Efficient generation of pareto-optimal topologies for compliance optimization

In 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 fixed-point 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. Copyright (C) 2011 John Wiley & Sons, Ltd.