Mixed variational formulations for structural topology optimization based on the phase-field approach

We propose a variational principle combining a phase-field functional for structural topology optimization with a mixed (three-field) Hu–Washizu functional, then including directly in the formulation equilibrium, constitutive, and compatibility equations. The resulting mixed variational functional is then specialized to derive a classical topology optimization formulation (where the amount of material to be distributed is an a priori assigned quantity acting as a global constraint for the problem) as well as a novel topology optimization formulation (where the amount of material to be distributed is minimized, hence with no pre-imposed constraint for the problem). Both formulations are numerically solved by implementing a mixed finite element scheme, with the second approach avoiding the introduction of a global constraint, hence respecting the convenient local nature of the finite element discretization. Furthermore, within the proposed approach it is possible to obtain guidelines for settings proper values of phase-field-related simulation parameters and, thanks to the combined phase-field and Hu–Washizu rationale, a monolithic algorithm solution scheme can be easily adopted. An insightful and extensive numerical investigation results in a detailed convergence study and a discussion on the obtained final designs. The numerical results clearly highlight differences between the two formulations as well as advantages related to the monolithic solution strategy; numerical investigations address both two-dimensional and three-dimensional applications.

Performance as a Constraint: An Improved Wisdom of Crowds Using Performance Regularization

Quality assurance is one of the most important problems in crowdsourcing and human computation, and it has been extensively studied from various aspects. Typical approaches for quality assurance include unsupervised approaches such as introducing task redundancy (i.e., asking the same question to multiple workers and aggregating their answers) and supervised approaches such as using worker performance on past tasks or injecting qualification questions into tasks in order to estimate the worker performance. In this paper, we propose to utilize the worker performance as a global constraint for inferring the true answers. The existing semi-supervised approaches do not consider such use of qualification questions. We also propose to utilize the constraint as a regularizer combined with existing statistical aggregation methods. The experiments using heterogeneous multiple-choice questions demonstrate that the performance constraint not only has the power to estimate the ground truths when used by itself, but also boosts the existing aggregation methods when used as a regularizer.

A Global Constraint for the Exact Cover Problem: Application to Conceptual Clustering

We introduce the exactCover global constraint dedicated to the exact cover problem, the goal of which is to select subsets such that each element of a given set belongs to exactly one selected subset. This NP-complete problem occurs in many applications, and we more particularly focus on a conceptual clustering application. We introduce three propagation algorithms for exactCover, called Basic, DL, and DL+: Basic ensures the same level of consistency as arc consistency on a classical decomposition of exactCover into binary constraints, without using any specific data structure; DL ensures the same level of consistency as Basic but uses Dancing Links to efficiently maintain the relation between elements and subsets; and DL+ is a stronger propagator which exploits an extra property to filter more values than DL. We also consider the case where the number of selected subsets is constrained to be equal to a given integer variable k, and we show that this may be achieved either by combining exactCover with existing constraints, or by designing a specific propagator that integrates algorithms designed for the NValues constraint. These different propagators are experimentally evaluated on conceptual clustering problems, and they are compared with state-of-the-art declarative approaches. In particular, we show that our global constraint is competitive with recent ILP and CP models for mono-criterion problems, and it has better scale-up properties for multi-criteria problems.