MCI) and Alzheimer’s disease (AD). The proposed model based on segmentation for the most involved areas in the disease hippocampus, the features of MRI brain images are extracted to build feature vector of the brain, then extracting the most significant features in neuroimaging to reduce the high dimensional space of MRI images to lower dimensional subspace, and submitted to machine learning classification technique. Moreover, the model is applied on different datasets to validate the efficiency which show that the new Bat-SVM model can yield promising acceptable level of accuracy reached to 95.36 % using maximum number of bats equal to 50 and number of generation equal to 10.

Robust control for fuzzy electric power steering system: A two-layer performance approach

This study investigates the angle tracking control of the electric power steering system, which is underactuated and with (possibly fast) time-varying uncertainties. We design the control based on constraint-following, that is, formulating the tracking goal as servo constraints. To tackle the uncertainty, especially the mismatched uncertainty, a robust control is proposed with two-layer performance: deterministically guaranteed and fuzzily optimized. Particularly, the control design is implemented in three steps. First, without considering uncertainty, a nominal control is designed. Second, an uncertainty decomposition technique is presented to account for uncertainty, which creatively allocates the mismatched uncertainty for the robust control design that also builds on the nominal system control. The robust scheme is deterministic without using any “if–then” rules and guarantees uniform boundedness and uniform ultimate boundedness for the system, that is, the deterministically guaranteed performance. Third, by using fuzzy set theory to describe uncertainty, a fuzzy-based performance index, including system performance and control cost, is introduced. A control parameter optimal design problem is formulated and analytically solved, that is, the fuzzily optimized performance. The effectiveness of the proposed approach is illustrated by rigorous proof and the simulation results on the electric power steering system.

Non-singleton interval type-2 fuzzy PID control for high precision electro-optical tracking system

In this paper, two non-singleton interval type-2 fuzzy PID (NIT2F-PID) controllers for the high precision electro-optical tracking system (ETS) are presented to improve anti-interference ability. Specifically, two types of non-singleton fuzzifiers, including type-1 (T1) and type-2 (T2), are considered to construct the proposed NIT2F-PID (N1IT2F-PID and N2IT2F-PID) controllers. Faced with the optimization problem of parameters, particle swarm optimization (PSO), quantum-behaved PSO (QPSO), weighted QPSO (WQPSO) and improved QPSO with adaptive coefficients (LTQPSO) are employed for comparison of convergence performance to optimize the parameters of controllers. In addition, to demonstrate the superiority of the proposed NIT2F-PID controllers, PID, singleton T1 fuzzy PID (ST1F-PID), singleton interval T2 fuzzy PID (SIT2F-PID), T1 non-singleton interval T2 fuzzy (N1IT2F) and T2 non-singleton interval T2 fuzzy (N2IT2F) controllers are also designed. All of these controllers are tested under the circumstances of step disturbance and sinusoidal disturbance. At last, a series of simulation analyses and experimental results explicitly show performance of proposed NIT2F-PID controllers are superior to their counterparts.

MATHEMATICAL MODELLING OF ONE-GROUP GAS-HYDRAULIC CIRCUIT OF THERMAL POWER PLANT STEAM BOILER AUXILIARIES

The paper presents algebraic mathematical models of centrifugal mechanisms that operate in the power boiler gas-hydraulic circuit. The models have been built by means of head-flow curve approximation. The head-flow curve depends on the centrifugal mechanism blade rotating speed and guide vane angle. The least squares method has been applied for centrifugal mechanism head-curve approximation on the basis of experimental or numerical data. Different configurations for the connections of centrifugal mechanisms in the power boiler gas-hydraulic circuit have been considered, relationships for their performance assessment obtained, and efficiency factors for various methods of their capacity control introduced. The state equation for a complex gas-hydraulic network in the problem of its efficiency analysis has been obtained with application of Kirchhoff laws. Numerical algorithms have been developed to solve group control parameter optimization problems for the considered connections of centrifugal mechanisms. Features of mathematical models for groups of series-, parallel- and complex-connected centrifugal mechanisms with different head curves in the power boiler maintenance system have been specified. An optimal group control problem for a group of centrifugal mechanisms has been formulated and solved under various power boiler modes. For the feed pumps, individual frequency control proves to be the most effective method, while for the boiler draft mechanisms group frequency regulation turns out to be the most efficient. In a typical summer month, implementation of energy-efficient centrifugal mechanism capacity regulation method in a Thermal Power Plant is shown to result in auxiliary electricity consumption reduction by 10.96 % as compared with available actual data.

Linear Optimization in Uncertain Environment: Sensitivity of the Solution to the Belief Degree

Uncertainty theory has been initiated in 2007 by Liu, as an axiomatically developed notion, which considers the uncertainty on data as a belief degree on the domain expert’s opinion. Uncertain linear optimization is devised to model linear programs in an uncertain environment. In this paper, we investigate the relation between uncertain linear optimization and parametric programming. It is denoted that the problem can be converted to parametric linear optimization problem, at which belief degrees play the role of parameters, and parametric linear optimization with its rich literature provides insightful interpretations. In a point of view, a strictly complementary optimal solution of problem is known for the belief degree [Formula: see text], as well as the associated optimal partition. One may be interested in knowing the region of belief degrees (parameters) where this optimal partition remains invariant for all parameter values (belief degrees) in this region. We consider the linear optimization problem with uncertain rim data, i.e., the right-hand side and the objective function data. The known results in the literature are translated to the language of uncertainty theory, and managerial interpretations are provided. The methodology is illustrated via concrete examples.

Genetic algorithm for dynamic parameters estimation of the machine tool worktable using the residual vibration signal

In this article, the residual vibration signal of the worktable of the machine tool is used to identify its dynamic parameters. By analyzing the time-domain characteristics of the residual vibration signal, it is found that the signal has the similar attenuation characteristics to the impulse response of the second-order underdamped system, so a new method for identifying the dynamic parameters of the worktable is proposed. In this method, the impulse response model of the second-order underdamped system is used to describe the residual vibration signal, so the parameter identification problem based on the time-domain signal is transformed into the optimization problem of the model parameters. Then, the dynamic parameters can be determined by using the genetic algorithm. The results of the genetic algorithm are compared with the results of the autoregressive moving average method, which is a commonly used parameter identification method based on the time-domain signal. It was found that the results of the model-based method proposed in this article are more accurate than the autoregressive moving average method.

Levitin–Polyak well-posedness for equilibrium problems with the lexicographic order

The aim of this work is to investigate optimization-related problems with the objective spaces ordered by the lexicographic cones, including parametric lexicographic equilibrium problems and optimization problems with lexicographic equilibrium constraints. We introduce concepts of Levitin–Polyak well-posedness for these problems and establish a number of sufficient conditions for such properties. The assumptions are imposed directly on the data of the problems and really verifiable. We do not need to suppose the existence (and/or convexity, compactness) of the solution set because it is proved using the mentioned assumptions on the data. Moreover, our assumptions are more relaxed than those which are usually imposed.

Parametric identification of thermophysical characteristics of heat-protective decaying materials

The paper presents a method of identifying the thermophysical properties of heat-protective materials of complex multi-component composition used in structures to meet the specified requirements for their resistance to external temperature influence. The research is dedicated to the study of a thermal barrier coating material containing chemically active components that enter into a chemical decomposition process, accompanied by the heat absorption. The equivalent specific heat capacity of the material reflects its thermophysical properties, taking into account the endothermic reaction. The equivalent specific heat capacity is identified by solving the inverse heat conduction problem using the results of temperature measurement in a multi-layer structure element during the thermophysical experiment. Regularization of this incorrect inverse problem is performed when it is transformed into a mini-max parametric problem of semi-infinite optimization. The results of differential thermal analysis and known qualitative laws of endothermic reactions make it possible to narrow the set of feasible solutions to the level of a compact set of piecewise continuous functions of a special structure, which provides a reduction to the parametric optimization problem. The minimax problem is solved by an alternance optimization method. The results obtained confirm the effectiveness of the proposed method for solving applied problems.

Throughput Analysis of Small Cell Networks Under D-TDD and FFR

Dynamic time-division duplex (D-TDD) has emerged as an effective solution to accommodate the unaligned downlink and uplink traffic in small cell networks. However, the flexibility of traffic configuration also introduces additional inter-cell interference. In this letter, we study the effectiveness of applying fractional frequency reuse (FFR) as an interference coordination technique for D-TDD small cell networks. We derive the analytical expressions of downlink and uplink mean packet throughput (MPT), then study a network parameter optimization problem to maximize MPT while guaranteeing each user's throughput. Numerical results corroborate the benefits of the proposed FFR-based D-TDD in terms of improving throughput.

Generation of synchronized configuration space trajectories with workspace path constraints for an ensemble of robots

We present an approach to generate path-constrained synchronous motion for the coupled ensemble of robots. In this article, we refer to serial-link manipulators and mobile bases as robots. We assume that the relative motion constraints among the objects in the environment are given. We represent the motion constraints as path constraints and pose the problem of path-constrained synchronous trajectory generation as a non-linear optimization problem. Our approach generates configuration space trajectories for the robots to manipulate the objects such that the given motion constraints among the objects are satisfied. We present a method that formulates the problem as a discrete parameter optimization problem and solves it using successive constraint refinement techniques. The method adaptively selects the parametric representation of the configuration variables for a given scenario. It also generates an approximate solution as the starting point for the successive constraint refinement stages to reduce the computation time. We discuss in detail why successive constraint refinement strategies are useful for solving this class of problems. We demonstrate the effectiveness of the proposed method on challenging test cases in simulation and physical environments with high-degree-of-freedom robotic systems.