Automated Problem Decomposition for the Boolean Domain with Genetic Programming

Researchers have been interested in exploring the regularities and modularity of the problem space in genetic programming (GP) with the aim of decomposing the original problem into several smaller subproblems. The main motivation is to allow GP to deal with more complex problems. Most previous works on modularity in GP emphasise the structure of modules used to encapsulate code and/or promote code reuse, instead of in the decomposition of the original problem. In this paper we propose a problem decomposition strategy that allows the use of a GP search to find solutions for subproblems and combine the individual solutions into the complete solution to the problem

On the stable recovery of the sparsest overcomplete representations in presence of noise

Let x be a signal to be sparsely decomposed over a redundant dictionary A, i.e., a sparse coefficient vector s has to be found such that x=As. It is known that this problem is inherently unstable against noise, and to overcome this instability, the authors of [Stable Recovery; Donoho et.al., 2006] have proposed to use an "approximate" decomposition, that is, a decomposition satisfying ||x - A s|| < \delta, rather than satisfying the exact equality x = As. Then, they have shown that if there is a decomposition with ||s||_0 < (1+M^{-1})/2, where M denotes the coherence of the dictionary, this decomposition would be stable against noise. On the other hand, it is known that a sparse decomposition with ||s||_0 < spark(A)/2 is unique. In other words, although a decomposition with ||s||_0 < spark(A)/2 is unique, its stability against noise has been proved only for highly more restrictive decompositions satisfying ||s||_0 < (1+M^{-1})/2, because usually (1+M^{-1})/2 << spark(A)/2. This limitation maybe had not been very important before, because ||s||_0 < (1+M^{-1})/2 is also the bound which guaranties that the sparse decomposition can be found via minimizing the L1 norm, a classic approach for sparse decomposition. However, with the availability of new algorithms for sparse decomposition, namely SL0 and Robust-SL0, it would be important to know whether or not unique sparse decompositions with (1+M^{-1})/2 < ||s||_0 < spark(A)/2 are stable. In this paper, we show that such decompositions are indeed stable. In other words, we extend the stability bound from ||s||_0 < (1+M^{-1})/2 to the whole uniqueness range ||s||_0 < spark(A)/2. In summary, we show that "all unique sparse decompositions are stably recoverable". Moreover, we see that sparser decompositions are "more stable".Comment: Accepted in IEEE Trans on SP on 4 May 2010. (c) 2010 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other users, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works for resale or redistribution to servers or lists, or reuse of any copyrighted components of this work in other work

Beyond Reuse Distance Analysis: Dynamic Analysis for Characterization of Data Locality Potential

Emerging computer architectures will feature drastically decreased flops/byte (ratio of peak processing rate to memory bandwidth) as highlighted by recent studies on Exascale architectural trends. Further, flops are getting cheaper while the energy cost of data movement is increasingly dominant. The understanding and characterization of data locality properties of computations is critical in order to guide efforts to enhance data locality. Reuse distance analysis of memory address traces is a valuable tool to perform data locality characterization of programs. A single reuse distance analysis can be used to estimate the number of cache misses in a fully associative LRU cache of any size, thereby providing estimates on the minimum bandwidth requirements at different levels of the memory hierarchy to avoid being bandwidth bound. However, such an analysis only holds for the particular execution order that produced the trace. It cannot estimate potential improvement in data locality through dependence preserving transformations that change the execution schedule of the operations in the computation. In this article, we develop a novel dynamic analysis approach to characterize the inherent locality properties of a computation and thereby assess the potential for data locality enhancement via dependence preserving transformations. The execution trace of a code is analyzed to extract a computational directed acyclic graph (CDAG) of the data dependences. The CDAG is then partitioned into convex subsets, and the convex partitioning is used to reorder the operations in the execution trace to enhance data locality. The approach enables us to go beyond reuse distance analysis of a single specific order of execution of the operations of a computation in characterization of its data locality properties. It can serve a valuable role in identifying promising code regions for manual transformation, as well as assessing the effectiveness of compiler transformations for data locality enhancement. We demonstrate the effectiveness of the approach using a number of benchmarks, including case studies where the potential shown by the analysis is exploited to achieve lower data movement costs and better performance.Comment: Transaction on Architecture and Code Optimization (2014

Total and selective reuse of Krylov subspaces for the resolution of sequences of nonlinear structural problems

This paper deals with the definition and optimization of augmentation spaces for faster convergence of the conjugate gradient method in the resolution of sequences of linear systems. Using advanced convergence results from the literature, we present a procedure based on a selection of relevant approximations of the eigenspaces for extracting, selecting and reusing information from the Krylov subspaces generated by previous solutions in order to accelerate the current iteration. Assessments of the method are proposed in the cases of both linear and nonlinear structural problems.Comment: International Journal for Numerical Methods in Engineering (2013) 24 page

A Software Architecture for Knowledge-Based Systems

. The paper introduces a software architecture for the specification and verification of knowledge-based systems combining conceptual and formal techniques. Our focus is component-based specification enabling their reuse. We identify four elements of the specification of a knowledge-based system: a task definition, a problem-solving method, a domain model, and an adapter. We present algebraic specifications and a variant of dynamic logic as formal means to specify and verify these different elements. As a consequence of our architecture we can decompose the overall specification and verification task of the knowledge-based systems into subtasks. We identify different subcomponents for specification and different proof obligations for verification. The use of the architecture in specification and verification improves understandability and reduces the effort for both activities. In addition, its decomposition and modularisation enables reuse of components and proofs. Ther..

Adaptation and implementation of a process of innovation and design within a SME

A design process is a sequence of design phases, starting with the design requirement and leading to a definition of one or several system architectures. For every design phase, various support tools and resolution methods are proposed in the literature. These tools are however very difficult to implement in an SME, which may often lack resources. In this article we propose a complete design process for new manufacturing techniques, based on creativity and knowledge re-use in searching for technical solutions. Conscious of the difficulties of appropriation in SME, for every phase of our design process we propose resolution tools which are adapted to the context of a small firm. Design knowledge has been capitalized in a knowledge base. The knowledge structuring we propose is based on functional logic and the design process too is based on the functional decomposition of the system, and integrates the simplification of the system architecture, from the early phases of the process. For this purpose, aggregation phases and embodiment are proposed and guided by heuristics