  This paper proposes two novel approaches to perform more suitable sensitivity
analyses for discrete topology optimization methods. To properly support them,
we introduce a more formal description of the Bi-directional Evolutionary
Structural Optimization (BESO) method, in which the sensitivity analysis is
based on finite variations of the objective function. The proposed approaches
are compared to a naive strategy; to the conventional strategy, referred to as
First-Order Continuous Interpolation (FOCI) approach; and to a strategy
previously developed by other researchers, referred to as High-Order Continuous
Interpolation (HOCI) approach. The novel Woodbury approach provides exact
sensitivity values and is a better alternative to HOCI. Although HOCI and
Woodbury approaches may be computationally prohibitive, they provide useful
expressions for a better understanding of the problem. The novel Conjugate
Gradient Method (CGM) approach provides sensitivity values with arbitrary
precision and is computationally viable for a small number of steps. The CGM
approach is a better alternative to FOCI since, for appropriate initial
conditions, it is always more accurate than the conventional strategy. The
standard compliance minimization problem with volume constraint is considered
to illustrate the methodology. Numerical examples are presented together with a
broad discussion about BESO-type methods.
