Improved constraint-aggregation methods

• We develop constraint-aggregation methods for bound-constrained design optimization.
• We introduce induced aggregates: a new class of constraint-aggregation method.
• We examine the properties of induced aggregates and their numerical implementation.
• We develop a post-optimality technique to assess the impact of constraint-aggregation.
• We apply these techniques to two stress-constrained mass-minimization problems.

Many constraints in design-optimization problems take the form of bounds on a physical quantity over a domain. These infinite-dimensional constraints are often addressed through aggregation methods that approximate the bound in a differentiable manner. However, the most common constraint-aggregation methods exhibit mesh dependence; as the mesh spacing decreases, the aggregation function diverges. In addition, there are no established methods to assess the impact of constraint aggregation on the optimized design. To address these deficiencies, we propose a new class of constraint-aggregation method that we call induced aggregates. We examine the properties of these aggregation methods, describe their numerical implementation, and test their numerical accuracy on a pressure-loaded circular cylinder test case. Furthermore, we propose a post-optimality estimation technique to assess the impact of the constraint-aggregation method on the design. We use this method to examine the optimized mass obtained from two stress-constrained mass minimization problems: a variable-thickness sheet problem and a wingbox design problem.