Solving Differential Equation by Modified Genetic Algorithms

    المعادلة التفاضلية(DE) هي معادلة رياضياتية تحتوي على مشتقات كمتغير، ومن امثلتها  المعادلات التي تمثل الكميات الفيزيائية، في هذه الورقة قدمنا ​​تعديل على الطريقة التي تقترح بان يكون حل المعادلات التفاضلية الاعتيادية (EDO) من الدرجة الثانية على شكل متعددة الحدود وباستخدام الخوازمية التطورية(ES)تجد معاملات الحل المقترح [1] .طريقتنا تقترح ايضا متعددة حدود لحل المعادلات التفاضلية الاعتيادية (EDO) ولكل الدرجات وليس للدرجة الثانية فقط ونستخدم الخورارزميه الجينية(GA) بدل الخوارزمية التطورية (ES) لايجاد معاملات متعددة الحدود ,وكذلك استخدمنا متعددة الحدود لحل المعادلات التفاضلية الجزئية(DEP) وباستخدام الخوارزمية الجينية (GA) لايجاد معاملات متعددة الحدود التي تمثل حل المعادلات التفاضلية الجزئية حيث تستخدم استراتيجيات التطورسلسلة من الخطوات التطورية المستندة دالة التقييم ومن خلال سلسلة من الطفرات على حل فردي  وليس على مجموعة من الحلول على خلاف الخوارزمية الجينية [2]. استخدمنا امثلة عددية تظهر دقة اسلوبنا مقارنة مع بعض الاساليب العددية  المعروفة مع نسبة خطأ اقل بكثير مقارنة مع افضل الحلول بالطرق العددية   Differential equation is a mathematical equation which contains the derivatives of a variable, such as the equation which represent physical quantities, In this paper  we introduced modified on the method which proposes a polynomial to solve the ordinary differential equation (ODEs) of second order and by using the evolutionary algorithm to find the coefficients of the propose a polynomial [1] . Our method propose a polynomial to solve the ordinary differential equations (ODEs) of nth  order and partial differential equations(PDEs) of order two  by using the Genetic algorithm to find the coefficients of the propose a polynomial ,since Evolution Strategies (ESs) use  a string representation of the solution to some problem and attempt to evolve a good solution through a series of fitness –based evolutionary steps .unlike (GA)  ,an ES will typically not use a population of solution but instead will make a sequence of mutations of an individual solution ,using fitness as a guide[2] . A numerical example with good result show the accuracy of our method compared with some existing methods .and the best error of method it’s not much larger than the error in best of the numerical method solutions

Fine-grained Tournament Selection Operator in Genetic Algorithms

Tournament selection is one of the most popular selection operators in Genetic Algorithms. Recently, its popularity is increasing because this operator is well suited for Parallel Genetic Algorithms applications. In this paper, new selection operator is proposed. The new operator, which should be an improvement of the tournament selection, is named ``Fine-grained Tournament Selection'' (FGTS). It is shown that classical tournament selection is a special case of the FGTS and that new operator preserves its good features. Furthermore, theoretical estimations for the FGTS are made. Estimations for the FGTS are similar to those for the classical tournament selection. Finally, classical tournament selection, rank-based selection and FGTS are experimentally compared on a real world NP-hard problem and the obtained results are discussed

Personalized Health Monitoring Using Evolvable Block-based Neural Networks

This dissertation presents personalized health monitoring using evolvable block-based neural networks. Personalized health monitoring plays an increasingly important role in modern society as the population enjoys longer life. Personalization in health monitoring considers physiological variations brought by temporal, personal or environmental differences, and demands solutions capable to reconfigure and adapt to specific requirements. Block-based neural networks (BbNNs) consist of 2-D arrays of modular basic blocks that can be easily implemented using reconfigurable digital hardware such as field programmable gate arrays (FPGAs) that allow on-line partial reorganization. The modular structure of BbNNs enables easy expansion in size by adding more blocks. A computationally efficient evolutionary algorithm is developed that simultaneously optimizes structure and weights of BbNNs. This evolutionary algorithm increases optimization speed by integrating a local search operator. An adaptive rate update scheme removing manual tuning of operator rates enhances the fitness trend compared to pre-determined fixed rates. A fitness scaling with generalized disruptive pressure reduces the possibility of premature convergence. The BbNN platform promises an evolvable solution that changes structures and parameters for personalized health monitoring. A BbNN evolved with the proposed evolutionary algorithm using the Hermite transform coefficients and a time interval between two neighboring R peaks of ECG signal, provides a patient-specific ECG heartbeat classification system. Experimental results using the MIT-BIH Arrhythmia database demonstrate a potential for significant performance enhancements over other major techniques

Non-linear model predictive energy management strategies for stand-alone DC microgrids

Due to substantial generation and demand fluctuations in stand-alone green micro-grids, energy management strategies (EMSs) are becoming essential for the power sharing purpose and regulating the microgrids voltage. The classical EMSs track the maximum power points (MPPs) of wind and PV branches independently and rely on batteries, as slack terminals, to absorb any possible excess energy. However, in order to protect batteries from being overcharged by realizing the constant current-constant voltage (IU) charging regime as well as to consider the wind turbine operational constraints, more flexible multivariable and non-linear strategies, equipped with a power curtailment feature, are necessary to control microgrids. This dissertation work comprises developing an EMS that dynamically optimises the operation of stand-alone dc microgrids, consisting of wind, photovoltaic (PV), and battery branches, and coordinately manage all energy flows in order to achieve four control objectives: i) regulating dc bus voltage level of microgrids; ii) proportional power sharing between generators as a local droop control realization; iii) charging batteries as close to IU regime as possible; and iv) tracking MPPs of wind and PV branches during their normal operations. Non-linear model predictive control (NMPC) strategies are inherently multivariable and handle constraints and delays. In this thesis, the above mentioned EMS is developed as a NMPC strategy to extract the optimal control signals, which are duty cycles of three DC-DC converters and pitch angle of a wind turbine. Due to bimodal operation and discontinuous differential states of batteries, microgrids belong to the class of hybrid dynamical systems of non-Filippov type. This dissertation work involves a mathematical approximation of stand-alone dc microgrids as complementarity systems (CSs) of Filippov type. The proposed model is used to develop NMPC strategies and to simulate microgrids using Modelica. As part of the modelling efforts, this dissertation work also proposes a novel algorithm to identify an accurate equivalent electrical circuit of PV modules using both standard test condition (STC) and nominal operating cell temperature (NOCT) information provided by manufacturers. Moreover, two separate stochastic models are presented for hourly wind speed and solar irradiance levels

Implementación de un algoritmo memético para resolver el problema de corte de materiales aplicado a la producción de barras de acero para hormigón

El país ha vivido durante los últimos años un aumento en el PBI que lo ha colocado como unos de los principales países de la región. Este crecimiento se debe al aumento sostenido de la producción en diversos sectores. Por cifras del Ministerio de Economía y Finanzas (MEF), el sector de construcción, a cargo del Ministerio de Vivienda y Construcción representa uno de los principales contribuyentes al PBI interno (MEF), con un aporte del 5% al indicador. Además, se proyecta un crecimiento de 7% sostenido en los próximos años, por encima del promedio nacional. Esto ayudará a impulsar los sectores primarios y secundarios relacionados. Así que se vuelve prioritaria la elaboración de soluciones que aumenten la eficiencia en el consumo de recursos a todo nivel. En particular, este proyecto plantea abordar la producción de las barras de acero para hormigón a nivel industrial. La actividad productiva por la cual el acero fundido es convertido en barras de acero grandes, que serán a su vez cortadas en longitud para conseguir barras más pequeñas, que son usadas en la manufactura y la construcción de edificios. Estas son las conocidas como barras de acero para hormigón. El proceso consta de dos partes principalmente: ● La elaboración de barras largas estándar por el proceso de colada y ● Una segunda fase de corte para obtener los productos finales, barras de acero para hormigón, según el tamaño solicitado por los clientes. Aunque la producción de la barra grande (primaria) se realiza en una línea de ensamblaje a partir de acero fundido, lo que la vuelve virtualmente infinita y modificable en tamaño, las barras pequeñas se elaboran a partir de un tamaño estándar que cada fábrica utiliza para la manufactura. Para elaborar la producción de barras estándar, se toman en cuenta las negociaciones entre los ejecutivos de ventas y los clientes potenciales, obteniéndose requerimientos de producción. Dichos requerimientos son luego incluidos en la programación del periodo tomando en cuenta la disponibilidad de material (acero fundido). Debido a esto, aunque la primera etapa de corte es limpia por la naturaleza de la fabricación, en la segunda se pueden producir desperdicios y pérdidas, pues las barras grandes no siempre se utilizan al cien por ciento en la creación de barras de acero para hormigón. El problema entonces es de corte de materiales, el cual consiste en conseguir un número de piezas de diferentes largos que deben ser cortadas de una fuente, de tal forma que se cumpla con la demanda de largos y se produzcan optimizando una función objetivo. Por lo mencionado este trabajo de fin de carrera, plantea implementar un algoritmo memético para resolver el problema de corte de materiales aplicado a la producción de barras de acero para hormigón. Objetivo General Implementar un algoritmo memético para resolver el problema de corte de materiales aplicado a la producción de barras de acero para hormigón. Objetivos Específicos O1. Definir la función objetivo a evaluar para los algoritmos genético y memético O2. Diseñar un algoritmo memético como alternativa de solución para el problema de corte de materiales unidimensional de barras de acero para hormigón O3. Adaptar un algoritmo genético obtenido de la revisión de la literatura como alternativa de solución para el problema de corte de materiales de barras de acero para hormigón O4. Implementar los algoritmos propuestos en un módulo de ejecución de algoritmos O5. Realizar experimentación mediante pruebas numéricas para comparar el desempeño entre ambas alternativas de solución

A Parallel Genetic Algorithm for the Set Partitioning Problem

This paper describes a parallel genetic algorithm developed for the solution of the set partitioning problem- a difficult combinatorial optimization problem used by many airlines as a mathematical model for flight crew scheduling. The genetic algorithm is based on an island model where multiple independent subpopulations each run a steady-state genetic algorithm on their own subpopulation and occasionally fit strings migrate between the subpopulations. Tests on forty real-world set partitioning problems were carried out on up to 128 nodes of an IBM SP1 parallel computer. We found that performance, as measured by the quality of the solution found and the iteration on which it was found, improved as additional subpopulations were added to the computation. With larger numbers of subpopulations the genetic algorithm was regularly able to find the optimal solution to problems having up to a few thousand integer variables. In two cases, high- quality integer feasible solutions were found for problems with 36, 699 and 43,749 integer variables, respectively. A notable limitation we found was the difficulty solving problems with many constraints