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  • About
  • The Global ETD Search service is a free service for researchers to find electronic theses and dissertations. This service is provided by the Networked Digital Library of Theses and Dissertations.
    Our metadata is collected from universities around the world. If you manage a university/consortium/country archive and want to be added, details can be found on the NDLTD website.
161

Dual Satellite Coverage using Particle Swarm Optimization

Ojeda Romero, Juan Andre 29 October 2014 (has links)
A dual satellite system in a Low Earth Orbit, LEO, would be beneficial to study the electromagnetic occurrences in the magnetosphere and their contributions to the development of the aurora events in the Earth's lower atmosphere. An orbit configuration is sought that would increase the total time that both satellites are inside the auroral oval. Some additional objectives include minimizing the total fuel cost and the average angle between the satellites' radius vectors. This orbit configuration is developed using a series of instantaneous burns applied at each satellite's perigee. An analysis of the optimal solutions generated by a Particle Swarm Optimization method is completed using a cost function with different weights for the time, fuel, and angle terms. Three different scenarios are presented: a single burn case, a double burn case, and a four burn case. The results are calculated using two different orbital mechanics models: an unperturbed two-body simulation and a two-body simulation with added Earth's equatorial bulge effects. It is shown that the added perturbation reduces the total event time in the optimal solutions generated. Specific weights for the cost function are recommended for further studies. / Master of Science
162

A multi-objective optimisation framework for MED-TVC seawater desalination process based on particle swarm optimisation

Al-hotmani, Omer M.A., Al-Obaidi, Mudhar A.A.R., Li, Jian-Ping, John, Yakubu M., Patel, Rajnikant, Mujtaba, Iqbal 25 March 2022 (has links)
Yes / Owing to the high specific energy consumption associated with thermal desalination technologies such as Multi Effect Distillation (MED), there is a wide interest to develop a cost-effective desalination technology. This study focuses on improving the operational, economic, and environmental perspectives of hybrid MED-TVC (thermal vapour compression) process via optimisation. Application of particle swarm optimisation (PSO) in several engineering disciplines have been noted but its potential has not been exploited fully in desalination technologies especially MED-TVC in the past. A multi-objective non-linear optimisation framework based on PSO is constructed here. Two of our earlier models have been used to predict the key process performance and cost indicators. The models are embedded within the PSO optimisation algorithm to develop a new hybrid optimisation model which minimises the total freshwater production cost, total specific energy consumption and brine flow rate while maintaining a fixed freshwater production for a given number of effects and seawater conditions. The steam flow rate and temperature are considered as control variables of the optimisation problem to achieve the objective function. The PSO has successfully achieved the optimum indexes for the hybrid MED-TVC process for a wide range of number of effects. It also shows a maximum reduction of freshwater production cost by 36.5%, a maximum energy saving by 32.1% and a maximum reduction of brine flow rate by 38.3%, while maintaining the productivity of freshwater.
163

A decision support system for vessel speed decision in maritime logistics using weather archive big data

Lee, Habin, Aydin, N., Choi, Y., Lekhavat, S., Irani, Zahir 06 2017 (has links)
Yes / Speed optimization of liner vessels has significant economic and environmental impact for reducing fuel cost and Green House Gas (GHG) emission as the shipping over maritime logistics takes more than 70% of world transportation. While slow steaming is widely used as best practices for liner shipping companies, they are also under the pressure to maintain service level agreement (SLA) with their cargo clients. Thus, deciding optimal speed that minimizes fuel consumption while maintaining SLA is managerial decision problem. Studies in the literature use theoretical fuel consumption functions in their speed optimization models but these functions have limitations due to weather conditions in voyages. This paper uses weather archive data to estimate the real fuel consumption function for speed optimization problems. In particular, Copernicus data set is used as the source of big data and data mining technique is applied to identify the impact of weather conditions based on a given voyage route. Particle swarm optimization, a metaheuristic optimization method, is applied to find Pareto optimal solutions that minimize fuel consumption and maximize SLA. The usefulness of the proposed approach is verified through the real data obtained from a liner company and real world implications are discussed.
164

Multi-modal Aggression Identification Using Convolutional Neural Network and Binary Particle Swarm Optimization

Kumari, K., Singh, J.P., Dwivedi, Y.K., Rana, Nripendra P. 10 January 2021 (has links)
Yes / Aggressive posts containing symbolic and offensive images, inappropriate gestures along with provocative textual comments are growing exponentially in social media with the availability of inexpensive data services. These posts have numerous negative impacts on the reader and need an immediate technical solution to filter out aggressive comments. This paper presents a model based on a Convolutional Neural Network (CNN) and Binary Particle Swarm Optimization (BPSO) to classify the social media posts containing images with associated textual comments into non-aggressive, medium-aggressive and high-aggressive classes. A dataset containing symbolic images and the corresponding textual comments was created to validate the proposed model. The framework employs a pre-trained VGG-16 to extract the image features and a three-layered CNN to extract the textual features in parallel. The hybrid feature set obtained by concatenating the image and the text features were optimized using the BPSO algorithm to extract the more relevant features. The proposed model with optimized features and Random Forest classifier achieves a weighted F1-Score of 0.74, an improvement of around 3% over unoptimized features.
165

Beam Steering of Time Modulated Antenna Arrays Using Particle Swarm Optimization

Abusitta, M.M., Abd-Alhameed, Raed, Elfergani, Issa T., Adebola, A.D., Excell, Peter S. 22 March 2011 (has links)
Yes / In this paper, a simple switching process is employed to steer the beam of a vertically polarised circular antenna array. This is a simple method, in which the difference resulting from the induced currents when the radiating/loaded element is connected/disconnected from the ground plane. A time modulated switching process is applied through particle swarm optimisation. / Electronics and Telecommunications
166

Metodologia de otimização em dois níveis para a geração de sinal sub-ótimo de excitação e estimação de parâmetros de sistemas não lineares restritos

Costa, Exuperry Barros 15 September 2017 (has links)
Submitted by Geandra Rodrigues (geandrar@gmail.com) on 2018-01-11T17:29:03Z No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Approved for entry into archive by Adriana Oliveira (adriana.oliveira@ufjf.edu.br) on 2018-01-23T13:44:17Z (GMT) No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) / Made available in DSpace on 2018-01-23T13:44:17Z (GMT). No. of bitstreams: 1 exuperrybarroscosta.pdf: 14654639 bytes, checksum: f25579d82da6242e77a04745322538ad (MD5) Previous issue date: 2017-09-15 / O presente trabalho propõe uma nova metodologia de Geração de Sinal Sub-Ótimo de Excitação e Estimação Ótima de Parâmetros de sistemas não lineares. É proposto que a avaliação de cada sinal deva considerar, entre outros fatores, a diferença entre os parâmetros reais da planta e os obtidos pela estimação. Entretanto esta métrica não é trivial de ser obtida uma vez que os valores reais são desconhecidos. Para tanto é adotada a hipótese de que, se um sistema real puder ser razoavelmente aproximado por uma caixa branca, é possível utilizar este modelo como referência para indicar o impacto de um sinal sobre a estimação paramétrica. Desta forma, é utilizada uma metodologia de otimização dividida em dois níveis: (i) Nível Interno; para um dado sinal de excitação um método de otimização não linear busca o conjunto ótimo de parâmetros que minimiza o erro entre os sinais de saída do modelos original e do de referência. (ii) No nível externo um método de otimização baseado em meta-heurística é responsável por encontrar o melhor sinal de excitação com base na função custo composta de uma soma ponderada de métricas que consideram o erro entre os sinais de saída do modelo otimizado e do de referência, a diferença quadrática entre seus parâmetros, e o custo em relação ao tempo e espaço necessários para executar o experimento. Portanto, a aplicação da metodologia proposta vem suprir a necessidade de estimar sistemas não lineares apropriadamente, encontrando um conjunto de parâmetros capaz de generalizar o comportamento do sistema real, através de um sinal de excitação que cumpra requisitos práticos do processo. A eficácia da metodologia proposta é analisada em detalhes através de resultados obtidos utilizando sistemas de fluídos, sistemas caóticos e de robótica móvel, tanto sobre rodas quanto subaquática. / The present work proposes a novel methodology for Sub-Optimal Excitation Signal Generation and Optimal Parameter Estimation of nonlinear systems. It is proposed that the evaluation of each signal must to take into account, among other factors, the difference between real system parameters and the obtained by estimation. However, this metric is not trivially obtained once the real parameters values are unknown. To do so it is adopted the hypothesis that, if the system can be fairly approximate by a white box model, it is possible to use this model as a benchmark to indicate the impact of a signal on a parametric estimation. In this way, the method uses an optimization methodology divided into two levels: (i) Inner Level; For a given excitation signal a nonlinear optimization method searches for the optimal set of parameters that minimizes the error between the output signals of the original and the benchmark models. (ii) At the outer level, an optimization method based on metaheuristics is responsible for finding the best excitation signal, based on the cost function composed of a weighted sum of metrics, that considers the error between the output signals of the optimized model and the benchmark, the quadratic difference between its parameters, and the cost in relation to the time and space required to execute the experiment. Thus, the application of the proposed methodology comes to supply the need to estimate nonlinear systems appropriately, finding a set of parameters capable of generalizing the behavior of the real system, through an excitation signal that fulfills practical requirements of the process. The proposed methodology is analyzed in detail through results obtained using fluid systems, chaotic systems and mobile robotics, both wheeled and underwater.
167

Otimização de sistemas hidrotérmicos de geração por meio de meta-heurísticas baseadas em enxame de partículas / Optimization of hydrothermal generating systems by means of particle swarm based meta-heuristics

Deus, Guilherme Resende 02 February 2016 (has links)
Submitted by Cássia Santos (cassia.bcufg@gmail.com) on 2017-07-03T12:59:51Z No. of bitstreams: 2 Dissertação - Guilherme Resende Deus - 2016.pdf: 3406372 bytes, checksum: aaa431a0fa0dd2323a74cf35fb63f892 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Luciana Ferreira (lucgeral@gmail.com) on 2017-07-10T11:44:22Z (GMT) No. of bitstreams: 2 Dissertação - Guilherme Resende Deus - 2016.pdf: 3406372 bytes, checksum: aaa431a0fa0dd2323a74cf35fb63f892 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-07-10T11:44:22Z (GMT). No. of bitstreams: 2 Dissertação - Guilherme Resende Deus - 2016.pdf: 3406372 bytes, checksum: aaa431a0fa0dd2323a74cf35fb63f892 (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-02-02 / The objective of this work is to find reasonable solutions to the problem of optimization of hydrothermal generating systems by means of metaheuristics based on particle swarms. The proposed problem is complex, dynamic, nonlinear and presents some stochastic variables. The study consisted of the implementation of particle swarm algorithms, more specifically the variants of the Particle Swarm Optimization (PSO) algorithm: LSSPSO, ABeePSO and KFPSO. The algorithms were run in a mill simulator containing data from eight National Interconnected System mills during the five year period. The results were compared with the studies using the Nonlinear Programming (NLP) algorithm, and it was concluded that although the presented meta-heuristics were able to obtain a Final Storage Energy value equal to NLP, they did not have a generation cost Equivalent to or less than the Nonlinear Programming method. / O trabalho objetiva encontrar soluções razoáveis para o problema de otimização de sistemas hidrotérmicos de geração por meio de meta-heurísiticas baseadas em enxame de partículas. O problema proposto é complexo, dinâmico, não linear e apresenta algumas variáveis estocásticas. O estudo consistiu na implementação de algoritmos baseados em enxame de partículas, mais especificamente das variantes do algoritmo Particle Swarm Optimization (PSO): LSSPSO, ABeePSO e KFPSO. Os algoritmos foram executados em um simulador de usinas que contém dados de oito usinas do Sistema Interligado Nacional durante o período de cinco anos. Os resultados foram comparados com os estudos que utilizam o algoritmo de Programação Não-Linear (PNL), e conclui-se que apesar de as meta-heurísticas apresentadas conseguirem obter um valor de Energia Armazenada Final igual ao PNL, não obtiveram um custo de geração equivalente ou inferior ao método de Programação Não-Linear.
168

Shape Optimization of the Hydraulic Machine Flow Passages / Shape Optimization of the Hydraulic Machine Flow Passages

Moravec, Prokop January 2020 (has links)
Tato dizertační práce se zabývá vývojem optimalizačního nástroje, který je založen na metodě Particle swarm optimization a je poté aplikován na dva typy oběžných kol radiálních čerpadel.
169

Ray-Tracing Modeling of Grating Lobe Level Reduction by Using a Dielectric Dome Antenna / Strål-Spårnings-Modellering av Sänkning av Gallerlobsnivå Genom att Använda en Dielektrisk Kupolantenn

Jonasson, Lukas January 2023 (has links)
With the newly deployed fifth-generation telecommunications system and upcoming sixth-generation, high-gain antennas with hemispherical scanning capabilities are of high interest. Phased array antennas allow for fast scanning capabilities with electronic beam-steering. In an effort to reduce the number of antenna elements while maintaining the antenna aperture size, the element spacing is increased. However sparse arrays introduce grating lobes in the radiation pattern. An interesting solution to reduce the grating lobes is to integrate a lens with the array. Further, simulating the radiation pattern with a ray-tracing algorithm and the geometrical optics approximation makes for fast simulation times. The presented ray-tracing algorithm in this work speeds up the simulation by 43 times compared to a two-dimensional full-wave simulation. To model the full radiation pattern the rays are shot out from a single point across a set angular space. To emulate an element pattern the rays are excited with a set amplitude distribution. Here, two different methods of obtaining the amplitude are presented and compared to a two-dimensional full-wave COMSOL model. The lens is made from a dielectric, constructed from the conics equation with applied conformal matching layers. The ray path and phase distribution are calculated with Snell's law, the amplitude distribution at the lens aperture is calculated through the ray tube theory, and the radiation pattern with the Kirchhoff Diffraction formula. To optimize the lens shape and an array offset, the ray-tracing algorithm is coupled with a Particle Swarm Optimization algorithm. Two different arrays are used in this thesis, the first constructed from open-ended waveguides and the second using sub-arrays of the same waveguides. The optimized lens for the first array shows that a grating lobe suppression between 1.1-2.0 dB is achievable with a main lobe reduction between 0.2-0.3 dB for scanning to -20 degrees. For the array with sub-arrays, the main lobe suppression is between 0.3-0.9 dB, with a grating lobe suppression of up to 4.0 dB. / Med det nyligen lanserade femte generationens telekommunikationssystem och den kommande sjätte generationen är högförstärkningsantenner med halvsfäriska skanningsmöjligheter av stort intresse. Fasade array-antenner möjliggör snabb skanningskapacitet med elektronisk strålstyrning. I ett försök att minska antalet antennelement samtidigt som antennöppningens storlek bibehålls, ökas elementavståndet. Men glesa arrayer introducerar gallerlober i strålningsmönstret. En intressant lösning för att minska gallerloberna är att integrera en lins med arrayen. Vidare, simulering av strålningsmönstret med en strålspårningsalgoritm och den geometriska optiska approximationen ger snabba simuleringstider. Den presenterade strålspårningsalgoritmen i detta arbete snabbar upp simuleringen med 43 gånger jämfört med en tvådimensionell helvågssimulering. För att modellera hela strålningsmönstret skjuts strålarna ut från en enda punkt över ett fast vinkelutrymme. För att efterlikna ett elementmönster exciteras strålarna med en inställd amplitudfördelning. Här presenteras två olika metoder för att erhålla amplituden och jämförs med en tvådimensionell fullvågs-COMSOL-modell. Linsen är gjord av ett dielektrika konstruerat från koniska ekvationen med applicerade konforma matchande lager. Strålvägen och fasfördelningen beräknas med Snell-lagen, amplitudfördelningen vid linsöppningen beräknas genom strålrörsteorin och strålningsmönstret med Kirchhoff-diffraktionsformeln. För att optimera linsformen och en arrayförskjutning är strålspårningsalgoritmen kopplad med en Particle Swarm algoritm. Två olika arrayer används i denna avhandling, den första konstruerad av vågledare med öppen ände och den andra med hjälp av sub-arrayer av samma vågledare. Den optimerade linsen för den första arrayen visar att en gallerlobsundertryckning mellan 1,1-2,0 dB kan uppnås med en huvudlobsreduktion mellan 0,2-0,3 dB för skanning till -20 grader. För arrayen med sub-arrayer är undertryckningen av huvudloben mellan 0,3-0,9 dB, med en gallerlobundertryckning på upp till 4,0 dB.
170

The development of some rotationally invariant population based optimization methods

Ras, Marthinus Nicolaas 03 1900 (has links)
Thesis (MScEng)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this study we consider the lack of rotational invariance of three different population based optimization methods, namely the particle swarm optimization (PSO) algorithm, the differential evolution (DE) algorithm and the continuous-parameter genetic algorithm (CPGA). We then propose rotationally invariant versions of these algorithms. We start with the PSO. The so-called classical PSO algorithmis known to be variant under rotation, whereas the linear PSO is rotationally invariant. This invariance however, comes at the cost of lack of diversity, which renders the linear PSO inferior to the classical PSO. The previously proposed so-called diverse rotationally invariant (DRI) PSO is an algorithm that aims to combine both diversity and invariance. This algorithm is rotationally invariant in a stochastic sense only. What is more, the formulation depends on the introduction of a random rotation matrix S, but invariance is only guaranteed for ‘small’ rotations in S. Herein, we propose a formulation which is diverse and strictly invariant under rotation, if still in a stochastic sense only. To do so, we depart with the linear PSO, and then we add a self-scaling random vector with a standard normal distribution, sampled uniformly from the surface of a n-dimensional unit sphere. For the DE algorithm, we show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant DE formulation in which the crossover operation takes place in an orthogonal base constructed using Gramm-Schmidt orthogonalization. We propose two new formulations by firstly considering a very simple rotationally invariant formulation using constant mutation and whole arithmetic crossover. This rudimentary formulation performs badly, due to lack of diversity. We then introduce diversity into the formulation using two distinctly different strategies. The first adjusts the crossover step by perturbing the direction of the linear combination between the target vector and the mutant vector. This formulation is invariant in a stochastic sense only. We add a self-scaling random vector to the unaltered whole arithmetic crossover vector. This formulation is strictly invariant, if still in a stochastic sense only. In this study we consider the lack of rotational invariance of three different population based optimization methods, namely the particle swarm optimization (PSO) algorithm, the differential evolution (DE) algorithm and the continuous-parameter genetic algorithm (CPGA). We then propose rotationally invariant versions of these algorithms. We start with the PSO. The so-called classical PSO algorithmis known to be variant under rotation, whereas the linear PSO is rotationally invariant. This invariance however, comes at the cost of lack of diversity, which renders the linear PSO inferior to the classical PSO. The previously proposed so-called diverse rotationally invariant (DRI) PSO is an algorithm that aims to combine both diversity and invariance. This algorithm is rotationally invariant in a stochastic sense only. What is more, the formulation depends on the introduction of a random rotation matrix S, but invariance is only guaranteed for ‘small’ rotations in S. Herein, we propose a formulation which is diverse and strictly invariant under rotation, if still in a stochastic sense only. To do so, we depart with the linear PSO, and then we add a self-scaling random vector with a standard normal distribution, sampled uniformly from the surface of a n-dimensional unit sphere. For the DE algorithm, we show that the classic DE/rand/1/bin algorithm, which uses constant mutation and standard crossover, is rotationally variant. We then study a previously proposed rotationally invariant DE formulation in which the crossover operation takes place in an orthogonal base constructed using Gramm-Schmidt orthogonalization. We propose two new formulations by firstly considering a very simple rotationally invariant formulation using constant mutation and whole arithmetic crossover. This rudimentary formulation performs badly, due to lack of diversity. We then introduce diversity into the formulation using two distinctly different strategies. The first adjusts the crossover step by perturbing the direction of the linear combination between the target vector and the mutant vector. This formulation is invariant in a stochastic sense only. We add a self-scaling random vector to the unaltered whole arithmetic crossover vector. This formulation is strictly invariant, if still in a stochastic sense only. For the CPGA we show that a standard CPGA using blend crossover and standard mutation, is rotationally variant. To construct a rotationally invariant CPGA it is possible to modify the crossover operation to be rotationally invariant. This however, again results in loss of diversity. We introduce diversity in two ways: firstly using a modified mutation scheme, and secondly, following the same approach as in the PSO and the DE, by adding a self-scaling random vector to the offspring vector. This formulation is strictly invariant, albeit still in a stochastic sense only. Numerical results are presented for the variant and invariant versions of the respective algorithms. The intention of this study is not the contribution of yet another competitive and/or superior population based algorithm, but rather to present formulations that are both diverse and invariant, in the hope that this will stimulate additional future contributions, since rotational invariance in general is a desirable, salient feature for an optimization algorithm. / AFRIKAANSE OPSOMMING: In hierdie studie bestudeer ons die gebrek aan rotasionele invariansie van drie verskillende populasiegebaseerde optimeringsmetodes, met name die partikel-swerm optimerings (PSO) algoritme, die differensi¨ele evolusie (DE) algoritme en die kontinue-parameter genetiese algoritme (KPGA). Ons stel dan rotasionele invariante weergawes van hierdie algoritmes voor. Ons beginmet die PSO. Die sogenaamde klassieke PSO algoritme is bekend dat dit variant is onder rotasie, terwyl die lineˆere PSO rotasioneel invariant is. Hierdie invariansie lei tot ’n gebrek aan diversiteit in die algoritme, wat beteken dat die lineˆere PSO minder goed presteer as die klassieke PSO. Die voorheen voorgestelde sogenaamde diverse rotasionele invariante (DRI) PSO is ’n algoritme wat beoog om beide diversiteit en invariansie te kombineer. Hierdie algoritme is slegs rotasioneel invariant in ’n stogastiese sin. Boonop is die formulering afhanklik van ’n willekeurige rotasie matriks S, maar invariansie is net gewaarborg vir ’klein’ rotasies in S. In hierdie studie stel ons ’n formulering voor wat divers is en streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. In hierdie formulering, vertrek ons met die lineˆere PSO, en voeg dan ’n self-skalerende ewekansige vektor met ’n standaard normaalverdeling by, wat eenvormig van die oppervlakte van ’n n-dimensionele eenheid sfeer geneem word. Vir die DE algoritme toon ons aan dat die klassieke DE/rand/1/bin algoritme, wat gebruik maak van konstante mutasie en standaard kruising rotasioneel variant is. Ons bestudeer dan ’n voorheen voorgestelde rotasionele invarianteDE formulering waarin die kruisingsoperasie plaasvind in ’n ortogonale basis wat gekonstrueer wordmet behulp van die Gramm-Schmidt ortogonalieseringsproses. Verder stel ons dan twee nuwe formulerings voor deur eerstens ’n baie eenvoudige rotasionele invariante formulering te oorweeg, wat konstante mutasie en volledige rekenkundige kruising gebruik. Hierdie elementˆere formulering onderpresteer as gevolg van die afwesigheid van diversiteit. Ons voeg dan diversiteit by die formulering toe, deur gebruik te maak van twee afsonderlike strategie ¨e. Die eerste verander die kruisings stap deur die rigting van die lineˆere kombinasie tussen die teiken vektor en die mutasie vektor te perturbeer. Hierdie formulering is slegs invariant in ’n stogastiese sin. In die ander formulering, soos met die nuwe rotasionele invariante PSO, voeg ons bloot ’n self-skalerende ewekansige vektor by die onveranderde volledige rekenkundige kruisingsvektor. Hierdie formulering is streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. Vir die KPGA wys ons dat die standaard KPGA wat gemengde kruising en standaard mutasies gebruik, rotasioneel variant is. Om ’n rotasionele invariante KPGA te konstrueer is dit moontlik om die kruisingsoperasie aan te pas. Dit veroorsaak weereens ’n verlies aan diversiteit. Ons maak die algoritmes divers op twee verskillende maniere: eerstens deur gebruik te maak van ’n gewysigde mutasie skema, en tweedens deur die selfde aanslag te gebruik as in die PSO en die DE, deur ’n self-skalerende ewekansige vektor by die nageslag vektor te voeg. Hierdie formulering is streng invariant onder rotasie, selfs al is dit steeds net in ’n stogastiese sin. Numeriese resultate word vir die variante en invariante weergawe van die onderskeie algoritmes verskaf. Die doel van hierdie studie is nie die bydrae van bloot nog ’n kompeterend en/of beter populasiegebaseerde optimeringsmetode nie, maar eerder om formulerings voor te lê wat beide divers en invariant is, met die hoop dat dit in die toekoms bykomende bydraes sal stimuleer, omdat rotasionele invariansie in die algemeen ’n aantreklike, belangrike kenmerk is vir ’n optimerings algoritme.

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