The nodal locations and cross-sectional areas of the feasible solution are next optimized to obtain an approximate optimal configuration under stress constraints.
Based on revising some modified BFGS update formulae, we construct some new quadratic approximation models to develop several approximate optimal stepsizes.
Moreover, for the nonconvex case, we also design a new approximation model to generate an approximate optimal stepsize for gradient methods.
On the other hand, the approximate optimal solution for each single-objective optimization problem is also obtained by solving the special case of problem (left ({widetilde {mbox{{P}}3}} right)).
An integrated Lagrangian relaxation and tabu search method is devised for approximating optimal problem solutions through an iterative optimization-evaluation process.
As underlined in the overview of the literature summarized here, almost all the recent, effective procedures designed for approximating optimal solutions to multi-objective combinatorial optimization problems are based on a blend of techniques, called hybrid metaheuristics.
Approximate optimal results from the TPTV model utilizing a linear approximation architecture under the TD framework can then be compared to this exact solution.
Then, for the boundary control design, we apply the control parameterization method to obtain an approximate optimal parameter selection problem that can be solved using nonlinear optimization techniques such as Sequential Quadratic Programming (SQP).
The approximate optimal results were obtained using DSLC-FOA for three structural engineering design optimization problems as examples of applications.
