Large-scale structural optimization problems are often difficult to solve with reasonable efficiency and accuracy. Such problems are often characterized by constraint functions which are not explicitly defined. Constraint and gradient functions are usually expensive to evaluate. An optimization approach which uses the NLPQL sequential quadratic programming algorithm of Schittkowski, integrated with the Automated Structural Optimization System (ASTROS) is tested. The traditional solution approach involves the formulation and solution of an explicitly defined approximate problem during each iteration. This approach is replaced by a simpler approach in which the approximate problem is eliminated. In the simpler approach, each finite element analysis is followed by one iteration of the optimizer. To compensate for the cost of additional analyses incurred by the elimination of the approximate problem, a much more restrictive active set strategy is used. The approach is applied to three large structures problems, including one with constraints from multiple disciplines. Results and algorithm performance comparisons are given. Although not much computational efficiency is gained, the alternative approach gives accurate solutions. The largest of the three problems, which had 1527 design variables and 6124 constraints was solved with ASTROS for the first time using a direct method. The resulting design represents the lowest weight feasible design recorded to date. Optimization, Structural optimization, Nonlinear programming, Sequential quadratic programming, Active set strategies.

The problem addressed is the general nonlinear programming problem: finding a local minimizer for a nonlinear function subject to a mixture of nonlinear equality and inequality constraints. The methods studied are in the class of sequential quadratic programming (SQP) algorithms, which have previously proved successful for problems of moderate size. Our goal is to devise an SQP algorithm that is applicable to large-scale optimization problems, using sparse data structures and storing less curvature information but maintaining the property of superlinear convergence. The main features are: 1. The use of a quasi-Newton approximation to the reduced Hessian of the Lagrangian function. Only an estimate of the reduced Hessian matrix is required by our algorithm. The impact of not having available the full Hessian approximation is studied and alternative estimates are constructed. 2. The use of a transformation matrix Q. This allows the QP gradient to be computed easily when only the reduced Hessian approximation is maintained. 3. The use of a reduced-gradient form of the basis for the null space of the working set. This choice of basis is more practical than an orthogonal null-space basis for large-scale problems. The continuity condition for this choice is proven. 4. The use of incomplete solutions of quadratic programming subproblems. Certain iterates generated by an active-set method for the QP subproblem are used in place of the QP minimizer to define the search direction for the nonlinear problem. An implementation of the new algorithm has been obtained by modifying the code MINOS. Results and comparisons with MINOS and NPSOL are given for the new algorithm on a set of 92 test problems.

With contributions by specialists in optimization and practitioners in the fields of aerospace engineering, chemical engineering, and fluid and solid mechanics, the major themes include an assessment of the state of the art in optimization algorithms as well as challenging applications in design and control, in the areas of process engineering and systems with partial differential equation models.

Structural design problems are often modeled using finite element methods. Such models are often characterized by constraint functions that are not explicitly defined in terms of the design variables. These functions are typically evaluated through numerical finite element analysis (FEA). Optimizing large-scale structural design models requires computationally expensive FEAs to obtain function and gradient values. An optimization approach which uses the SCP sequential convex programming algorithm of Zillober, integrated as the optimizer in the Automated Structural Optimization System (ASTROS), is tested. The traditional approach forms an explicitly defined approximate subproblem at each design iteration that is solved using the method of modified feasible directions. In an alternative approach, the SCP subroutine is called to formulate and solve the approximate subproblem. The SCP method is an implementation of the Method of Moving Asymptotes algorithm with five different asymptote determination strategies. This study investigates the effect of different asymptote determination strategies and constraint retention strategies on computational efficiency. The approach is tested on three large-scale structural design models, including one with constraints from multiple disciplines. Results and comparisons to the traditional approach are given. The largest of the three models, which had 1527 design variables and 6124 constraints, was solved to optimality with ASTROS for the first time using a mathematical programming method. The structural weight of the resulting design is 9% lower than the previously recorded minimum weight.