Method Of Feasible Directions Research Articles

A safety assessment model based on belief rule base with new optimization method

Safety assessment is an important aspect of health management for complex system. Belief rule base (BRB) is one of the expert systems which can handle uncertainty, ambiguity and conflicting information. In safety assessment based on BRB, its initial parameters are determined by experts and then modified by optimization models. In current studies, some intelligent optimization algorithms are applied, and the parameters are trained based on the generated random population. The optimized parameters and structure of BRB by these optimization models may lose physical meaning, and it loses interpretability. Thus, to ensure the modeling transparency and traceability, a safety assessment model based BRB with a new optimization method based on the method of feasible direction (MFD) is developed for the first time, where the gradient of output to model parameters is deduced. Moreover, the convergence of the optimization method is proved to ensure that the optimized parameters are optimal solutions. In the new optimization model, the parameters are trained based on the output gradient of BRB analytical model that can keep the transparency of modeling process and ensure the interpretability of the constructed safety assessment model. A case study is conducted to illustrate the effect of the developed safety assessment model.

Intelligent optimization model of actuator adjustment based on feasible direction method and genetic algorithm

The strip flatness control in tandem cold rolling has the characteristics of fast response speed and many influencing factors. The calculation accuracy of the flatness control actuator adjustment directly affects the strip flatness quality. In order to further improve the flatness quality, an intelligent optimization model for actuator adjustment is established, and the model is solved based on the feasible direction method and genetic algorithm. The field test results show that the model proposed in this paper can significantly improve the strip flatness quality, and at the same time, the model has higher stability and can meet the requirements of online flatness adjustment.

Nonlinear Programming: Theories and Algorithms of Some Unconstrained Optimization Methods (Steepest Descent and Newton’s Method)

Nonlinear programming problem (NPP) had become an important branch of operations research, and it was the mathematical programming with the objective function or constraints being nonlinear functions. There were a variety of traditional methods to solve nonlinear programming problems such as bisection method, gradient projection method, the penalty function method, feasible direction method, the multiplier method. But these methods had their specific scope and limitations, the objective function and constraint conditions generally had continuous and differentiable request. The traditional optimization methods were difficult to adopt as the optimized object being more complicated. However, in this paper, mathematical programming techniques that are commonly used to extremize nonlinear functions of single and multiple (n) design variables subject to no constraints are been used to overcome the above challenge. Although most structural optimization problems involve constraints that bound the design space, study of the methods of unconstrained optimization is important for several reasons. Steepest Descent and Newton’s methods are employed in this paper to solve an optimization problem.

Structural Modelling and Optimization of the Double-Ducted Fan UAV

This paper aims to model and optimize the structure of a double-ducted fan UAV (unmanned aerial vehicle). The structural model of the UAV is established based on main technical requirements. Aluminum alloy is selected in UAV structure. The static analysis of UAV is performed using finite element method. The section thicknesses of UAV are optimized by a feasible direction method. The optimized structure weight of the UAV is reduced by 18%. This paper provides some useful reference for the structural modelling and optimization of double-ducted fan UAV.

Optimal design to reduce torque ripple of IPM motor with radial based function meta-model considering design sensitivity analysis

In this study, optimum design process to reduce a torque ripple was presented for an interior permanent magnet (IPM) type electric traction motor. Firstly, 2-D electromagnetic finite element analysis was conducted to analyze the characteristics of the torque ripple in a view of magnetic saturation as well as cogging torque. Then, design factors of stator shape and rotor shape affecting to the torque ripple was selected as design variables. Secondly, using selected design variables, sensitivity analysis was performed to select design variable more affecting to the torque ripple and output torque by using design of experiments method. Thirdly, radial based function meta-model was constructed based on the results of the design of experiments (DOE). Finally, the optimum design was performed by using the constructed meta-model and method of feasible direction. By using the presented optimum design process, it is confirmed that the torque ripple of the optimum design was reduced to compare with the initial design and that output torque performance of the optimum design was maintained.

Optimal Cloud Resource Allocation With Cost Performance Tradeoff Based on Internet of Things

Internet of Things (IoT) still faces many challenges, one of which is how to efficiently and effectively allocate the cloud resources in order to obtain the desired quality of service (QoS) for the IoT users and communication domains. To face the above challenges, this paper first identifies that there is an issue of cost performance tradeoff, which is stemmed from various limited resources in the IoT systems and the competing services requirements. We second propose a nonlinear optimization model that attacks the resource allocation problem. Within the constraints of resources and service demands, this model seeks to maximize the suggested IoT cost performance ratio. We then find that the problem can be treated as a quasiconcave maximization problem. We are able to reduce the original problem to a pseudoconcave maximization problem and thereby identify a local solution, which is proved to be exactly the desired global one. We therefore propose a feasible direction method and design its corresponding algorithm to yield the desired solution. Finally, we provide a numerical example to demonstrate the theoretical findings of resource allocation and the proposed algorithm for the cloud computing based on IoT systems. The mathematical results and method proposed in this paper can act as designing guidelines for resource allocation and managements, computing scheduling, and networking protocol designing in the cloud infrastructure of IoT.

Fault Diagnosis of Complex Processes Using Sparse Kernel Local Fisher Discriminant Analysis.

As an outstanding discriminant analysis technique, Fisher discriminant analysis (FDA) gained extensive attention in supervised dimensionality reduction and fault diagnosis fields. However, it typically ignores the multimodality within the measured data, which may cause infeasibility in practice. In addition, it generally incorporates all process variables without emphasizing the key faulty ones when modeling the complex process, thus leading to degraded fault classification capability and poor model interpretability. To ease the above two drawbacks of conventional FDA, this brief presents an advantageously sparse local FDA (SLFDA) model, it first preserves the within-class multimodality by introducing local weighting factors into scatter matrix. Then, the responsible faulty variables are identified automatically through the elastic net algorithm, and the current optimization problem is subsequently settled through the feasible gradient direction method. Since then, the local data structure characteristics are exploited from both the sample dimension and variable dimension so that the fault diagnosis performance and model interpretability are significantly enhanced. In addition, we naturally extend SLFDA model to nonlinear variant (i.e., sparse kernel local FDA) by the kernel trick, which is substantially more resistant to strong nonlinearity. The simulation studies on Tennessee Eastman (TE) benchmark process and real-world diesel engine working process both validate that the novel diagnosis strategy is more accurate and reliable than the existing state-of-the-art methods.

Scaled accuracy based power allocation for multi-target tracking with colocated MIMO radars

A colocated MIMO radar system can offer enhanced multi-target tracking (MTT) performance due to its agile multibeam working mode, in which multiple transmit beams are synthesized simultaneously using probing signals from individual colocated transmitters. To ensure that the limited transmitting power resource of a colocated MIMO radar is exploited effectively, in this paper, a scaled accuracy based power allocation framework (SA-PAF) is proposed for MTT. For a given total power budget, an overall MTT performance objective is optimized by adjusting the transmit power of each beam based on the feedback information in the tracking recursion cycle. An overall cost function (OCF), which is a combination of individual target cost functions (ITCF), is designed as the overall performance objective of the optimization problem. The necessity of ITCF is due to the fact that the impact of the state estimation error on the objective function should be different for each target due to its unique importance (or threat level) and the corresponding tracking accuracy requirement among multiple targets. The proposed OCF can quantify the global MTT performance while properly taking into account different target priorities through ITCFs. To formulate the OCF based framework as an optimization problem, we use the exponential function that employs the posterior Cramér–Rao lower bound (PCRLB) as the tracking performance measure as the instantiation of ITCF. It is shown that the proposed scheme is non-convex in the presence of a clutter. Then, the Zoutendijk method of feasible directions (ZMFD) is used to find the suboptimal power allocation solutions. Simulation results verify the superiority of the proposed power allocation algorithm in terms of achieving the effective overall performance of MTT while taking into account the differences targets priorities.

Sparse Exponential Discriminant Analysis and Its Application to Fault Diagnosis

Discriminant analysis, as a popular supervised classification method, has been successfully used in fault diagnosis, which, however, involves a linear combination of all variables, and thus may result in poor model interpretability and inaccurate classification performance. In this paper, a sparse exponential discriminant analysis (SEDA) algorithm is proposed for addressing those issues. The sparse discriminant model is developed by introducing the penalty of lasso or elastic net into the exponential discriminant analysis algorithm, so that the key variables responsible for the fault can be automatically selected. Since the formulated model is nonconvex, it is recast as an iterative convex optimization problem using the minorization–maximization algorithm. After that, a feasible gradient direction method is developed to solve the optimization problem effectively. The sparse solutions indicate the key faulty information to improve classification performance, and thus distinguish different faults more accurately. A simulation process and a real industrial process are used to test the performance of the proposed method, and the experimental results show that the SEDA algorithm can isolate the faulty variables and simplify the discriminant model by discarding variables with little significance.

A Bilevel Optimization Approach to Coordination of Distributed Model Predictive Control Systems

A novel algorithm is proposed to coordinate distributed model predictive control (DMPC) systems. The main goal of coordinated distributed model predictive (CDMPC) is to improve the performance of an existing decentralized MPC system, which neglects the interactions among subsystems. In the first scenario, an analytic approach derives the global optimal solution to the plant-wide problem in the absence of inequality constraints in local controllers. In the second scenario, an iterative approach determines a local optimal solution to the general CDMPC problem based on the method of feasible directions. The proposed CDMPC algorithm is capable of stabilizing open-loop unstable dynamics.

Shape design sensitivity and optimization for two-temperature generalized magneto-thermoelastic problems using time-domain DRBEM

ABSTRACTThe main purpose of this article is to propose an efficient shape optimization technique based on the time-domain dual reciprocity boundary element method (DRBEM) to solve the two-temperature generalized magneto-thermoelastic problems. An implicit differentiation method was used to compute the shape design sensitivity of an approximate DRBEM solution with respect to design variables. The feasible direction method was suggested and implemented for use with the golden-section search technique for minimizing the weight objective function while satisfying all constraints. The optimum shape design of a square plate with a hole is used as the numerical example to verify the accuracy of the proposed technique.

Buckling load optimization of laminated composite stepped columns

This paper deals with critical buckling load optimization of symmetric angle-ply laminated stepped flat columns under axial compression load. The design objective is the maximization of the critical buckling load and the design variable is the fiber orientations in the layers of the laminates. The classical laminate plate theory is used for the finite element solution of the laminated stepped flat columns. The modified feasible direction (MFD) method is used for the optimization routine. For this purpose, a program based on FORTRAN is exploited. Finally, the optimization results are presented for width ratios (b/B), ratios of fillet radius (<TEX>$r_1/r_2$</TEX>), aspect ratios (L/B) and boundary conditions. The results are presented in graphical and tabular forms and the results are compared.

Hybrid Biogeography-based Optimization Algorithm for Solving Nonlinear Bilevel Programming

The article deals with a class of nonlinear bilevel programming problems in which the follower’s objective is a quasi-concave function, and a new hybrid biogeography-based optimization algorithm is proposed to search for the value of the leader’s variables. First, an extreme point searching approach is constructed to obtain the optimal solution of the follower’s programming. An efficient mutation operator is then designed by using Zoutendijk feasible direction method so that it can generate high quality potential offspring. Furthermore, a new fitness function is established that can be easily used to force the individuals moving toward the feasible region and improve the feasible solutions gradually. Under some assumptions, theoretical analysis of the algorithm has been presented. Finally, to verify the effectiveness of the algorithm, numerical experiments on 8 test problems are made and performance analysis verify the proposed algorithm can converge to the global optimal solution of bilevel programming problems.

An improved lattice structure design optimization framework considering additive manufacturing constraints

PurposeMethods to optimize lattice structure design, such as ground structure optimization, have been shown to be useful when generating efficient design concepts with complex truss-like cellular structures. Unfortunately, designs suggested by lattice structure optimization methods are often infeasible because the obtained cross-sectional parameter values cannot be fabricated by additive manufacturing (AM) processes, and it is often very difficult to transform a design proposal into one that can be additively designed. This paper aims to propose an improved, two-phase lattice structure optimization framework that considers manufacturing constraints for the AM process.Design/methodology/approachThe proposed framework uses a conventional ground structure optimization method in the first phase. In the second phase, the results from the ground structure optimization are modified according to the pre-determined manufacturing constraints using a second optimization procedure. To decrease the computational cost of the optimization process, an efficient gradient-based optimization algorithm, namely, the method of feasible directions (MFDs), is integrated into this framework. The developed framework is applied to three different design examples. The efficacy of the framework is compared to that of existing lattice structure optimization methods.FindingsThe proposed optimization framework provided designs more efficiently and with better performance than the existing optimization methods.Practical implicationsThe proposed framework can be used effectively for optimizing complex lattice-based structures.Originality/valueAn improved optimization framework that efficiently considers the AM constraints was reported for the design of lattice-based structures.

Laminate circular cylindrical shell

The paper deals with a numerical approach of optimal design modelling of laminate circular cylindrical shell. For thin-walled shells the classical shell theory is capable of accurately predicting the shell behaviour. In the frame of numerical optimization of circular cylindrical shell there is made the minimization of weight subject to displacement constraint. Thickness of layers is taken as design variable. In the example there is found the thickness of the shell laminate roof under constant pressure loading using Modified Feasible Direction method.

Energy-Efficient Chance-Constrained Resource Allocation for Multicast Cognitive OFDM Network

In this paper, an energy-efficient resource allocation problem is modeled as a chance-constrained programming for multicast cognitive orthogonal frequency division multiplexing (OFDM) network. The resource allocation is subject to constraints in service quality requirements, total power, and probabilistic interference constraint. The statistic channel state information (CSI) between cognitive-based station (CBS) and primary user (PU) is adopted to compute the interference power at the receiver of PU, and we develop an energy-efficient chance-constrained subcarrier and power allocation algorithm. Support vector machine (SVM) is employed to compute the probabilistic interference constraint. Then, the chance-constrained resource allocation problem is transformed into a deterministic resource allocation problem, and Zoutendijk’s method of feasible direction is utilized to solve it. Simulation results demonstrate that the proposed algorithm not only achieves a tradeoff between energy efficiency and satisfaction index, but also guarantees the probabilistic interference constraint very well.

Toward Cost-Efficient Content Placement in Media Cloud: Modeling and Analysis

Cloud-centric media network (CCMN) was previously proposed to provide cost-effective content distribution services for user-generated contents (UGCs) based on media cloud. CCMN service providers orchestrate cloud resources to deliver UGCs in a pay-per-use style, with an objective to minimize the operational monetary cost. The monetary cost depends on the actual usage of cloud resources (e.g., computing, storage, and bandwidth), which in turn, is affected by the content placement strategy. In this paper, we investigate this cost-optimal content placement problem. Specifically, it is formulated into a constrained optimization problem, in which the objective is to minimize the total monetary cost, with respect to the resource capacity. We tackle this problem via a two-step strategy. The first step focuses on the placement for a single content, which is mapped into a $k$ -center problem. Using a graph-theoretic approach, we derive and verify a logarithmic model between the optimal mean hop distance from viewers to contents, and the optimal number of content replicas. The second step leverages this analytical result to solve the cost optimization problem, via a feasible direction method. The analysis is substantiated via numerical simulations, using a set of data traces from a top content website. This investigation suggests that the optimal number of content replica for each title follows a power-law distribution in respect to its popularity rank. Moreover, it reveals a fundamental tradeoff between the storage and bandwidth cost. Finally, compared to existing heuristics, our proposed algorithm is able to obtain the optimal placement strategy, with lower computational complexity.

Isogeometric Shape Optimization of Ferromagnetic Materials in Magnetic Actuators

We present an isogeometric shape optimization method for the design of magnetic actuators. The objective is to maximize the magnetic force of actuators, which tends to be highly dependent on the geometry around air gap. The isogeometric shape optimization is known to be robust for the actuator design, since it can preserve the exact geometry during the design optimization. Using the Maxwell stress tensor method, the magnetic force is calculated through the isogeometric analysis. The analytical design sensitivity provides geometric exactness due to the use of non-uniform rational B-splines basis functions. The optimization problem is solved using a gradient-based algorithm of modified method of feasible directions. To demonstrate the robustness of the isogeometric method, the geometric dependence of magnetic forces is investigated. In addition, the isogeometric optimization method is applied to the design problems of linear and rotating actuators, which yields the optimal shape of the ferromagnetic materials around the air gap.

MPEC Model and Feasible Direction Method for Asymmetric Signal-Controlled Network Design Problem

MPEC Model and Feasible Direction Method for Asymmetric Signal-Controlled Network Design Problem

A zero-sum game of resource allocation: Attacker against defender

The paper studies a zero-sum game of resource allocation. Each player can use several types of facilities limited by its budget. The attacker's payoff is the probability of its strategy to overcome a defender's strategy. The authors derive the existence conditions of pure and mixed strategy solutions in the game. The method of feasible directions is considered for finding maximin and minimax strategies.