Method Of Feasible Directions Research Articles

Frequency optimization of laminated composite spherical shells

AbstractThis paper deals with frequency optimization of symmetrically laminated angle-ply spherical shells. The design objective is the maximization of the fundamental frequency, and the design variable is the fiber orientation in the layers. The first-order shear deformation theory and nine-node isoparametric finite element model are used for the finite element solution of the laminates. The modified feasible direction (MFD) method is used for the optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the numerical analysis is carried out to investigate the effects of geometrical parameters and boundary conditions on the optimal designs, and the results are compared.

A Continuous Relaxation Method for Multiuser Detection Problem

Based on the binary quadratic programming model of the code division multiple access maximum likelihood multiuser detection problem, a detection strategy by the continuous relaxation method is presented. The proposed method relaxes the binary quadratic programming as a nonlinear programming, which is a quadratic objective function with simple quadratic constraints. A feasible direction method is used to solve the nonlinear programming. Based on the KKT solution of the nonlinear programming, a near optimal solution is obtained for the multiuser detection problem. Simulation results show that the bit error rate performances of a detection strategy based on the continuous relaxation method is low. Furthermore, average CPU time of continuous relaxation method is much lower than that of the semidefinite programming relaxation method, especially for the large-scale detection problems. This approach provides good approximations to the optimal maximum likelihood performance.

Aerodynamic Optimization Study of a Coaxial Rotor in Hovering Flight

A primary design goal with a coaxial rotor is to minimize the combined sources of losses on the upper and lower rotors that have their source in aerodynamic interference. To this end, parametric studies were conducted using a free-vortex wake method to study the aerodynamic interference effects of changing interrotor spacing, blade twist rates, and blade planform on the interdependent loads produced on the upper and lower rotors, respectively. A formal, multistep optimization process was then conducted by coupling the aerodynamic method to an optimization approach based on the method of feasible directions, the goal being to expeditiously find the individual blade geometries that would give the highest levels of efficiency from the coaxial as a system. Because of the inherent aerodynamic differences between the upper and lower rotors of a coaxial, it is shown that the best performing coaxial rotors may require the use of different blade shapes on each rotor, but substantially different blade designs may also achieve similar values of aerodynamic efficiency. It is also shown that the nonconvexity of the design problem for a coaxial rotor may limit the usefulness of formal optimization methods, and extensive parametric studies may still be required in the process of design.

Thermal buckling load optimization of laminated plates with different intermediate line supports

This paper deals with critical thermal buckling load optimization of symmetrically laminated four layered angle-ply plates with one or two different intermediate line supports. The design objective is the maximization of the critical thermal buckling load and a design variable is the fibre orientation in the layers. The first order shear deformation theory and nine-node isoparametric finite element model are used for the finite element solution of the laminates. The modified feasible direction (MFD) method is used for the optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the numerical analysis is carried out to investigate the effects of location of the internal line supports, plate aspect ratios and boundary conditions on the optimal designs and the results are compared.

Метод возможных направлений в задачах нелинейного программирования для биматричных игр

Метод возможных направлений в задачах нелинейного программирования для биматричных игр

Fault-Tolerant Control of a Nonlinear Process with Input Constraints

A Fault-Tolerant Control (FTC) methodology has been presented for nonlinear processes being imposed by control input constraints. The proposed methodology uses a combination of Feedback Linearization and Model Predictive Control (FLMPC) schemes. The resulting constraints in the transformed process will be dependent on the actual evolving states, making their incorporation in the design context a non-trivial task. A feasible direction method has been integrated in the design procedure based on active set technique to resolve the challenging constraint–based FLMPC problem. The formulated FLMPC design method is utilized to develop a FTC scheme by providing a set of backup control configurations for a CSTR benchmark process. The successful performance of the proposed FTC methodology has been demonstrated via a category of common fault scenarios by exercising an arbitrary replacement of control configurations through a supervisor to maintain the CSTR operation at an unstable desired steady-state point.

Frequency optimization of laminated composite plates with different intermediate line supports

AbstractThis paper deals with frequency optimization of symmetrically laminated 4-layered angle-ply plates with one or two different intermediate line supports. The design objective is the maximization of the fundamental frequency and the design variable is the fiber orientation in the layers. The first order shear deformation theory and nine-node isoparametric finite element model are used for finding the natural frequencies of laminates. The modified feasible direction method is used for the optimization routine. For this purpose, a program based on FORTRAN is used. Finally, the numerical analysis is carried out to investigate the effects of location of the internal line supports, plate aspect ratios and boundary conditions on the optimal designs and the results are compared.

Thermal buckling load optimization of laminated folded composite plates

Abstract In this study, thermal buckling load optimization of symmetrically laminated composite folded plates subjected to uniformly distributed temperature load is investigated. The objective function is to maximize the critical temperature capacity of laminates and the fiber orientation is considered as a design variable. The first-order shear deformation theory is used to study thermal buckling response of the laminates. The modified feasible direction method is used as the optimization routine. For this purpose, a program based on Fortran is used for the optimization. Finally, the significant effects of crank angles, plate lengths and boundary conditions on the optimum results are demonstrated and the results are compared.

Shape optimal design of structures with dual boundary elements

This paper is concerned with the numerical implementation of the dual boundary element method for shape optimal design of two-dimensional linear elastic structures. The design objective is to minimize the structural compliance, subject to an area constraint. Sensitivities of objective and constraint functions, derived by means of Lagrangean approach and the material derivative concept with an adjoint variable technique, are computed through analytical expressions that arise from optimality conditions. The dual boundary element method, used for the discretization of the state problem, applies the stress equation for collocation on the design boundary and the displacement equation for collocation on other boundaries. The use of the stress boundary integral equation, discretized with discontinuous quadratic elements, allows an efficient and accurate computation of stresses on the design boundary. The perturbation field is described with linear continuous elements, in which the position of each node is defined by a design variable. Continuity along the design boundary is assured by forcing the end points of each discontinuous boundary element to be coincident with a design node. The optimization problem is solved by the modified method of feasible directions available in the program ADS. Examples of a plate with a hole are analyzed with the present method, for different loading conditions. The accuracy and efficiency of the implementation described herein make this formulation ideal for the study of shape optimal design of structures.

Packing equal circles into a circle with circular prohibited areas

The paper considers the problem of packing a maximal number of identical circles of a given radius into a multiconnected domain. The domain is a circle with prohibited areas to be finite unions of circles of given radii. We construct a mathematical model of the problem and investigate its characteristics. The starting points are constructed in a random way or on the ground of the hexagonal lattice. To find the local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are applied. We compare our results with the benchmark instances of packing circles into circular and annular containers. A number of numerical examples are given.

Packing congruent spheres into a multi‐connected polyhedral domain

AbstractIn this paper, we have considered a problem of packing the maximal number of congruent spheres into a multi‐connected polyhedral domain. A mathematical model of the problem has been formulated on the basis of Φ functions. This paper proposes a special way of constructing starting points. To find local maxima, a modification of the Zoutendijk method of feasible directions and a strategy of active inequalities are used. We developed a special approach to search for an approximation to a global maximum. A number of numerical examples are also provided.

Feasible direction method for bilevel programming problem

In this article, we investigate the application of feasible direction method for an optimistic non-linear bilevel programming problem. The convex lower level problem of an optimistic non-linear bilevel programming problem is replaced by relaxed KKT conditions. The feasible direction method developed by Topkis and Veinott [D.M. Topkis and A.F.jun. Veinott, On the convergence of some feasible direction algorithms for nonlinear programming, SIAM J. Control Optim. 5(1967), pp. 268–279] is applied to the auxiliary problem to get a Bouligand stationary point for an optimistic bilevel programming problem.

Cuckoo search algorithm for the selection of optimal machining parameters in milling operations

In this research, a new optimization algorithm, called the cuckoo search algorithm (CS) algorithm, is introduced for solving manufacturing optimization problems. This research is the first application of the CS to the optimization of machining parameters in the literature. In order to demonstrate the effectiveness of the CS, a milling optimization problem was solved and the results were compared with those obtained using other well-known optimization techniques like, ant colony algorithm, immune algorithm, hybrid immune algorithm, hybrid particle swarm algorithm, genetic algorithm, feasible direction method, and handbook recommendation. The results demonstrate that the CS is a very effective and robust approach for the optimization of machining optimization problems.

Solving an optimization packing problem of circles and non-convex polygons with rotations into a multiply connected region

This paper deals with the packing problem of circles and non-convex polygons, which can be both translated and rotated into a strip with prohibited regions. Using the Φ-function technique, a mathematical model of the problem is constructed and its characteristics are investigated. Based on the characteristics, a solution approach to the problem is offered. The approach includes the following methods: an optimization method by groups of variables to construct starting points, a modification of the Zoutendijk feasible direction method to search for local minima and a special non-exhaustive search of local minima to find an approximation to a global minimum. A number of numerical results are given. The numerical results are compared with the best known ones.

Optimal Error Correction and Methods of Feasible Directions

The main objective of this study is to discuss the optimum correction of linear inequality systems and absolute value equations (AVE). In this work, a simple and efficient feasible direction method will be provided for solving two fractional nonconvex minimization problems that result from the optimal correction of a linear system. We will show that, in some special-but frequently encountered-cases, we can solve convex optimization problems instead of not-necessarily-convex fractional problems. And, by using the method of feasible directions, we solve the optimal correction problem. Some examples are provided to illustrate the efficiency and validity of the proposed method.

A new hybrid differential evolution algorithm for the selection of optimal machining parameters in milling operations

This paper presents a novel hybrid optimization approach based on differential evolution algorithm and receptor editing property of immune system. The purpose of the present research is to develop a new optimization approach to solve optimization problems in the manufacturing industry. The proposed hybrid approach is applied to a case study for milling operations to show its effectiveness in machining operations. The results of the hybrid approach for the case study are compared with those of hybrid particle swarm algorithm, ant colony algorithm, immune algorithm, hybrid immune algorithm, genetic algorithm, feasible direction method and handbook recommendation.

Effect of Concrete Cost on Optimum Design of I-Steel Girder Bridges

Composite Reinforced Concrete (RC) Slab on steel I-girder bridges are widely used in the world and the optimum design of these bridges is always raised as a big question. There are many factors effect on the cost of optimum design like length, width of the bridge and else. This paper presents the effect of varying concrete cost, with keeping the steel cost constant, on the optimum design of steel I-girder bridges. The orthotropic plate theory for RC deck slab analysis was used in this study, considering span as simply supported. The problem of optimum cost of steel bridges is formulated as that of minimization of initial cost (IC) for all the bridge, which consists of substructure cost and superstructure cost. The performance constraints in the forms of flexural failure, deflection failure are based on the American Association of State Highway and Transportation Officials (AASHTO) 1989 [14th Edition]. The Sequential Unconstrained Minimization Technique (SUMT) is used to produce required optimizations for costs. A factor called Cost Ratio* which is representing the relation between concrete cost and steel cost was introduced, to show the varying concrete cost comparing with steel cost. The computer program called CPSAO is written with FORTRAN has been built to carry out computation, consisting of the analysis, design and optimization subroutines based on the feasible direction method. It has been considered that the RC deck slab and steel girders as an equivalent orthotropic plate, to find the optimum design for a bridge. To demonstrate the effect of concrete cost on the optimum design of steel I-girder bridges, different lengths of bridges and different values of cost ratio were used. The effect of these parameters on the total cost and others parameters has been presented in graphical forms. It is found that increasing concrete cost (i.e. decreasing cost ratio) leads to increase bridge cost, but meantime makes cost of superstructure and substructure closer.

A feasible direction method for image restoration

In this work, a feasible direction method is proposed for computing the regularized solution of image restoration problems by simply using an estimate of the noise present on the data. The problem is formulated as an optimization problem with one quadratic constraint. The proposed method computes a feasible search direction by inexactly solving a trust region subproblem with the truncated Conjugate Gradient method of Steihaug. The trust region radius is adjusted to maintain feasibility and a line-search globalization strategy is employed. The global convergence of the method is proved. The results of image denoising and deblurring are presented in order to illustrate the effectiveness and efficiency of the proposed method.

Combinational Methods of Vehicle Frontal Crashworthiness Optimization Based on Conceptual Model

Through full factor analysis of the stiffness of the components which have potential influence on vehicle front impacts, through sensitivity analysis of vehicle front impacts using Linear Regression Method, the stiffness significantly affected the impacts are chosen as the optimization variables. The vehicle intrusion and the deceleration waveform of B pillar are weighted as the optimization objective. The Latin Hypercube Sampling Method is used to do sampling; a response surface of the calculation results is established using Kriging Method; the optimization is done using Method of Feasible Direction, finally the most optimal car body stiffness is determined, and which can provide the basis for frontal crash safety design of the electric vehicle.

A feasible direction method for the semidefinite program with box constraints

In this paper, we try to solve the semidefinite program with box constraints. Since the traditional projection method for constrained optimization with box constraints is not suitable to the semidefinite constraints, we present a new algorithm based on the feasible direction method. In the paper, we discuss two cases: the objective function in semidefinite programming is linear and nonlinear, respectively. We establish the convergence of our algorithm, and report the numerical experiments which show the effectiveness of the algorithm.