SOLVING A SPECIAL CLASS OF MULTIPLE OBJECTIVE LINEAR FRACTIONAL PROGRAMMING PROBLEMS

In this paper a feasible direction method is presented to find all efficient extreme points for a special class of multiple objective linear fractional programming problems, when all denominators are equal. This method is based on the conjugate gradient projection method, so that we start with a feasible point and then a sequence of feasible directions towards all efficient adjacent extremes of the problem can be generated. Since methods based on vertex information may encounter difficulties as the problem size increases, we expect that this method will be less sensitive to problem size. A simple production example is given to illustrate this method.

Thermal buckling load optimization of laminated general quadrilateral and trapezoidal thin plates

This paper deals with thermal buckling load optimization of symmetrically laminated angle-ply general quadrilateral and trapezoidal thin plates. The objective function is to maximize the critical temperature capacity of the quadrilateral and trapezoidal laminated plates and the fiber orientation is considered as a design variable. The mathematical formulation is based on the classical laminated plate theory for the frequency analysis. The modified feasible direction method is used as the optimization routine. Therefore, a program based on FORTRAN is used. Finally, the significant effects of aspect ratios, boundary conditions, taper ratios and unsymmetric trapezoidal plates on the optimal results are investigated and the results are compared.

A Conjugate Gradient Type Method for the Nonnegative Constraints Optimization Problems

We are concerned with the nonnegative constraints optimization problems. It is well known that the conjugate gradient methods are efficient methods for solving large-scale unconstrained optimization problems due to their simplicity and low storage. Combining the modified Polak-Ribière-Polyak method proposed by Zhang, Zhou, and Li with the Zoutendijk feasible direction method, we proposed a conjugate gradient type method for solving the nonnegative constraints optimization problems. If the current iteration is a feasible point, the direction generated by the proposed method is always a feasible descent direction at the current iteration. Under appropriate conditions, we show that the proposed method is globally convergent. We also present some numerical results to show the efficiency of the proposed method.

A Feasible Direction Method for Design of FIR Filters with SP2 Coefficients

Based on the semidefinite programming relaxation of the design of FIR digital filters with SP2 coefficients, a feasible direction method is presented. Coupled with a randomized method, and a suboptimal solution is obtained for the problem. Furthermore, its convergence result is given. Simulation results demonstrate that the feasible direction method is an efficient method.

Frequency optimization of laminated composite plates with different intermediate line supports

This 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

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.