Efficient generation of pareto‐optimal topologies for compliance optimization

Abstract

SUMMARYIn multi-objective optimization, a design is defined to be pareto-optimal if no other design exists that is better with respect to one objective, and as good with respect to other objectives. In this paper, we first show that if a topology is pareto-optimal, then it must satisfy certain properties associated with the topological sensitivity field, i.e. no further comparison is necessary. This, in turn, leads to a deterministic, i.e. non-stochastic, method for efficiently generating pareto-optimal topologies using the classic fixedpoint iteration scheme. The proposed method is illustrated, and compared against SIMP-based methods, through numerical examples. In this paper, the proposed method of generating pareto-optimal topologies is limited to bi-objective optimization, namely compliance-volume and compliance-compliance. The future work will focus on extending the method to non-compliance and higher dimensional pareto optimization.

On some properties of the compliance-volume fraction Pareto front in topology optimization useful for material selection.

“…In the previous paragraphs, sufficiently small changes to the topologies along the Pareto front are shown to keep κ concave. The proof in 12 that was used can be adapted to show that small shape deformations along the Pareto front also keep κ opt concave. Therefore, for a Pareto front along which the topologies vary continuously, κ opt is concave and n ≤ 1.…”