! "# # $# # % &’()’* +,- . $,/ 0/ 0010-2 030, !"#$% 4 %"$#$% $+ 5 Topology optimization is a systematic method of generating designs that maximize specific objectives. While it offers significant benefits over traditional shape optimization, topology optimization can be computationally demanding and laborious. Even a simple 3D compliance optimization can take several hours. Further, the optimized topology must typically be manually interpreted and translated into a CAD-friendly and manufacturing friendly design. This poses a predicament: given an initial design, should one optimize its topology? In this paper, we propose a simple metric for predicting the benefits of topology optimization. The metric is derived by exploiting the concept of topological sensitivity, and is computed via a finite element swapping method. The efficacy of the metric is illustrated through numerical examples. ,+0%0, Design is an iterative process; with the advent of advanced computing methods, various strategies have been proposed to reduce design cycles. Topology optimization [1] is one such method to construct and discover novel designs. In topology optimization, one starts with an initial design, on which a structural problem is posed; see Figure 1. !"#$ % In this example, it is assumed that the initial design coincides with the allowable design space, but this need not be the case. Then, using finite element analysis (FEA), and one of the various topology optimization methods such as SIMP [2]–[5], evolutionary [6]–[8], or level-set [9]–[11], an optimal topology is constructed. For the problem posed in Figure 1, if the objective is compliance, the optimal topology for a volume fraction of 0.5, in the absence of other constraints, is illustrated in Figure 2(A). On the other hand, if the objective is the p- norm von Mises stress [12], an optimal topology is illustrated in Figure 2(B). Such insights can be particularly valuable during the initial stages of design. "! & !#!!’ () !#* () %