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Hierarchical module discovery
Abstract and Figures
Top-down hierarchical or recursive problem decomposition is a familiar and highly successful approach to design and optimization in engineering domains. However, top-down decomposition of a system or problem into more manageable parts requires a priori domain knowledge of what kinds of subsystems are feasible and what kinds of subsystem interfaces are manageable. To a large extent this depends on knowledge of existing components that have previously been identified as useful 'building-blocks' in the problem domain. In this paper we overview recent work that has developed an abstract model of automatic module discovery. In an abstract domain, our method discovers modules hierarchically in a bottom-up fashion that allows their re-use in subsequent higher-level structures. This method discovers modules without any a priori knowledge of the problem's modular structure. We outline our approach and results.
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... Firstly, only considering the strength of intra-module and inter-module interactions is sometimes overly simplistic when applied to complex dynamical systems. Sometimes the functional behavior of one module is strongly dependent on the inter-module interaction, despite a week interaction [109]. Secondly, it is necessary to consider the " size " of modules ( " granularity " ). ...
... Even one physical property can use different scale units, such as meter and millimeter for distance. It is difficult to 49 [109]. That is, the real value of a physical interaction is not necessary a good indicator of interaction between two subsystems from the view of modularity. ...
Due to their many advantages, modular structures commonly exist in artificial and natural systems, and the concept of modular product design has recently received extensive attention from the engineering research community. Although some work has been done on modularity, most of it is qualitative and exploratory in nature, and little is quantitative. One reason for this gap is the lack of a clear definition of modularity. This thesis begins with a detailed discussion on the concepts of“modularity” and “module.” Based on the background presented here, a mutual information-based method is proposed to quantify modularity. The method is based on the view that coupling is information flow instead of real physical interactions. Information flow can be quantified by mutual information, which is based on randomness (or uncertainty). Since most engineering products can be modeled as stochastic systems and therefore have randomness, the mutual information-based method can be applied in very general cases, and it is shown that the commonly existing linkage counting modularity measure is a special case of the mutual information-based modularity measure. The mutual information-based method is applicable to final design products. But at the early stage of the engineering design process, there are generally only function diagrams. To exploit the benefits of modularity as early as possible, a minimal description length principle-based modularity measure is proposed to determine the modularity of graph structures, which can represent function diagrams. The method is used as criteria to hierarchically decompose abstract graph structures and the real function structure of an HP printer by evolutionary computation. Due to the specialty of genome representations in evolutionary computation, new genetic operators are developed to determine optimal hierarchical decompositions. This quantitative modularity measure has been developed to synthesize modular engineering products, especially by evolutionary design. There are many factors affecting evolving modular structures, such as genome representation, fitness function, learning, and task structure. The thesis preliminarily studies the effects of the modularity of tasks on the modularity of products in evolutionary computation. Using feed-forward neural networks as examples, the results show that the effects are task-dependent and rely on the amount of resources available for the tasks
... Recently, issues such improving the "innovativeness" and the scalability of evolutionary search have attracted renewed interest to the study of modularity in the evolutionary computation community. For instance see [5,6,7]. From our perspective, modularity implies not only the hierarchical organization of components from one level of complexity to the next, but also the ability to freely reuse components. ...
We introduce the concept of modularity-preserving representations. If a representation is modularity-preserving, the existence of modularity in the problem space is translated into a corresponding
modularity in the search space. This kind of representation allows us to analyze the impact of modularity at the genomic level.
We investigate the question of what constitutes a module at the genomic level of evolutionary search and provide a static
analysis of how to identify good and bad modules based on their ability to reduce the search space, thus, biasing the search
space towards a solution. We also prove, under a set of assumptions, that the systematic encapsulation of lower order modules
into higher order modules does not change the size or bias of a search space and that this process produces a hierarchy of
equivalent search spaces.
... One encouraging thought on the path towards better understanding complex systems is that most observed complex systems have a hierarchical modular structure [Wat03,CR05]. ...
We are continuously challenged by ever increasing problem complexity and the need to develop algorithms that can solve complex problems and solve them within a reasonable amount of time. Modularity is thought to reduce problem complexity by decomposing large problems into smaller and less complex subproblems. In practice, introducing modularity into evolutionary algorithm representations appears to improve search performance; however, how and why modularity improves performance is not well understood. In this thesis, we seek to better understand the effects of modularity on search. In particular, what are the effects of module creation on the search space structure and how do these structural changes affect performance? We define a theoretical and empirical framework to study modularity in evolutionary algorithms. Using this framework, we provide evidence of the following. First, not all types of modularity have an effect on search. We can have highly modular spaces that in essence are equivalent to simpler non-modular spaces. This is the case, because these spaces achieve higher degree of modularity without changing the fundamental structure of the search space. Second, for the cases when modularity actually has an effect on the fundamental structure of the search space, if left without guidance, it would only crowd and complicate the space structure resulting in a harder space for most search algorithms. Finally, we have the case when modularity not only has an effect in the search space structure, but most importantly, module creation can be guided by problem domain knowledge. When this knowledge can be used to estimate the value of a module in terms of its contribution toward building the solution, then modularity is extremely effective. It is in this last case that creating high value modules or low value modules has a direct and decisive impact on performance. The results presented in this thesis help to better understand, in a principled way, the effects of modularity on search. Better understanding the effects of modularity on search is a step forward in the larger issue of evolutionary search applied to increasingly complex problems.
"UMI:3045918." Thesis (Ph. D.)--Brandeis University, 2002. Includes bibliographical references (p. 311-321). Photocopy. s
The Building-Block Hypothesis appeals to the notion of problem decomposition slid the assembly of solutions from sub-solutions. Accordingly, there have been many varieties of GA test problems with a structure based on building-blocks. Many of these problems use deceptive fitness functions to model interdependency between the bits within a block. However. very few have any model of interdependency between building-blocks; those that do are not consistent in the type of interaction used intra-block and inter-block. This paper discusses the inadequacies of the various Lest problems in the literature and clarifies the concept of building-block interdependency. We formulate a principled model of hierarchical interdependency that can be applied through many levels in a consistent manner and introduce Hierarchical If-and-only-if (H-IFF) as a canonical example. We present some empirical results of GAs on H-IFF showing that if population diversity is maintained and linkage is tight then the GA is able to identify and manipulate building-blocks over many levels of assembly, as the Building-Block Hypothesis suggests.
