Application of α -stable mutation in a hierarchic evolutionary inverse solver

Obuchowicz, Adam K.; Smółka, Maciej

doi:10.1016/j.jocs.2015.12.006

Cited by 5 publications

(5 citation statements)

References 10 publications

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“…Three of them [14][15][16] deal with multi-objective optimization, underlining the polyhedral nature of many complex problems. Complex networks [20] are prominently featured in one contribution [13] and other different hard complex optimization problems are considered in four contributions [14][15][16][17]. Finally, one of the contributions [18] tackles the use of agent-based metaheuristic computing, a prime example of complex collective system [21] -see also [22].…”

Section: An Overview Of This Special Issuementioning

confidence: 99%

“…This thematic special issue revolves around the intersection of metaheuristic optimization techniques and complex systems from two different perspectives, namely the use of metaheuristics as a tool for analyzing, modeling or designing complex systems, or the utilization of metaheuristics approaches which are themselves complex systems due to its particular internal structure. We have gathered six papers [13][14][15][16][17][18] targeted to cover algorithmic and implementation aspects of such complex meta-heuristics in both discrete and continuous domains, as well as applications to complex systems. Some contributions to this thematic special issue are extended versions of results communicated at the EvoCOMPLEX track of the EvoApplications conference [19], held in Copenhagen, 8-10 April 2015 as a part of the EvoStar event.…”

Section: Introductionmentioning

confidence: 99%

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Complex metaheuristics

Cotta

Schaefer

2016

Journal of Computational Science

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a b s t r a c tComplexity is a prevalent feature of numerous natural and artificial systems and as such has attracted much scientific interest in the last decades. The pursuit of computational tools capable of analyzing, modeling or designing systems exhibiting this complex nature -in which the properties of the system are not evident at the bottom level but emerge from its global structure -is a major issue. Metaheuristics can play here an important role due to its intrinsic adaptability and powerful optimization capabilities. In many regards, metaheuristics are also examples of complex systems since their behavior emanates from the orchestrated interplay of simpler algorithmic components. This bidirectional connection between metaheuristics and complex systems offers numerous avenues for fruitful research.

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Section: An Overview Of This Special Issuementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Complex metaheuristics

Cotta

Schaefer

2016

Journal of Computational Science

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“…The aÀstable distribution is considered as the generalization of the Gaussian one. Although the first application of this distribution appeared in the work of Mandelbrot [16], where the financial time series were analyzed, the aÀstable distributions and processes have found various applications, including economy [17][18][19][20][21][22][23], physics [24][25][26][27], signal processing [28][29][30][31], computer science [32][33][34][35], geology and geophysics [36][37][38], biology [39][40][41][42], and many other fields. The aÀstable distributions are also considered for climate data modelling, see, e.g., [43][44][45][46].…”

Section: Introductionmentioning

confidence: 99%

Application of non-Gaussian multidimensional autoregressive model for climate data prediction

Broszkiewicz-Suwaj

Wyłomańska

2021

Int J Adv Eng Sci Appl Math

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From the point of view of agriculture, ecology, or environmental engineering, the capability of forecasting meteorological variables in the long and short term is crucial. Short-term forecasts enabling the planning of field work in agriculture, management of mass events, or tourism are important, while long-term forecasts related to advancing climate change are also very interesting. In the literature, there are known many approaches that can be used to forecast climate time series. The most common is based on the statistical modelling of the corresponding data, and the prediction is made on the fitted model. There are known one-dimensional approaches, where single variables are modeled separately; however, in the last decade, there appears a new trend which assumes the importance of the relationship between different time series. This is the approach considered in this paper. We propose to examine the climate data (temperature and precipitation) using the multidimensional vector autoregressive model (VAR). However, because in the time series we observe non-Gaussian behaviour, the classical VAR model can not be applied and the multidimensional Gaussian noise is replaced by the $$\alpha -$$ α - stable one. This model was previously analyzed by the authors in the context of financial data description where also non-Gaussian characteristics are observed. The main goal of this paper is to answer the question whether there are reasons to go from the Gaussian model to the generalized models, like $$\alpha -$$ α - stable based. The second purpose is to link total precipitation data with temperature time series. In the classical approach, precipitation was treated as a variable not correlated with temperature, which, as we will show in the paper, is inconsistent with reality. We hope the presented in this paper results open new areas of interest related to climate data modelling and prediction.

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“…We mention here that the a-stable distribution was introduced by Lévy and Khinchine in [16,17] and the standardized mathematical background, which contributed to the increased interest in the a-stable-based models, was provided by Gnedenko and Kolomogorov [18], Feller [19], Zolotarev [20], Weron [21], and later in the 1990s Shao and Nikias [22], Janicki and Weron [23] and Samorodnitsky and Taqqu [24]. Since the first significant application provided by Mandelbrot in [25], the astable distribution is commonly applied in finance and economics [26][27][28][29][30][31][32][33], physics [34][35][36], signal processing [37][38][39], computer science [40,41], geology and geophysics [42,43], biology [44,45], and many other fields.…”

Section: Introductionmentioning

confidence: 99%

Spatial components dependence for bidimensional time-constant AR(1) model with $$\alpha $$-stable noise and triangular coefficients matrix

Grzesiek

2021

Int J Adv Eng Sci Appl Math

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In this paper, we examine the bidimensional time-constant autoregressive model of order 1 with $$\alpha $$ α -stable noise. We focus on the case of the triangular coefficients matrix for which one of the spatial components of the model simplifies to the one-dimensional autoregressive time series. We study the asymptotic behaviour of the cross-codifference and the cross-covariation applied to describe the dependence in time between the spatial components of the model. As a result, we formulate the theorem about the asymptotic relation between both measures, which is consistent with the result that is correct for the case of the non-triangular coefficients matrix.

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Application of α -stable mutation in a hierarchic evolutionary inverse solver

Cited by 5 publications

References 10 publications

Complex metaheuristics

Complex metaheuristics

Application of non-Gaussian multidimensional autoregressive model for climate data prediction

Spatial components dependence for bidimensional time-constant AR(1) model with $$\alpha $$-stable noise and triangular coefficients matrix

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