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Making and breaking power laws in evolutionary algorithm population dynamics

Memetic Computing 2009年第2期1卷 125-137页

作者： Whitacre, James M. Sarker, Ruhul A. Pham, Q. Tuan School of Chemical Sciences and Engineering University of New South Wales Sydney 2052 Australia School of Information Technology and Electrical Engineering University of New South Wales ADFA Campus Canberra 2600 Australia

Deepening our understanding of the characteristics and behaviors of population-based search algorithms remains an important ongoing challenge in Evolutionary Computation. To date however, most studies of Evolutionary algorithms have only been able to take place within tightly restricted experimental conditions. For instance, many analytical methods can only be applied to canonical algorithmic forms or can only evaluate evolution over simple test functions. analysis of EA behavior under more complex conditions is needed to broaden our understanding of this population-based search process. This paper presents an approach to analyzing EA behavior that can be applied to a diverse range of algorithm designs and environmental conditions. The approach is based on evaluating an individual's impact on population dynamics using metrics derived from genealogical graphs. From experiments conducted over a broad range of conditions, some important conclusions are drawn in this study. First, it is determined that very few individuals in an EA population have a significant influence on future population dynamics with the impact size fitting a power law distribution. The power law distribution indicates there is a non-negligible probability that single individuals will dominate the entire population, irrespective of population size. Two EA design features are however found to cause strong changes to this aspect of EA behavior: (1) the population topology and (2) the introduction of completely new individuals. If the EA population topology has a long path length or if new (i.e. historically uncoupled) individuals are continually inserted into the population, then power law deviations are observed for large impact sizes. It is concluded that such EA designs can not be dominated by a small number of individuals and hence should theoretically be capable of exhibiting higher degrees of parallel search behavior. © 2009 Springer-Verlag.

关键词： algorithm analysis Evolutionary algorithms Genealogical graphs Historical coupling Optimization Population dynamics Population topology

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On the Generalized Frechet Distance and its Applications 22

On the Generalized Frechet Distance and its Applications

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30th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems (ACM SIGSPATIAL GIS)

作者： Gutschlag, Theodor Storandt, Sabine Univ Konstanz Constance Germany

ISBN: (纸本)9781450395298

Measuring the similarity of spatio-temporal trajectories in a sensible fashion is an important building block for applications such as trajectory clustering or movement pattern analysis. However, typically employed similarity measures only take the spatial components of the trajectory into account, or are complicated combinations of different measures. In this paper we introduce the so called Generalized Frechet distance, which extends the well-known Frechet distance. For two polygonal curves of length n and m in d-dimensional space, the Generalized Frechet distance enables an individual weighting of each dimension on the similarity value by using a convex function. This allows to integrate arbitrary data dimensions as e.g. temporal information in an elegant,flexible and application-aware manner. We study the Generalized Frechet Distance for both the discrete and the continuous version of the problem, prove useful properties, and present efficient algorithms to compute the decision and optimization problem. In particular, we prove that for d is an element of O(1) the asymptotic running times of the optimization problem for the continuous version are O(nm log(nm)) under realistic assumptions, and O(nm) for the discrete version for arbitrary weight functions. Therefore the theoretical running times match those of the classical Frechet distance. In our experimental evaluation, we demonstrate the usefulness of the Generalized Frechet distance and study the practical behaviour of our algorithms. On sets of real-world trajectories, we confirm that the weighting of the spatial and temporal dimensions heavily impacts the relative similarity, and hence the ability to tailor the measure to the application is a useful tool.

关键词： Trajectory similarity Frechet distance algorithm analysis

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Financial Forecasting by improved fragmentation algorithm of Granular Fragment Based mining

Financial Forecasting by improved fragmentation algorithm of...

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International Conference on Pervasive Computing (ICPC)

作者： Patil, Suhas Argiddi, Rajesh Apte, Sulabha Walchand Inst Technol Dept Comp Sci Solapur India

ISBN: (纸本)9781479962723

Many algorithms of the existing methods are used for stock predictions. Most of stock predictions use static stored data for their analysis of algorithms. JStock framework is implemented as was proposed earlier to analyze improved fragmentation algorithm using dynamic online live data. Open source software is used for implementation which uses yahoo finance and Google finance for extraction of data and displaying the results. In this paper the implementation of JStock framework is discussed. The improved Fragmentation algorithm and its usage removed all previous disadvantages of using static data. JStock is open source software which has a legal way of extracting data from yahoo finance. The extracted data then has been processed by fragmentation algorithm of granular based inter-transactions associations and comparisons of various indicators are also done. The data is then successfully shown in Bar Charts and Pie charts to check the maximum profit in Stock Exchange of specific company. This implementation can be used for any companies all over the world. Different Indian sector companies are used for results and analysis. The results are very simple and can be used very easily for every newbie in Stock Market. The framework can be further used for newly proposed algorithms for more accurate and precise results for Stock predictions, which is otherwise very much fluctuating and highly unpredictable. The stream of data can be used for big data analytics too for all financial companies.

关键词： Data Stream Framework Open Source Software Fragment Based Mining Association mining Stock Data Application Software algorithm analysis

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Phenotype Search Trajectory Networks for Linear Genetic Programming 6th

Phenotype Search Trajectory Networks for Linear Genetic Prog...

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26th European Conference on Genetic Programming (EuroGP) Held as Part of EvoStar

作者： Hu, Ting Ochoa, Gabriela Banzhaf, Wolfgang Queens Univ Sch Comp Kingston ON K7L 2N8 Canada Univ Stirling Stirling FK9 4LA Scotland Michigan State Univ BEACON Ctr Study Evolut Act Dept Comp Sci & Engn E Lansing MI 48864 USA Michigan State Univ Ecol Evolut & Behav Program E Lansing MI 48864 USA

ISBN: (纸本)9783031295720;9783031295737

In this study, we visualise the search trajectories of a genetic programming system as graph-based models, where nodes are genotypes/phenotypes and edges represent their mutational transitions. We also quantitatively measure the characteristics of phenotypes including their genotypic abundance (the requirement for neutrality) and Kolmogorov complexity. We connect these quantified metrics with search trajectory visualisations, and find that more complex phenotypes are under-represented by fewer genotypes and are harder for evolution to discover. Less complex phenotypes, on the other hand, are over-represented by genotypes, are easier to find, and frequently serve as stepping-stones for evolution.

关键词： Neutral networks Genotype-to-phenotype mapping algorithm modeling algorithm analysis Search trajectories Complex networks Visualisation Kolmogorov complexity

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algorithms for circuits and circuits for algorithms: Connecting the tractable and intractable

Algorithms for circuits and circuits for algorithms: Connect...

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International Congress of Mathematicians (ICM)

作者： Williams, Ryan Stanford Univ Dept Comp Sci Stanford CA 94305 USA

ISBN: (纸本)9788961058070

The title of this paper highlights an emerging duality between two basic topics in algorithms and complexity theory. algorithms for circuits refers to the design of algorithms which can analyze finite logical circuits or Boolean functions as input, checking a simple property about the complexity of the underlying function. For instance, an algorithm determining if a given logical circuit C has an input that makes C output true would solve the NP-complete Circuit-SAT problem. Such an algorithm is unlikely to run in polynomial time, but could possibly be more efficient than exhaustively trying all possible inputs to the circuit. Circuits for algorithms refers to the modeling of "complex" uniform algorithms with "simple" Boolean circuit families, or proving that such modeling is impossible. For example, can every exponential-time algorithm be simulated using Boolean circuit families of only polynomial size? It is widely conjectured that the answer is no, but the present mathematical tools available are still too crude to resolve this kind of separation problem. This paper surveys these two generic subjects and the connections that have been developed between them, focusing on connections between non-trivial circuit-analysis algorithms and proofs of circuit complexity lower bounds.

关键词： circuit complexity algorithm analysis satisfiability lower bounds derandomization learning exact algorithms parameterized algorithms

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Towards Cryptanalysis Of Prime Numbers 3

Towards Cryptanalysis Of Prime Numbers

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3rd International Conference on Computer and Information Sciences (ICCOINS)

作者： Yusuf, Bashir Kagara Mahmood, Ahmad Kamil Sulaiman, Suziah Univ Teknol PETRONAS Dept Comp & Informat Sci Seri Iskandar 32610 Malaysia

ISBN: (纸本)9781509025497

Natural numbers that defy decomposition into factors lower than themselves provide the basis for entrenching security in the public key encryption world. A variant algorithm of trial division of sieve of Eratosthenes, with its digits split into two unequal components and whose growth centered on displacement from its immediate neighbors (i.e., Polignac and Goldbach theorems) was fashioned out. As challenged by Euler's verdict on non-existence of a function that completely generates only primes, our formulation was based both upon multiple linear regression analysis hoping to find a multi-variate function, of degree at most 3, which can predict primes and comparison to Akaike Information Criterion (AIC) for model selection. About 20 billion lower primes of digits less than or equal 12 were subjected to various validation techniques (e.g., Sloane's A006988) and other heuristics for benchmarking purposes. Our results reveal certain desirable features illuminating prime patterns regardless of their chaotic camouflage.

关键词： AIC Best Modeling algorithm analysis Cubic Functions Multiple Linear Regression analysis Prime Pairs

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Statistical Approach to Calculation of Number of Network Motifs

Statistical Approach to Calculation of Number of Network Mot...

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International Siberian Conference on Control and Communications (SIBCON)

作者： Yudin, E. B. Zadorozhnyi, V. N. Omsk State Tech Univ Omsk Russia

ISBN: (纸本)9781479971039

The development of efficient algorithms for the analysis of network motifs is a direction in Network Science, which is of great importance in the study of communication networks, social, biological and other networks. Detection and calculation of number of network motifs are closely related to the counting of typical isomorphic subgraphs in large graphs. The article proposes to accelerate this process by using the Monte Carlo method. Examples of counting of typical subgraphs with 3 and 4 vertices in the undirected graph are given. The proposed approach can also be extended to analysis of directed graphs.

关键词： network motifs algorithm analysis subgraph counting

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Search Trajectories Networks of Multiobjective Evolutionary algorithms 25th

Search Trajectories Networks of Multiobjective Evolutionary ...

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25th International Conference on the Applications of Evolutionary Computation (EvoApplications) Held as Part of EvoStar Conference

作者： Lavinas, Yuri Aranha, Claus Ochoa, Gabriela Univ Tsukuba Tsukuba Ibaraki Japan Univ Stirling Stirling Scotland

ISBN: (纸本)9783031024627;9783031024610

Understanding the search dynamics of multiobjective evolutionary algorithms (MOEAs) is still an open problem. This paper extends a recent network-based tool, search trajectory networks (STNs), to model the behavior of MOEAs. Our approach uses the idea of decomposition, where a multiobjective problem is transformed into several single-objective problems. We show that STNs can be used to model and distinguish the search behavior of two popular multiobjective algorithms, MOEA/D and NSGA-II, using 10 continuous benchmark problems with 2 and 3 objectives. Our findings suggest that we can improve our understanding of MOEAs using STNs for algorithm analysis.

关键词： algorithm analysis Search trajectories Continuous optimization Visualization Multi-objective optimization

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THE CONVEX-HULL OF RANDOM BALLS

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ADVANCES IN APPLIED PROBABILITY 1993年第2期25卷 373-394页

作者： AFFENTRANGER, F DWYER, RA N CAROLINA STATE UNIV DEPT COMP SCI RALEIGH NC 27695 USA

While the convex hull of n d-dimensional balls is not a polytope, it does have an underlying combinatorial structure similar to that of a polytope. In the worst case, its combinatorial complexity can be of order OMEGA(n right perpendicular d\2 left perpendicular). The thrust of this work is to show that its complexity is typically much smaller, and that it can therefore be constructed more quickly on average than in the worst case. To this end, four models of the random d-ball are developed, and the expected combinatorial complexity of the convex hull of n independent random d-balls is investigated for each. As n grows without bound, these expectations are O(1), O(n(d-1)/(d+4)), O(1) (for d = 2 only), and O(n(d-1)/(d+3)).

关键词： GEOMETRIC PROBABILITY INTEGRAL GEOMETRY COMPUTATIONAL GEOMETRY POLYTOPES algorithm analysis

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Evaluating numerical ODE/DAE methods, algorithms and software

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JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2006年第2期185卷 244-260页

作者： Söderlind, G Wang, L Lund Univ Ctr Math Sci SE-22100 Lund Sweden

Until recently, the testing of ODE/DAE software has been limited to simple comparisons and benchmarking. The process of developing software from a mathematically specified method is complex: it entails constructing control structures and objectives, selecting iterative methods and termination criteria, choosing norms and many more decisions. Most software constructors have taken a heuristic approach to these design choices, and as a consequence two different implementations of the same method may show significant differences in performance. Yet it is common to try to deduce from software comparisons that one methods better than another. Such conclusions are not warranted, however, unless the testing is carried out under true ceteris paribus conditions. Moreover, testing is an empirical science and as such requires a formal test protocol;without it conclusions are questionable, invalid or even false. We argue that ODE/DAE software can be constructed and analyzed by proven, "standard" scientific techniques instead of heuristics. The goals are computational stability, reproducibility, and improved software quality. We also focus on different error criteria and norms, and discuss modifications to D-ASPK and R(ADAU)5. Finally, some basic principles of a test protocol are outlined and applied to testing these codes on a variety of problems. (c) 2005 Published by Elsevier B.V.

关键词： software testing test protocols computational stability ODE software DAE software work/precision adaptive time-stepping mathematical software algorithm analysis

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