Closing the gap: Improved bounds on optimal POMDP solutions

POMDP algorithms have made significant progress in recent years by allowing practitioners to find good solutions to increasingly large problems. Most approaches (including point-based and policy iteration techniques) operate by refining a lower bound of the optimal value function. Several approaches (e.g., HSVI2, SARSOP, grid-based approaches and online forward search) also refine an upper bound. However, approximating the optimal value function by an upper bound is computationally expensive and therefore tightness is often sacrificed to improve efficiency (e.g., sawtooth approximation). In this paper, we describe a new approach to efficiently compute tighter bounds by i) conducting a prioritized breadth first search over the reachable beliefs, ii) propagating upper bound improvements with an augmented POMDP and iii) using exact linear programming (instead of the sawtooth approximation) for upper bound interpolation. As a result, we can represent the bounds more compactly and significantly reduce the gap between upper and lower bounds on several benchmark problems. Copyright © 2011, Association for the Advancement of Artificial Intelligence. All rights reserved.

Effect of inclusions and holes on the stiffness and strength of honeycombs

A finite element study has been performed on the effects of holes and rigid inclusions on the elastic modulus and yield strength of regular honeycombs under biaxial loading. The focus is on honeycombs that have already been weakened by a small degree of geometrical imperfection, such as a random distribution of fractured cell walls, as these imperfect honeycombs resemble commercially available metallic foams. Hashin-Shtrikman lower and upper bounds and self-consistent estimates of elastic moduli are derived to provide reference solutions to the finite element calculations. It is found that the strength of an imperfect honeycomb is relatively insensitive to the presence of holes and inclusions, consistent with recent experimental observations on commercial aluminum alloy foams.