Current Design Point Research Articles

A COMPREHENSIVE SOLUTION FOR ENHANCING THE EFFICIENCY AND THE ROBUSTNESS OF THE SLP ALGORITHM

Three techniques are introduced to improve the performance of the SLP algorithm. These techniques are implemented through three stages. The first stage adaptively adjusts the constraint objectives based on the current design point. This process makes the linearized constraint equation close to the current design. The second stage computes the move limits which are to be imposed on the design variables. The calculation of move limits avoids the uncertainty of determination of these values. The third stage utilizes approximate efficient reanalysis methods to do inexact line search in the direction determined by linear programming (LP). The efficiency of locating the optimum solution is increased. Incorporating these techniques into the conventional sequential linear programming (SLP) algorithm enhances the efficiency and the robustness of the algorithm. Several examples are illustrated.

An efficient shape optimization technique of a two-dimensional body based on the boundary element method

An efficient approximation method to determine the optimum shape of the minimum weight of a body subjected to stress and displacement constraints is suggested by using the boundary element method. The objective function of weight is approximated to an expansion of a second-order Taylor series and the stress and displacement constraints to expansions of a first-order Taylor series, based on the boundary element sensitivity analysis at the current design point. The approximated subproblem is then solved by a linear complementary pivot method. Design variable reduction techniques of isoparametric interpolation and trigonometric series interpolation for the design boundary shape are also adopted for reducing the degrees of freedom of the design problems.

Calculation of the move limits for the sequential linear programming method

AbstractThe sequential linear programming (SLP) method is one of the easiest optimization techniques used to treat non‐linear optimization problems. The successful application of the method is based on the proper choice of the move limits, which are unfortunately uncertain in the SLP algorithm. To enhance the efficiency and reliability of the SLP algorithm, six methods are proposed to calculate the move limits. The first three methods use the constraint equations to compute the minimum variations needed from the current design point to reach the constraint boundaries. The fourth method incorporates the cost function information as well as the constraints to figure out the move limits. The last two methods form a quadratic programming (QP) subproblem and solve for the change of the quadratic cost function. The move limits used in SLP are then computed from the estimated change of the linear cost function from the QP solution. Four numerical examples are employed to demonstrate the solution process by the methods proposed. The advantages and disadvantages of these methods are discussed.

Design Sensitivity Analysis of Three-Dimensional Body by Boundary Element Method and Its Application to Shape Optimization.

A design sensitivity calculation technique based on the implicit differentiation method is fomulated for isoparametric boundary elements for three-dimensional(3D) shape optimization problems. The practical sensitivity equations for boundary displacements and stresses are derived, and efficiency and accuracy of the technique are compared with the semi-analytic method by implementing the sensitivity analysis of typical and basic shape design problems numerically. The sensitivity calculation technique is then applied to the minimum weight design problems of 3D bodies under stress constraints, such as the shape optimization of the ellipsoidal cavity in a cube and the connecting rod, where the Taylor series approximation, based on the boundary element sensitivity analysis at current design point, is adopted for the efficient implementation of the optimization.