Clustered genetic search in continuous landscape exploration

Schaefer, Robert; Adamska, Katarzyna; Telega, Henryk

doi:10.1016/j.engappai.2004.04.014

Cited by 14 publications

(20 citation statements)

References 12 publications

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“…The above theory supports the stochastic strategies of multimodal analysis gathered in [14,19]. It may be also used to study the features of a Clustered Genetic Search (CGS) [21,27] and Hierarchic Memetic Strategy (HMS) dedicated for approximating lowlands and their basins of attraction [15,16]. The solving of real-world engineering ill-posed inverse problems from Classes C.6 -C.9 by the methods mentioned above is presented in papers [2,3,11,22,23].…”

Section: Conclusion and Perspective Of Applicationsmentioning

confidence: 62%

Misfit Landforms Imposed by Ill-Conditioned Inverse Parametric Problems

Łoś

Smółka

Schaefer

et al. 2018

csci

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In this paper, we put forward a new topological taxonomy that allows us to distinguish and separate multiple solutions to ill-conditioned parametric inverse problems appearing in engineering, geophysics, medicine, etc. This taxonomy distinguishes the areas of insensitivity to parameters called the landforms of the misfit landscape, be it around minima (lowlands), maxima (uplands), or stationary points (shelves). We have proven their important separability and completeness conditions. In particular, lowlands, uplands, and shelves are pairwise disjoint, and there are no other subsets of the positive measure in the admissible domain on which the misfit function takes a constant value. The topological taxonomy is related to the second, "local" one, which characterizes the types of ill-conditioning of the particular solutions. We hope that the proposed results will be helpful for a better and more precise formulation of ill-conditioned inverse problems and for selecting and profiling complex optimization strategies used in solving these problems.

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Section: Conclusion and Perspective Of Applicationsmentioning

confidence: 62%

Misfit Landforms Imposed by Ill-Conditioned Inverse Parametric Problems

Łoś

Smółka

Schaefer

et al. 2018

csci

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“…The broad review of stochastic, population-based methods of solving global optimization problems in continuous domains involving multiple local minimizers is reported in Pardalos and Romeijn handbook [36], while the population-based methods dedicated to the ill-conditioned multimodal global optimization problems was discusses in the Preuss book [39]. The information about some specialized strategies (HGS, HMS, CGS and EMAS) can be found in our former papers [4,6,13,17,47,50,53,[55][56][57]64].…”

Section: Deterministic and Stochastic Strategies Of Solving Ill-conditioned Problemsmentioning

confidence: 99%

“…Such fitness imposes the chaotic behavior of the searching process, which can be recognized by analyzing Hðx t Þ in several consecutive steps (see e.g. [50,60,64]). 8.…”

Section: Remarkmentioning

confidence: 99%

Understanding measure-driven algorithms solving irreversibly ill-conditioned problems

et al. 2021

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The paper helps to understand the essence of stochastic population-based searches that solve ill-conditioned global optimization problems. This condition manifests itself by presence of lowlands, i.e., connected subsets of minimizers of positive measure, and inability to regularize the problem. We show a convenient way to analyze such search strategies as dynamic systems that transform the sampling measure. We can draw informative conclusions for a class of strategies with a focusing heuristic. For this class we can evaluate the amount of information about the problem that can be gathered and suggest ways to verify stopping conditions. Next, we show the Hierarchic Memetic Strategy coupled with Multi-Winner Evolutionary Algorithm (HMS/MWEA) that follow the ideas from the first part of the paper. We introduce a complex, ergodic Markov chain of their dynamics and prove an asymptotic guarantee of success. Finally, we present numerical solutions to ill-conditioned problems: two benchmarks and a real-life engineering one, which show the strategy in action. The paper recalls and synthesizes some results already published by authors, drawing new qualitative conclusions. The totally new parts are Markov chain models of the HMS structure of demes and of the MWEA component, as well as the theorem of their ergodicity.

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“…Note that attraction basins within the continuous domain were often used for clustering and niching. Different clusters and niches were often considered as approximated attraction basins [99,100]; however, this is in contrast with the usual definition. Therefore, we found the "usual" attraction basins to be less investigated within the continuous domain.…”

Section: Rq5: Most Popular Topics For Attraction Basinsmentioning

confidence: 99%

Attraction Basins in Metaheuristics: A Systematic Mapping Study

2021

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Context: In this study, we report on a Systematic Mapping Study (SMS) for attraction basins in the domain of metaheuristics. Objective: To identify research trends, potential issues, and proposed solutions on attraction basins in the field of metaheuristics. Research goals were inspired by the previous paper, published in 2021, where attraction basins were used to measure exploration and exploitation. Method: We conducted the SMS in the following steps: Defining research questions, conducting the search in the ISI Web of Science and Scopus databases, full-text screening, iterative forward and backward snowballing (with ongoing full-text screening), classifying, and data extraction. Results: Attraction basins within discrete domains are understood far better than those within continuous domains. Attraction basins on dynamic problems have hardly been investigated. Multi-objective problems are investigated poorly in both domains, although slightly more often within a continuous domain. There is a lack of parallel and scalable algorithms to compute attraction basins and a general framework that would unite all different definitions/implementations used for attraction basins. Conclusions: Findings regarding attraction basins in the field of metaheuristics reveal that the concept alone is poorly exploited, as well as identify open issues where researchers may improve their research.

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Clustered genetic search in continuous landscape exploration

Cited by 14 publications

References 12 publications

Misfit Landforms Imposed by Ill-Conditioned Inverse Parametric Problems

Misfit Landforms Imposed by Ill-Conditioned Inverse Parametric Problems

Understanding measure-driven algorithms solving irreversibly ill-conditioned problems

Attraction Basins in Metaheuristics: A Systematic Mapping Study

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