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1

A hybrid model of heuristic algorithm and gradient descent to optimize neural networks

Mirkhan Amer, Çelebi Numan

Bulletin of the Polish Academy of Sciences. Technical Sciences

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2023

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Vol. 71, nr 6

art. no. e147924

EN

Training a neural network can be a challenging task, particularly when working with complex models and large amounts of training data, as it consumes significant time and resources. This research proposes a hybrid model that combines population-based heuristic algorithms with traditional gradient-based techniques to enhance the training process. The proposed approach involves using a dynamic population-based heuristic algorithm to identify good initial values for the neural network weight vector. This is done as an alternative to the traditional technique of starting with random weights. After several cycles of distributing search agents across the search domain, the training process continues using a gradient-based technique that starts with the best initial weight vector identified by the heuristic algorithm. Experimental analysis confirms that exploring the search domain during the training process decreases the number of cycles needed for gradient descent to train a neural network. Furthermore, a dynamic population strategy is applied during the heuristic search, with objects added and removed dynamically based on their progress. This approach yields better results compared to traditional heuristic algorithms that use the same population members throughout the search process.

2

Parameter identification and estimation for stage-structured population models

Coll Carmen, Sánchez Elena

International Journal of Applied Mathematics and Computer Science

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2019

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Vol. 29, no. 2

327--336

EN

A stage-structured population model with unknown parameters is considered. Our purpose is to study the identifiability of the model and to develop a parameter estimation procedure. First, we analyze whether the parameter vector can or cannot uniquely be determined with the knowledge of the input-output behavior of the model. Second, we analyze how the information in the experimental data is translated into the parameters of the model. Furthermore, we propose a process to improve the recursive values of the parameters when successive observation data are considered. The structure of the state matrix leads to an analysis of the inverse of a sum of rank-one matrices.

3

Koncepcja szkoleniowej bazy danych „Dynamiczna populacja” : projekt realizowany przez koło naukowe

Ptasznik A., Jeżewski P., Redzik A.

Zeszyty Naukowe Warszawskiej Wyższej Szkoły Informatyki

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2015

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nr 13

21--32

PL

W artykule opisano koncepcję realizowanej przez koło naukowe szkoleniowej bazy danych. Wskazano genezę projektu oraz jego główne założenia. Przedstawiona została realizacja podstawowych etapów projektu oraz wizja dalszego rozwoju systemu.

EN

The paper presents a concept of a Training Database, which is being implemented by Students Scientific Association. It characterizes the genesis of the project, along with its main principles. Realization of the fundamental stages of the project and the vision of the further development of the system has been shown.

4

Stochastic Populations, Power Law and Fitness Aggregation in Genetic Algorithms

Ma Z. S.

Fundamenta Informaticae

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2013

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Vol. 122, nr 3

173--206

EN

Natural populations are dynamic in both time and space. In biological populations such as insects, spatial distribution patterns are often studied as the first step to characterize population dynamics. In nature, the spatial distribution patterns of insect populations are considered as the emergent expression (property) of individual behaviors at population levels and are fine-tuned or optimized by natural selection. This inspiration prompts us to investigate the possibly similar mechanisms in Genetic Algorithms (GA) populations. In this study, we introduce the mathematical models for the spatial distribution patterns of insect populations to GA with the conjecture that the emulation of biological populations in nature may lead to computational improvement. In particular, we introduce three modeling approaches from the research of spatial distribution patterns of insect populations: (i) probability distribution modeling approach, (ii) aggregation index approach, and (iii) Taylor’s (1961, 1977) Power Law, Iwao’s (1968, 1976) Mean Crowding Model and Ma’s (1991c) population aggregation critical density (PACD), to characterize populations in GA. With these three approaches, we investigate four mappings from the research field of insect spatial distribution patterns to GA populations in order to search for possible counterpart mechanisms or features in GA. They are: (i) mapping insect spatial distribution patterns to GA populations or allowing GA populations to be controlled by stochastic distribution models that describe insect spatial distributions; (ii) mapping insect population distribution to GA population fitness distribution via Power Law and PACD modeling; (iii)mapping population aggregation dynamics to GA fitness progression across generations (or fitness aggregation dynamics in GA) via insect population aggregation index; (iv) mapping insect population sampling model to optimal GA population sizing. With regard to the mapping (i), the experiment results show the significant improvements in GA computational efficiency in terms of the reduced fitness evaluations and associated costs. This prompts us to suggest using probability distribution models, or what we call stochastic GA populations, to replace the fixed-size population settings. We also found the counterpart for the second mapping, the wide applicability of Power Law and Mean Crowding model to the fitness distribution in GA populations. The testing of the third and fourth mappings is very preliminary; we use example cases to suggest two further research problems: the potential to use fitness aggregation dynamics for controlling the number of generations iterated in GA searches, and the possibility to use fitness aggregation distribution parameters [(obtained in mapping (ii)] in determining the optimum population size in GA. A third interesting research problem is to investigate the relationship between mapping (i) and (iii), i.e., the controlling of both population sizes and population generations.