Learning (from) Deep Hierarchical Structure among Features

Data features usually can be organized in a hierarchical structure to reflect the relations among them. Most of previous studies that utilize the hierarchical structure to help improve the performance of supervised learning tasks can only handle the structure of a limited height such as 2. In this paper, we propose a Deep Hierarchical Structure (DHS) method to handle the hierarchical structure of an arbitrary height with a convex objective function. The DHS method relies on the exponents of the edge weights in the hierarchical structure but the exponents need to be given by users or set to be identical by default, which may be suboptimal. Based on the DHS method, we propose a variant to learn the exponents from data. Moreover, we consider a case where even the hierarchical structure is not available. Based on the DHS method, we propose a Learning Deep Hierarchical Structure (LDHS) method which can learn the hierarchical structure via a generalized fused-Lasso regularizer and a proposed sequential constraint. All the optimization problems are solved by proximal methods where each subproblem has an efficient solution. Experiments on synthetic and real-world datasets show the effectiveness of the proposed methods.

SMTS: Distributed, Visualized Constraint Solving

The inherent complexity of parallel computing makes development, resource monitor- ing, and debugging for parallel constraint-solving-based applications difficult. This paper presents SMTS, a framework for parallelizing sequential constraint solving algorithms and running them in distributed computing environments. The design (i) is based on a gen- eral parallelization technique that supports recursively combining algorithm portfolios and divide-and-conquer with the exchange of learned information, (ii) provides monitoring by visually inspecting the parallel execution steps, and (iii) supports interactive guidance of the algorithm through a web interface. We report positive experiences on instantiating the framework for one SMT solver and one IC3 solver, debugging parallel executions, and visualizing solving, structure, and learned clauses of SMT instances.

Constraint-handling techniques for generative product design systems in the mass customization context

Generative product design systems used in the context of mass customization are required to generate diverse solutions quickly and reliably without necessitating modification or tuning during use. When such systems are employed to allow for the mass customization of product form, they must be able to handle mass production and engineering constraints that can be time-consuming to evaluate and difficult to fulfill. These issues are related to how the constraints are handled in the generative design system. This article evaluates two promising sequential constraint-handling techniques and the often used weighted sum technique with regard to convergence time, convergence rate, and diversity of the design solutions. The application used for this purpose was a design system aimed at generating a table with an advanced form: a Voronoi diagram based structure. The design problem was constrained in terms of production as well as stability, requiring a time-consuming finite element evaluation. Regarding convergence time and rate, one of the sequential constraint-handling techniques performed significantly better than the weighted sum technique. Nevertheless, the weighted sum technique presented respectable results and therefore remains a relevant technique. Regarding diversity, none of the techniques could generate diverse solutions in a single search run. In contrast, the solutions from different searches were always diverse. Solution diversity is thus gained at the cost of more runs, but no evaluation of the diversity of the solutions is needed. This result is important, because a diversity evaluation function would otherwise have to be developed for every new type of design. Efficient handling of complex constraints is an important step toward mass customization of nontrivial product forms.

Study of the Sequential Constraint-Handling Technique for Evolutionary Optimization With Application to Structural Problems

Engineering design problems are most frequently characterized by constraints that make them hard to solve and time-consuming. When evolutionary algorithms are used to solve these problems, constraints are often handled with the generic weighted sum method or with techniques specific to the problem at hand. Most commonly, all constraints are evaluated at each generation, and it is also necessary to fine-tune different parameters in order to receive good results, which requires in-depth knowledge of the algorithm. The sequential constraint-handling techniques seem to be a promising alternative, because they do not require all constraints to be evaluated at each iteration and they are easy to implement. They nevertheless require the user to determine the ordering in which those constraints shall be evaluated. Therefore two heuristics that allow finding a satisfying constraint sequence have been developed. Two sequential constraint-handling techniques using the heuristics have been tested against the weighted sum technique with the ten-bar structure benchmark. They both performed better than the weighted sum technique and can therefore be easy to implement, and powerful alternatives for solving engineering design problems.