We analyze the betweenness centrality (BC) of nodes in large complex networks. In general, the BC is increasing with connectivity as a power law with an exponent $\eta$. We find that for trees or networks with a small loop density $\eta=2$ while a larger density of loops leads to $\eta<2$. For scale-free networks characterized by an exponent $\gamma$ which describes the connectivity distribution decay, the BC is also distributed according to a power law with a non universal exponent $\delta$. We show that this exponent $\delta$ must satisfy the exact bound $\delta\geq (\gamma+1)/2$. If the scale free network is a tree, then we have the equality $\delta=(\gamma+1)/2$.

Betweenness Centrality in Large Complex Networks

Using surrogate models in evolutionary search provides an efficient means of handling today's complex applications plagued with increasing high-computational needs. Recent surrogate-assisted evolutionary frameworks have relied on the use of a variety of different modeling approaches to approximate the complex problem landscape. From these recent studies, one main research issue is with the choice of modeling scheme used, which has been found to affect the performance of evolutionary search significantly. Given that theoretical knowledge available for making a decision on an approximation model a priori is very much limited, this paper describes a generalization of surrogate-assisted evolutionary frameworks for optimization of problems with objectives and constraints that are computationally expensive to evaluate. The generalized evolutionary framework unifies diverse surrogate models synergistically in the evolutionary search. In particular, it focuses on attaining reliable search performance in the surrogate-assisted evolutionary framework by working on two major issues: 1) to mitigate the 'curse of uncertainty' robustly, and 2) to benefit from the 'bless of uncertainty.' The backbone of the generalized framework is a surrogate-assisted memetic algorithm that conducts simultaneous local searches using ensemble and smoothing surrogate models, with the aims of generating reliable fitness prediction and search improvements simultaneously. Empirical study on commonly used optimization benchmark problems indicates that the generalized framework is capable of attaining reliable, high quality, and efficient performance under a limited computational budget.

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Generalizing Surrogate-Assisted Evolutionary Computation

It has long been observed that for practically any computational problem that has been intensely studied, different instances are best solved using different algorithms. This is particularly pronou...

Automated Algorithm Selection: Survey and Perspectives

The trade-off between obtaining a good distribution of Pareto-optimal solutions and obtaining them in a small computational time is an important issue in evolutionary multi-objective optimization (EMO). It has been well established in the EMO literature that although SPEA produces a better distribution compared to NSGA-II, the computational time needed to run SPEA is much larger. In this paper, we suggest a clustered NSGA-II which uses an identical clustering technique to that used in SPEA for obtaining a better distribution. Moreover, we propose a steady-state MOEA based on e-dominance concept and efficient parent and archive update strategies. Based on a comparative study on a number of two and three objective test problems, it is observed that the steady-state MOEA achieves a comparable distribution to the clustered NSGA-II with a much less computational time.

Towards a quick computation of well-spread pareto-optimal solutions

Complex continuous optimization problems widely exist nowadays due to the fast development of the economy and society. Moreover, the technologies like Internet of things, cloud computing, and big data also make optimization problems with more challenges including Many-dimensions, Many-changes, Many-optima, Many-constraints, and Many-costs. We term these as 5-M challenges that exist in large-scale optimization problems, dynamic optimization problems, multi-modal optimization problems, multi-objective optimization problems, many-objective optimization problems, constrained optimization problems, and expensive optimization problems in practical applications. The evolutionary computation (EC) algorithms are a kind of promising global optimization tools that have not only been widely applied for solving traditional optimization problems, but also have emerged booming research for solving the above-mentioned complex continuous optimization problems in recent years. In order to show how EC algorithms are promising and efficient in dealing with the 5-M complex challenges, this paper presents a comprehensive survey by proposing a novel taxonomy according to the function of the approaches, including reducing problem difficulty, increasing algorithm diversity, accelerating convergence speed, reducing running time, and extending application field. Moreover, some future research directions on using EC algorithms to solve complex continuous optimization problems are proposed and discussed. We believe that such a survey can draw attention, raise discussions, and inspire new ideas of EC research into complex continuous optimization problems and real-world applications.

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A survey on evolutionary computation for complex continuous optimization

Annotation. An overview of the design and development features of the Virtual Library information system was conducted. A new approach is proposed for designing and developing the Virtual Library information system for saving and development of e-books in the MARC 21 format. The model of information system Virtual Library is proposed.

The Virtual Library System Design and Development

The methods and means of using ontologies within systems for the categorization of textual content were created. Also, a method for optimizing the definition of which rubrics best relate to a certain text content was developed. The intellectual system that will use the methods developed earlier, as well as other research results was implemented. The results will allow users to easily filter their text content. The system developed has an intuitive user interface.

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Development of Information System for Textual Content Categorizing Based on Ontology.

The article describes the peculiarities of linguometry information technologies usage to determine the linguometric coefficients dynamics of the text content authorship. The linguistic and statistical analysis of the author texts within a certain time period takes advantage of the text content-monitoring based on the NLP methods to determine the set of stop words and to study n-grams. The latter is used in the methods of linguometry and stylometry to determine the linguometric coefficients dynamics of the ownership of the analyzed text to a specific author in percentage points. There is proposed a formal approach to the definition of the author’s style of the Ukrainian text in the article. The experimental results of the proposed method for determining the ownership of the analyzed text to a particular author upon the availability of the reference text fragment are obtained. The study was conducted on the basis of the Ukrainian scientific texts of a technical area.

Method for Determining Linguometric Coefficient Dynamics of Ukrainian Text Content Authorship

Peeking beyond peaks: Challenges and research potentials of continuous multimodal multi-objective optimization

There is a range of phenomena in continuous, global multi-objective optimization, that cannot occur in single-objective optimization. For instance, in some multi-objective optimization problems it is possible to follow continuous paths of gradients of straightforward weighted scalarization functions, starting from locally efficient solutions, in order to reach globally Pareto optimal solutions. This paper seeks to better characterize multimodal multi-objective landscapes and to better understand the transitions from local optima to global optima in simple, path-oriented search procedures.

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Michael Emmerich

Papers

The Virtual Library System Design and Development

Development of Information System for Textual Content Categorizing Based on Ontology.

Method for Determining Linguometric Coefficient Dynamics of Ukrainian Text Content Authorship

Peeking beyond peaks: Challenges and research potentials of continuous multimodal multi-objective optimization

Sliding to the global optimum: How to benefit from non-global optima in multimodal multi-objective optimization