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1

Artificial intelligence-powered pulse sequences in nuclear magnetic resonance and magnetic resonance imaging: historical trends, current innovations and perspectives

Tokarz Paweł

Scientiae Radices

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2024

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Vol. 3, Iss. 1

30--52

EN

This review article explores the historical background and recent advances in the application of artificial intelligence (AI) in the development of radiofrequency pulses and pulse sequences in nuclear magnetic resonance spectroscopy (NMR) and imaging (MRI). The introduction of AI into this field, which traces back to the late 1970s, has recently witnessed remarkable progress, leading to the design of specialized frameworks and software solutions such as DeepRF, MRzero, and GENETICS-AI. Through an analysis of literature and case studies, this review tracks the transformation of AI-driven pulse design from initial proof-of-concept studies to comprehensive scientific programs, shedding light on the potential implications for the broader NMR and MRI communities. The fusion of artificial intelligence and magnetic resonance pulse design stands as a promising frontier in spectroscopy and imaging, offering innovative enhancements in data acquisition, analysis, and interpretation across diverse scientific domains.

2

Searching for the best optimizer for an automated CAD system

Starzyński Jacek, Szmurło Robert, Rowiński Piotr, Michalski Andrzej, Watral Zbigniew, Wincenciak Stanisław

Przegląd Elektrotechniczny

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2023

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R. 99, nr 1

167--169

EN

It is recommend not to exceed the abstract length more than four lines. It is recommend not to exceed the abstract length more than four lines. It is recommend not to exceed the abstract length more than four lines. It is recommend not to exceed the abstract length more than four lines.

3

A brief review on hybrid energy storage systems for microgrid application

Ruchika Ruchika, Jain D. K.

Przegląd Elektrotechniczny

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2023

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R. 99, nr 4

70--76

EN

Microgrids are a local group of loads and energy that may or may not be connected to the traditional grid. Microgrids are particularly useful for improving the process and stability of the local electric grid and providing efficient, low-cost, clean energy.In case the central grid is down, microgrids can keep the power flowing by disconnecting or islanding from it. The microgrid’s generators and energy storage systems, then serve the microgrid’s customers until power is restored on the central grid. Energy storage systems (ESS) in microgrid are used to convert energy from one form to another that can be stored more easily and economically. A single energy storage system cannot be used for fulfilling the power needs due to limited capability, power density, energy and dynamic response and cost. Thus, hybrid energy store systems come into play. A hybrid energy storage system (HESS) has two or more energy storage systems to achieve appropriate power performance. Various configurations of hybrid energy storage systems have been proposed by researchers. A comparison has been drawn among some of such systems.

PL

Mikrosieci to lokalna grupa obciążeń i energii, które mogą, ale nie muszą być podłączone do tradycyjnej sieci. Mikrosieci są szczególnie przydatne do poprawy procesu i stabilności lokalnej sieci elektrycznej oraz dostarczania wydajnej, taniej i czystej energii. W przypadku awarii centralnej sieci mikrosieci mogą utrzymać przepływ energii, odłączając się od niej lub tworząc wyspę. Generatory mikrosieci i systemy magazynowania energii obsługują następnie klientów mikrosieci do czasu przywrócenia zasilania w sieci centralnej. Systemy magazynowania energii (ESS) w mikrosieciach służą do przekształcania energii z jednej formy w inną, która może być magazynowana łatwiej i taniej. Pojedynczy system magazynowania energii nie może być wykorzystany do zaspokojenia zapotrzebowania na moc ze względu na ograniczone możliwości, gęstość mocy, energię i reakcję dynamiczną oraz koszty. W grę wchodzą zatem hybrydowe systemy magazynowania energii. Hybrydowy system magazynowania energii (HESS) ma dwa lub więcej systemów magazynowania energii, aby osiągnąć odpowiednią wydajność energetyczną. Badacze zaproponowali różne konfiguracje hybrydowych systemów magazynowania energii. Dokonano porównania między niektórymi takimi systemami

4

Evolutionary algorithm for selecting dynamic signatures partitioning approach

Zalasiński Marcin, Laskowski Łukasz, Niksa-Rynkiewicz Tacjana, Cpałka Krzysztof, Byrski Aleksander, Przybyszewski Krzysztof, Trippner Paweł, Dong Shi

Journal of Artificial Intelligence and Soft Computing Research

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2022

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Vol. 12, No. 4

267--279

EN

In the verification of identity, the aim is to increase effectiveness and reduce involvement of verified users. A good compromise between these issues is ensured by dynamic signature verification. The dynamic signature is represented by signals describing the position of the stylus in time. They can be used to determine the velocity or acceleration signal. Values of these signals can be analyzed, interpreted, selected, and compared. In this paper, we propose an approach that: (a) uses an evolutionary algorithm to create signature partitions in the time and velocity domains; (b) selects the most characteristic partitions in terms of matching with reference signatures; and (c) works individually for each user, eliminating the need of using skilled forgeries. The proposed approach was tested using Biosecure DS2 database which is a part of the DeepSignDB, a database with genuine dynamic signatures. Our simulations confirmed the correctness of the adopted assumptions.

5

Analysis of modification of the evolutionary algorithm for sequencing production tasks

Ciepliński Piotr, Golak Sławomir, Wieczorek Tadeusz

Computer Methods in Materials Science

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2022

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Vol. 22, No. 3

157--166

EN

Evolutionary algorithms are one of the heuristic techniques used to solve task sequencing problems. An important example of such a problem is the issue of sequencing production tasks. The combinatorial optimization of task sequences allows the minimization of the cost or time of a set of production tasks by reducing the components of these values which are present in the transitions between tasks. This paper aims to analyze the influence of the production nature expressed by a set of production task parameters and a definition of the task transition cost on the effectiveness of the modification of the evolutionary algorithm based on new directed stochastic mutation operators. The research carried out included the influence of the space dimension of the task parameters, the number of levels of the value of the cost function, and a definition of this function. The results obtained allow us to assess the effectiveness of the directed mutation in task sequencing for productions of various natures.

6

Novel optimization method for mobile magnetostatic shield and test applications

Ralf Patrick Alexander, Kreischer Christian

Archives of Electrical Engineering

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2022

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Vol. 71, nr 3

627--639

EN

This article provides an optimized solution to the problem of passive shielding against static magnetic fields with any number of spherical shells. It is known, that the shielding factor of a layered structure increases in contrast to a single shell with the same overall thickness. For the reduction of weight and cost by given material parameters and available space the best system for the layer positions has to be found. Because classic magnetically shielded rooms are very heavy, this system will be used to develop a transportable Zero-Gauss-Chamber. To handle this problem, a new way was developed, in which for the first time the solution with regard to shielding and weight was optimized. Therefore, a solution for the most general case of spherical shells was chosen with an adapted boundary condition. This solution was expanded to an arbitrary number of layers and permeabilities. With this analytic solution a differential evolution algorithm is able to find the best partition of the shells. These optimized solutions are verified by numerical solutions made by the Finite Element Method (FEM). After that the solutions of different raw data are determined and investigated.

7

Evolutionary identification method for determining thermophysical parameters of hardening concrete

Długosz Adam, Pokorska Iwona, Jaskulski Roman, Glinicki Michał A.

Archives of Civil and Mechanical Engineering

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2021

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Vol. 21, no. 1

585--598

EN

The kinetics of heat transfer in hardening concrete is a key issue in engineering practice for erecting massive concrete structures. Prediction of the temperature fields in early age concrete should allow for proper control of the construction process to minimize temperature gradients and the peak temperatures, which is of particular importance for concrete durability. The paper presents a method of identification of the thermophysical parameters of early age concrete such as the thermal conductivity, the specific heat, and the heat generated by cement hydration in time. Proper numerical models of transient heat conduction problems were formulated by means of finite-element method, including two types of heat losses. The developed experimental–numerical approach included the transient temperature measurements in an isolated tube device and an in-house implementation of an evolutionary algorithm to solve the parameter identification task. Parametric Bezier curves were proposed to model heat source function, which allowed for identifying such function as a smooth curve utilizing a small number of parameters. Numerical identification tasks were solved for experimental data acquired on hardening concrete mixes differing in the type of cement and type of mineral aggregate, demonstrating the effectiveness of the proposed method (the mean-squared error less than 1 °C). The proposed approach allows for the identification of thermophysical parameters of early age concrete even for mixtures containing non-standard components while omitting drawbacks typical for classical optimization methods.

8

A new nondeterministic method for optimal selection of master degrees of freedom for dynamic condensation based on evolutionary optimization

Mucha Waldemar

Journal of Theoretical and Applied Mechanics

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2020

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Vol. 58 nr 2

445--458

EN

The following paper presents a new method for choosing a set of master degrees of freedom for the process of dynamic condensation in order to reduce a finite element model. The general rule is that the more degrees of freedom are eliminated, the more accurate the reduced model is. However, eliminating different subsets (of equal sizes) of degrees of freedom may influence the accuracy differently. Therefore, choosing an optimal subset is crucial. The presented method is based on multicriterial evolutionary optimization which makes it the first nondeterministic approach based on computational optimization technique for this application.

9

Evolutionary algorithm with a configurable search mechanism

Łapa Krystian, Cpałka Krzysztof, Laskowski Łukasz, Cader Andrzej, Zeng Zhigang

Journal of Artificial Intelligence and Soft Computing Research

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2020

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Vol. 10, No. 3

151--171

EN

In this paper, we propose a new population-based evolutionary algorithm that automatically configures the used search mechanism during its operation, which consists in choosing for each individual of the population a single evolutionary operator from the pool. The pool of operators comes from various evolutionary algorithms. With this idea, a flexible balance between exploration and exploitation of the problem domain can be achieved. The approach proposed in this paper might offer an inspirational alternative in creating evolutionary algorithms and their modifications. Moreover, different strategies for mutating those parts of individuals that encode the used search operators are also taken into account. The effectiveness of the proposed algorithm has been tested using typical benchmarks used to test evolutionary algorithms.

10

Decoupled homogenization of hyperelastic composite with carbon black inclusion

Poręba-Sebastjan Martyna, Kuś Wacław

Computer Methods in Materials Science

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2020

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Vol. 20, No. 1

14--21

EN

The goal of the paper is to present the application of decoupled homogenization method to the modeling of hyperelastic composite with inclusions. The method presented in the paper is illustrated by numerical analysis of a trunk door seal. The decoupled homogenization method was used to find macroscale properties of hyperelastic material. The method allows for the determination of the equivalent properties of a composite material based on its structure and the results of numerical experiments. Unlike the coupled method, the results are not transferred in every iteration between scales during computations which leads to lower calculation costs. The analyzed micro model consisted of a hyperelastic matrix and stiff inclusions in the form of spheres of carbon black material. The decoupled procedure uses evolutionary algorithm to obtain macro model material properties. The finite element method is used during analyses of micro scale models.

PL

Celem pracy było zastosowanie metody homogenizacji niesprzężonej do modelowania hipersprężystego kompozytu z wtrąceniami. Metodę przedstawioną w pracy ilustruje analiza numeryczna uszczelki drzwi. Metodę homogenizacji niesprzężonej zastosowano w celu określenia makroskopowych właściwości materiału hipersprężystego. Metoda pozwala wyznaczyć równoważne właściwości materiału kompozytowego na podstawie jego struktury i wyników eksperymentów numerycznych prowadzonych w skali mikro. W przeciwieństwie do metody sprzężonej wyniki nie są przenoszone w każdej iteracji między skalami, co prowadzi do obniżenia kosztów obliczeń. Analizowany mikro model składał się z osnowy z materiału hipersprężystego oraz sztywnych wtrąceń sadzy. Metoda niesprzężona wykorzystuje algorytm ewolucyjny, aby uzyskać właściwości materiału makro. Do analiz numerycznych użyto metody elementów skończonych.

11

On the efficiency of population-based optimization in finding best parameters for RGB-D visual odometry

Kostusiak Aleksander, Skrzypczyński Piotr

Journal of Automation Mobile Robotics and Intelligent Systems

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2019

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Vol. 13, No. 2

5--14

EN

Visual odometry estimates the transformations between consecutive frames of a video stream in order to recover the camera’s trajectory. As this approach does not require to build a map of the observed environment, it is fast and simple to implement. In the last decade RGBD cameras proliferated in roboTIcs, being also the sensors of choice for many practical visual odometry systems. Although RGB-D cameras provide readily available depth images, that greatly simplify the frame-to-frame transformations computaTIon, the number of numerical parameters that have to be set properly in a visual odometry system to obtain an accurate trajectory estimate remains high. Whereas seƫng them by hand is certainly possible, it is a tedious try-and-error task. Therefore, in this article we make an assessment of two population-based approaches to parameter opTImizaTIon, that are for long time applied in various areas of robotics, as means to find best parameters of a simple RGB-D visual odometry system. The optimization algorithms investigated here are particle swarm optimization and an evolutionary algorithm variant. We focus on the optimization methods themselves, rather than on the visual odometry algorithm, seeking an efficient procedure to find parameters that minimize the estimated trajectory errors. From the experimental results we draw conclusions as to both the efficiency of the optimization methods, and the role of particular parameters in the visual odometry system.

12

Zastosowanie algorytmów ewolucyjnych do wielokryterialnej optymalizacji rozwoju sieci dystrybucyjnej SN

Filipiak Sylwester, Nita Wojciech

Elektro Info

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2019

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nr 3

39--43

PL

Artykuł dotyczy programowania rozwoju sieci dystrybucyjnych SN. W artykule przedstawiono metodologię i obliczenia optymalizacyjne dla zadania planowania rozwoju sieci dystrybucji SN (w zakresie kwalifikacji do przebudowy linii napowietrznych). Głównym celem analiz i obliczeń była optymalizacja z odszukiwaniem zbioru rozwiązań Pareto-optymalnych. Artykuł opisuje algorytm ewolucyjny i przedstawia rezultaty obliczeń dla wybranej sieci dystrybucyjnej. Kontynuujemy zagadnienia opisane w artykule pt. „Zastosowanie algorytmu genetycznego do optymalizacji elektroenergetycznych sieci SN w zakresie kwalifikacji linii napowietrznych do przebudowy na linie kablowe” („elektro.info” 12/2018).

EN

The article concerns the programming of the development of SN distribution networks. The article presents the methodology and optimization calculations for the task of planning the development of the SN distribution network (in the scope of remodeling overhead lines). The main goal of the analyzes and calculations was optimization with the search for a set of Pareto-optimal solutions. The article describes an evolutionary algorithm and presents the results of calculations for a selected distribution network.

13

Handling insensitivity in multi-physics inverse problems using a complex evolutionary strategy

Sawicki Jakub, Smołka Maciej, Łoś Marcin, Schaefer Robert

Computer Methods in Materials Science

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2019

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Vol. 19, No. 1

2--11

EN

In this paper we present a complex strategy for the solution of ill posed, in-verse problems formulated as multiobjective global optimization ones. The strategy is capable of identifying the shape of objective insensitivity regions around connected components of Pareto set. The goal is reached in two phases. In the first, global one, the connected components of the Pareto set are localized and separated in course of the multi-deme, hierarchic memetic strategy HMS. In the second, local phase, the random sample uniformly spread over each Pareto component and its close neighborhood is obtained in the specially profiled evolutionary process using multiwinner selection. Finally, each local sample forms a base for the local approximation of a dominance function. Insensitivity region surrounding each connected component of the Pareto set is estimated by a sufficiently low level set of this approximation. Capabilities of the whole procedure was verified using specially-designed two-criterion benchmarks.

PL

Artykuł prezentuje złożoną strategię rozwiązywania źle postawionych problemów odwrotnych sformułowanych jako wielokryterialne zadania optymalizacji globalnej. Opisana strategia umożliwia identyfikację obszarów niewrażliwości funkcji celu wokół spójnych składowych zbioru Pareto. Cel jest osiągany w dwu etapach. W pierwszym z nich — globalnym — składowe spójne zbioru Pareto są lokalizowane i separowane przy pomocy wielopopulacyjnej hierarchicznej strategii memetycznej HMS. W etapie drugim — lokalnym — przy użyciu specjalnie sprofilowanego procesu ewolucyjnego wykorzystującego operator selekcji wyborczej z wieloma zwycięzcami produkowana jest losowa próbka rozłożona jednostajnie na każdej składowej i jej bliskim otoczeniu. Finalnie każda lokalna próbka jest użyta jako baza do zbudowania lokalnej aproksymacji funkcji dominacji. Zbiory poziomicowe tej aproksymacji dla odpowiednio niskich poziomów stanowią przybliżenie zbiorów niewrażliwości wokół składowych spójnych. Możliwości strategii zostały zweryfikowane przy użyciu specjalnie zaprojektowanych dwukryterialnych funkcji testowych.

14

Evaluation of evolutionary algorithms for the optimization of storm water drainage network for an urbanized area

Kumar Satish, Kaushal D. R., Gosain A. K.

Acta Geophysica

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2019

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Vol. 67, no. 1

149--165

EN

The studies pertaining to urban storm water drainage system have picked up importance lately in light of pluvial flooding. The flooding is mostly due to urban expansion, reduction in infiltration rate and environmental change. In order to minimize flooding, hydrologists are using conceptual rainfall–runoff models as a tool for predicting surface runoff and flood forecasting. Manual calibration is often a tedious process because of the involved subjectivity, which makes the automatic approach more preferable. In this study, three evolutionary algorithms (EAs), namely SFLA, GA and PSO, were used to calibrate SWMM parameters for the two study areas of the highly urbanized catchments of Delhi, India. The work incorporates auto-tuning of a widely used SWMM, via internal coupling of SWMM with all three EAs in MATLAB environment separately. Results were tested using statistical parameters, i.e., Nash–Sutcliffe efficiency (NSE), Percent Bias (PBIAS) and root-mean-square error–observations standard deviation ratio (RSR). GA results were in good agreement with the observed data in both the study area with NSE and PBIAS values lying between 0.60 and 0.91, and 1.29 and 7.41%, respectively. Also, RSR value was near zero, indicating reasonably good model performance. Subsequently, the model reasonably predicted the flooding hotspots that should be controlled to prevent any possible inundation of the surrounding areas. SFLA results were also promising, but better than PSO. Thus, the approach has demonstrated the potential use and combination of single-objective optimization algorithms and hydrodynamic models for assessing the risk in urban storm water drainage systems, providing valuable information for decision-makers.

15

Multi-Criteria Phase Sequence Optimization in Selected the Highest-Voltage Power Lines Using the Evolutionary Algorithm

Wasilewski Jacek, Kubek Paweł

Acta Energetica

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2019

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nr 2

73--79

EN

The article presents a model and results of multi-criteria phase sequence optimization for selected LV line strings in the Polish National Power System, in the context of minimizing the voltage and current asymmetry coefficients. The objective function, decision variables, task parameters, and state variables are characterized in detail. Criteria such as the capital expenditure necessary for line symmetrisation interlacing and voltage asymmetry coefficients were considered. The evolutionary algorithm was used to solve the optimization model presented above. To prioritize the criteria under consideration, the multi-criteria quasi-lexicographic approach was applied. The results are analysed in detail, as well as the input data uncertainty impact on the results.

PL

W artykule przedstawiono model i wyniki wielokryterialnej optymalizacji kolejności faz dla wybranych układów ciągów liniowych NN w KSP, w kontekście minimalizacji wartości współczynników asymetrii napięć i prądów. Scharakteryzowano szczegółowo funkcję celu, zmienne decyzyjne, parametry zadania oraz zmienne stanu. Rozważono kryteria, takie jak: nakład inwestycyjny konieczny do wykonania przeplotu symetryzacji linii (przeplotu) i współczynniki asymetrii napięć. Do rozwiązania przedstawio- nego wyżej modelu optymalizacyjnego wykorzystano algorytm ewolucyjny. W celu priorytetyzacji rozważanych kryteriów zastoso- wano wielokryterialne podejście quasi-leksykograficzne. Przedstawiono szczegółową analizę otrzymanych wyników wraz z analizą wpływu niepewności danych wejściowych na otrzymane wyniki.

16

Analiza istotności cech znamion skórnych dla celów diagnostyki czerniaka złośliwego

Mikołajczyk A., Grochowski M.

Zeszyty Naukowe Wydziału Elektrotechniki i Automatyki Politechniki Gdańskiej

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2018

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Nr 60

67--70

PL

Pomimo dynamicznego rozwoju metod uczenia maszynowego i ich wdrażania do praktyki lekarskiej, automatyczna analiza znamion skórnych wciąż jest nierozwiązanym problemem. Poniższy artykuł proponuje zastosowanie algorytmu ewolucyjnego do zaprojektowania, wytrenowania i przetestowania całych populacji klasyfikatorów (sztucznych sieci neuronowych) oraz ich iteracyjnego udoskonalania w każdej kolejnej populacji, w celu osiągnięcia jak najlepszej dokładności klasyfikacji znamion skórnych. Algorytm zwraca optymalny zestaw cech opisujących obraz dermatoskopowy wraz z proponowaną architekturą sieci neuronowej. Uzyskano dokładność równą 85,83%, swoistość równą 79,07% oraz czułość równą 92,60%.

EN

Despite the dynamic development of machine learning methods, automatic analysis of skin lesions is still open issue. The following article proposes the use of an evolutionary algorithm to design, train, and to test a whole population of classifiers (artificial neural networks) and to iteratively improve them in each subsequent population, in order to achieve the best possible accuracy in the classification of skin lesions task. The algorithm returns an optimal set of features describing the dermatoscopic image together with the proposed architecture of the neural network. High classification results were obtained, in particular: accuracy equal to 85.83%, specificity 79.07% and sensitivity 92.60%.

17

Algorytmy ewolucyjne w badaniach ankietowych

Mazur Z., Pec J.

Zeszyty Naukowe. Organizacja i Zarządzanie / Politechnika Śląska

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2018

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z. 130

439--457

EN

This article presents the possibility of using evolutionary algorithmic techniques in the field of questionnaire surveys. Also it has been extended through the introduction of two additional genetic operators outside the known from literature such as: cross-over, mutation or inversion. The newly defined operators in this article are “hardening of the gene” and “weakening of the gene” in order to increase the degree of reliability of the information received by the interviewers. The new algorithm is given in order to eliminate duplication of the chromosomes. This affects the process of modified basic genetic algorithm by reducing its workload. According to the authors the proposed solutions accepted and included in the methodology of the surveys will improve the quality and reliability of the data.

PL

W artykule przedstawiono możliwości, jakie stawiają do dyspozycji techniki ewolucyjne w obszarze badań ankieterskich. Rozszerzono je również poprzez wprowadzenie dwóch dodatkowych operatorów genetycznych. Poza znanymi z literatury przedmiotu operatorami genetycznymi, takimi jak krzyżowanie, mutacja czy inwersja, autorzy niniejszego artykułu wprowadzają dwa nowe operatory – operator „wzmocnienia genowego” oraz operator „osłabienia genowego” – umożliwiające zwiększenie stopnia wiarygodności informacji otrzymywanych przez ankieterów. Zaproponowano również algorytm eliminacji zdublowanych chromosomów, co ma wpływ na przebieg pracy podstawowego algorytmu genetycznego poprzez zmniejszenie jego pracochłonności obliczeniowej. Zdaniem autorów, zaproponowane rozwiązania, zaakceptowane i uwzględnione w metodyce badań ankietowych, wpłyną na poprawę jakości i wiarygodności pozyskanych danych.

18

A novel methodology for automated generation of flexible hardware architectures

Pedrino E., Gallon I. F., Valente F. J., Fernandes M. M., Ogasawara O., Roda V. O.

Przegląd Elektrotechniczny

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2018

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R. 94, nr 4

17--21

EN

The automated generation of hardware architectures is a powerful tool in the fully interconnected world. This work presents a new methodology based around Cartesian Genetic Programming for generating flexible hardware architectures. The solution is composed by an intelligent module developed in software which is responsible for the generation of the solution logic for the pretended architecture, and by a hardware module developed in Verilog-HDL, which converts the obtained solution logic into a hardware architecture in FPGA. Good results were reached and compared to other similar proposals found in the literature.

PL

W pracy przedstawiono nową metodologię opartą na Kartezjańskim Programie Genetycznym służącą do tworzenia elastycznych architektur sprzętowych. Rozwiązanie składa się z inteligentnego modułu opracowanego w oprogramowaniu odpowiedzialnym za generowanie logiki rozwiązania dla danej architektury oraz modułu sprzętowego opracowanego w Verilog-HDL, który przekształca otrzymany algorytm rozwiązania w architekturę sprzętową w układzie FPGA.

19

Reduced number of design parameters in optimum path synthesis with timing of four-bar linkage

Buśkiewicz J.

Journal of Theoretical and Applied Mechanics

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2018

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Vol. 56 nr 1

43--55

EN

The paper presents the method for the optimal synthesis of four-link mechanism generating open/closed paths with time prescription. Although the method is suitable for both closed and open paths, it enables decreasing the number of design parameters describing dimensions, orientation and position of a path generator. Compared to the methods presented in the references, this is a one-phase synthesis method; although the number of design parameters is reduced, the method does not require affine transformations to be performed on the synthesised mechanism. The effectiveness of the method is discussed based on examples of three paths, with two taken from the literature.

20

Properties of an α-clique approach to obtaining the hub and spoke structure in optimization of transportation systems

Mazbic-Kulma B., Owsinski J. W., Barski A., Sęp K., Stańczak J.

Control and Cybernetics

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2018

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Vol. 47, no. 2

173--189

EN

The paper is devoted to the analysis of a graph transformation, pertinent for the transport and logistic systems and their planning and management. Namely, we consider, for a given graph, representing some existing transport or logistic system, its transformation to a (non-equivalent) so-called ”hub-and-spoke” structure, known from both literature and practice of transportation and logistics. This structure is supposed to bring beneﬁts in terms of functioning and economic performance of the respective systems. The transformation into the ”hub-and-spoke” is not only non-equivalent (regarding the original graph of the system), but is also, in general, non unique. The structure sought is composed of two kinds of elements - nodes of the graph (stations, airports, havens, etc.), namely: the subgraph of hubs, which, in principle, ought to constitute a complete sub-graph (a clique), and the ”spokes”, i.e. the subsets of nodes, each of which is connected in the ultimate structure only with one of the hubs. The paper proposes a relaxation of the hub-and-spoke structure by allowing the hub subgraph not to be complete, but at least connected, with a deﬁnite ”degree of completeness” (alpha), from where the name of ”alpha-clique”. It is shown how such structures can be obtained and what are the resulting beneﬁts for various assumptions, regarding such structures. The beneﬁts are measured here with travel times. The desired structures are sought with an evolutionary algorithm. It is shown on an academic example how the results vary and how the conclusions, relevant for practical purposes, can be drawn from such analyses, done with the methods here presented.