Search results for: Nonlinear programming problem

Authors: Vasile Marinescu, Ionut Clementin Constantin, Alexandru Epureanu, Virgil Teodor

Abstract:

The Programmable Logic Controller (PLC) plays a vital role in automation and process control. Grafcet is used for representing the control logic, and traditional programming languages are used for describing the pure algorithms. Grafcet is used for dividing the process to be automated in elementary sequences that can be easily implemented. Each sequence represent a step that has associated actions programmed using textual or graphical languages after case. The programming task is simplified by using a set of subroutines that are used in several steps. The paper presents an example of implementation for a punching machine for sheets and plates. The use the graphical languages the programming of a complex sequential process is a necessary solution. The state of Grafcet can be used for debugging and malfunction determination. The use of the method combined with a set of knowledge acquisition for process application reduces the downtime of the machine and improve the productivity.

Keywords: Grafcet, Petrinet, PLC, punching.

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Authors: Badr M. Alshammari, T. Guesmi

Abstract:

This study presents a modified version of the artificial bee colony (ABC) algorithm by including a local search technique for solving the non-convex economic power dispatch problem. The local search step is incorporated at the end of each iteration. Total system losses, valve-point loading effects and prohibited operating zones have been incorporated in the problem formulation. Thus, the problem becomes highly nonlinear and with discontinuous objective function. The proposed technique is validated using an IEEE benchmark system with ten thermal units. Simulation results demonstrate that the proposed optimization algorithm has better convergence characteristics in comparison with the original ABC algorithm.

Keywords: Economic power dispatch, artificial bee colony, valve-point loading effects, prohibited operating zones.

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Authors: Hassan Zarei, Ali Vahidian Kamyad, Sohrab Effati

Abstract:

In this paper, a mathematical model of human immunodeficiency virus (HIV) is utilized and an optimization problem is proposed, with the final goal of implementing an optimal 900-day structured treatment interruption (STI) protocol. Two type of commonly used drugs in highly active antiretroviral therapy (HAART), reverse transcriptase inhibitors (RTI) and protease inhibitors (PI), are considered. In order to solving the proposed optimization problem an adaptive memetic algorithm with population management (AMAPM) is proposed. The AMAPM uses a distance measure to control the diversity of population in genotype space and thus preventing the stagnation and premature convergence. Moreover, the AMAPM uses diversity parameter in phenotype space to dynamically set the population size and the number of crossovers during the search process. Three crossover operators diversify the population, simultaneously. The progresses of crossover operators are utilized to set the number of each crossover per generation. In order to escaping the local optima and introducing the new search directions toward the global optima, two local searchers assist the evolutionary process. In contrast to traditional memetic algorithms, the activation of these local searchers is not random and depends on both the diversity parameters in genotype space and phenotype space. The capability of AMAPM in finding optimal solutions compared with three popular metaheurestics is introduced.

Keywords: HIV therapy design, memetic algorithms, adaptivealgorithms, nonlinear integer programming.

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Authors: Kwa-Sur Tam

Abstract:

This paper reviews various approaches that have been used for the modeling and simulation of large-scale engineering systems and determines their appropriateness in the development of a RICS modeling and simulation tool. Bond graphs, linear graphs, block diagrams, differential and difference equations, modeling languages, cellular automata and agents are reviewed. This tool should be based on linear graph representation and supports symbolic programming, functional programming, the development of noncausal models and the incorporation of decentralized approaches.

Keywords: Interdisciplinary, dynamic, functional programming, object-oriented.

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Authors: Cai-Wan Chang-Jian

Abstract:

This study presents a systematic analysis of the dynamic behaviors of a gear-bearing system with porous squeeze film damper (PSFD) under nonlinear suspension, nonlinear oil-film force and nonlinear gear meshing force effect. It can be found that the system exhibits very rich forms of sub-harmonic and even the chaotic vibrations. The bifurcation diagrams also reveal that greater values of permeability may not only improve non-periodic motions effectively, but also suppress dynamic amplitudes of the system. Therefore, porous effect plays an important role to improve dynamic stability of gear-bearing systems or other mechanical systems. The results presented in this study provide some useful insights into the design and development of a gear-bearing system for rotating machinery that operates in highly rotational speed and highly nonlinear regimes.

Keywords: Gear, PSFD, bifurcation, chaos.

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Authors: Mai S. Mabrouk, Nahed H. Solouma, Abou-Bakr M. Youssef, Yasser M. Kadah

Abstract:

Many digital signal processing, techniques have been used to automatically distinguish protein coding regions (exons) from non-coding regions (introns) in DNA sequences. In this work, we have characterized these sequences according to their nonlinear dynamical features such as moment invariants, correlation dimension, and largest Lyapunov exponent estimates. We have applied our model to a number of real sequences encoded into a time series using EIIP sequence indicators. In order to discriminate between coding and non coding DNA regions, the phase space trajectory was first reconstructed for coding and non-coding regions. Nonlinear dynamical features are extracted from those regions and used to investigate a difference between them. Our results indicate that the nonlinear dynamical characteristics have yielded significant differences between coding (CR) and non-coding regions (NCR) in DNA sequences. Finally, the classifier is tested on real genes where coding and non-coding regions are well known.

Keywords: Gene prediction, nonlinear dynamics, correlation dimension, Lyapunov exponent.

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Authors: R.K. Behera, S.Behera

Abstract:

In a wind power generator using doubly fed induction generator (DFIG), the three-phase pulse width modulation (PWM) voltage source converter (VSC) is used as grid side converter (GSC) and rotor side converter (RSC). The standard linear control laws proposed for GSC provides not only instablity against comparatively large-signal disturbances, but also the problem of stability due to uncertainty of load and variations in parameters. In this paper, a nonlinear controller is designed for grid side converter (GSC) of a DFIG for wind power application. The nonlinear controller is designed based on the input-output feedback linearization control method. The resulting closed-loop system ensures a sufficient stability region, make robust to variations in circuit parameters and also exhibits good transient response. Computer simulations and experimental results are presented to confirm the effectiveness of the proposed control strategy.

Keywords: Doubly fed Induction Generator, grid side converter, machine side converter, dc link, feedback linearization.

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Authors: Meng Hu, Lili Wang

Abstract:

In this paper, He-s amplitude frequency formulation is used to obtain a periodic solution for a nonlinear oscillator with fractional potential. By calculation and computer simulations, compared with the exact solution shows that the result obtained is of high accuracy.

Keywords: He's amplitude frequency formulation, Periodic solution, Nonlinear oscillator, Fractional potential.

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Authors: T. Mathumathi, S. Ganesh, R. Gunabalan

Abstract:

This work presents an approach for AC load flow based centralized model for congestion management in the forward markets. In this model, transaction maximizes its profit under the limits of transmission line capacities allocated by Independent System Operator (ISO). The voltage and reactive power impact of the system are also incorporated in this model. Genetic algorithm is used to solve centralized congestion management problem for multilateral transactions. Results obtained for centralized model using genetic algorithm is compared with Sequential Quadratic Programming (SQP) technique. The statistical performances of various algorithms such as best, worst, mean and standard deviations of social welfare are given. Simulation results clearly demonstrate the better performance of genetic algorithm over SQP.

Keywords: Congestion management, Genetic algorithm, Sequential quadratic programming.

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Authors: Hoda Aleali, Nastaran Mansour, Maryam Mirzaie

Abstract:

In this paper, we study the optical nonlinearities of Silver sulfide (Ag2S) nanostructures dispersed in the Dimethyl sulfoxide (DMSO) under exposure to 532 nm, 15 nanosecond (ns) pulsed laser irradiation. Ultraviolet–visible absorption spectrometry (UV-Vis), X-ray diffraction (XRD), and transmission electron microscopy (TEM) are used to characterize the obtained nanocrystal samples. The band gap energy of colloid is determined by analyzing the UV–Vis absorption spectra of the Ag2S NPs using the band theory of semiconductors. Z-scan technique is used to characterize the optical nonlinear properties of the Ag2S nanoparticles (NPs). Large enhancement of two photon absorption effect is observed with increase in concentration of the Ag2S nanoparticles using open Zscan measurements in the ns laser regime. The values of the nonlinear absorption coefficients are determined based on the local nonlinear responses including two photon absorption. The observed aperture dependence of the Ag2S NP limiting performance indicates that the nonlinear scattering plays an important role in the limiting action of the sample. The concentration dependence of the optical liming is also investigated. Our results demonstrate that the optical limiting threshold decreases with increasing the silver sulfide NPs in DMSO.

Keywords: Nanoscale materials, Silver sulfide nanoparticles, Nonlinear absorption, Nonlinear scattering, Optical limiting.

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Authors: Nuanwan Soonthornphisaj, Boonserm Kijsirikul

Abstract:

This paper presents a semi-supervised learning algorithm called Iterative-Cross Training (ICT) to solve the Web pages classification problems. We apply Inductive logic programming (ILP) as a strong learner in ICT. The objective of this research is to evaluate the potential of the strong learner in order to boost the performance of the weak learner of ICT. We compare the result with the supervised Naive Bayes, which is the well-known algorithm for the text classification problem. The performance of our learning algorithm is also compare with other semi-supervised learning algorithms which are Co-Training and EM. The experimental results show that ICT algorithm outperforms those algorithms and the performance of the weak learner can be enhanced by ILP system.

Keywords: Inductive Logic Programming, Semi-supervisedLearning, Web Page Categorization

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Authors: S. Sadi-Nezhad, K. Khalili Damghani, N. Pilevari

Abstract:

In this article, a mathematical programming model for choosing an optimum portfolio of investments is developed. The investments are considered as investment projects. The uncertainties of the real world are associated through fuzzy concepts for coefficients of the proposed model (i. e. initial investment costs, profits, resource requirement, and total available budget). Model has been coded by using LINGO 11.0 solver. The results of a full analysis of optimistic and pessimistic derivative models are promising for selecting an optimum portfolio of projects in presence of uncertainty.

Keywords: Fuzzy Programming, Fuzzy Knapsack, FuzzyCapital Budgeting, Fuzzy Project Selection

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Authors: Wen-Chi Liu

Abstract:

This study applies a simple and powerful nonlinear unit root test to test the validity of long-run purchasing power parity (PPP)  in a sample of 10 East-Asian countries (i.e., China, Hong Kong,  Indonesia, Japan, Korea, Malaysia, Philippines, Singapore, Taiwan  and Thailand) over the period of March 1985 to September 2008. The empirical results indicate that PPP holds true for half of these 10  East-Asian countries under study, and the adjustment toward PPP is found to be nonlinear and in an asymmetric way. 

 

Keywords: Purchasing Power Parity, East-Asian Countries, Nonlinear Unit Root Test, Asymmetry.

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Authors: C. Chitra, P. Subbaraj

Abstract:

The shortest path routing problem is a multiobjective nonlinear optimization problem with constraints. This problem has been addressed by considering Quality of service parameters, delay and cost objectives separately or as a weighted sum of both objectives. Multiobjective evolutionary algorithms can find multiple pareto-optimal solutions in one single run and this ability makes them attractive for solving problems with multiple and conflicting objectives. This paper uses an elitist multiobjective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA), for solving the dynamic shortest path routing problem in computer networks. A priority-based encoding scheme is proposed for population initialization. Elitism ensures that the best solution does not deteriorate in the next generations. Results for a sample test network have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed pareto-optimal solutions of dynamic routing problem in one single run. The results obtained by NSGA are compared with single objective weighting factor method for which Genetic Algorithm (GA) was applied.

Keywords: Multiobjective optimization, Non-dominated SortingGenetic Algorithm, Routing, Weighted sum.

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Authors: N. H. Adenan, M. S. M. Noorani

Abstract:

River flow prediction is an essential to ensure proper management of water resources can be optimally distribute water to consumers. This study presents an analysis and prediction by using nonlinear prediction method involving monthly river flow data in Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The phase space reconstruction involves the reconstruction of one-dimensional (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. Revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) have been employed to compare prediction performance for nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show the prediction results using nonlinear prediction method is better than ARIMA and SVM. Therefore, the result of this study could be used to develop an efficient water management system to optimize the allocation water resources.

Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.

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Authors: Mohd A. Mezher, Maysam F. Abbod

Abstract:

Genetic Folding (GF) a new class of EA named as is introduced for the first time. It is based on chromosomes composed of floating genes structurally organized in a parent form and separated by dots. Although, the genotype/phenotype system of GF generates a kernel expression, which is the objective function of superior classifier. In this work the question of the satisfying mapping-s rules in evolving populations is addressed by analyzing populations undergoing either Mercer-s or none Mercer-s rule. The results presented here show that populations undergoing Mercer-s rules improve practically models selection of Support Vector Machine (SVM). The experiment is trained multi-classification problem and tested on nonlinear Ionosphere dataset. The target of this paper is to answer the question of evolving Mercer-s rule in SVM addressed using either genetic folding satisfied kernel-s rules or not applied to complicated domains and problems.

Keywords: Genetic Folding, GF, Evolutionary Algorithms, Support Vector Machine, Genetic Algorithm, Genetic Programming, Multi-Classification, Mercer's Rules

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Authors: Shrawan Kumar, D. K. Lobiyal

Abstract:

In this paper, we propose improved versions of DVHop algorithm as QDV-Hop algorithm and UDV-Hop algorithm for better localization without the need for additional range measurement hardware. The proposed algorithm focuses on third step of DV-Hop, first error terms from estimated distances between unknown node and anchor nodes is separated and then minimized. In the QDV-Hop algorithm, quadratic programming is used to minimize the error to obtain better localization. However, quadratic programming requires a special optimization tool box that increases computational complexity. On the other hand, UDV-Hop algorithm achieves localization accuracy similar to that of QDV-Hop by solving unconstrained optimization problem that results in solving a system of linear equations without much increase in computational complexity. Simulation results show that the performance of our proposed schemes (QDV-Hop and UDV-Hop) is superior to DV-Hop and DV-Hop based algorithms in all considered scenarios.

Keywords: Wireless sensor networks, Error term, DV-Hop algorithm, Localization.

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Authors: Amin Almasi

Abstract:

Reliability assessment and risk analysis of rotating machine rotors in various overload and malfunction situations present challenge to engineers and operators. In this paper a new analytical method for evaluation of rotor under large deformation is addressed. Model is presented in general form to include also composite rotors. Presented simulation procedure is based on variational work method and has capability to account for geometric nonlinearity, large displacement, nonlinear support effect and rotor contacting other machine components. New shape functions are presented which capable to predict accurate nonlinear profile of rotor. The closed form solutions for various operating and malfunction situations are expressed. Analytical simulation results are discussed

Keywords: Large Deformation, Nonlinear, Rotor.

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Authors: F. Laaouad, M. Bouguerra, A. Hafaifa, A. Iratni

Abstract:

In this work, we treat the problems related to chemical and petrochemical plants of a certain complex process taking the centrifugal compressor as an example, a system being very complex by its physical structure as well as its behaviour (surge phenomenon). We propose to study the application possibilities of the recent control approaches to the compressor behaviour, and consequently evaluate their contribution in the practical and theoretical fields. Facing the studied industrial process complexity, we choose to make recourse to fuzzy logic for analysis and treatment of its control problem owing to the fact that these techniques constitute the only framework in which the types of imperfect knowledge can jointly be treated (uncertainties, inaccuracies, etc..) offering suitable tools to characterise them. In the particular case of the centrifugal compressor, these imperfections are interpreted by modelling errors, the neglected dynamics, no modelisable dynamics and the parametric variations. The purpose of this paper is to produce a total robust nonlinear controller design method to stabilize the compression process at its optimum steady state by manipulating the gas rate flow. In order to cope with both the parameter uncertainty and the structured non linearity of the plant, the proposed method consists of a linear steady state regulation that ensures robust optimal control and of a nonlinear compensation that achieves the exact input/output linearization.

Keywords: Compressor, Fuzzy logic, Surge control, Bilinearcontroller, Stability analysis, Nonlinear plant.

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Authors: Mohammad Moeini, Mehrdad Ghyabi, Kiarash Mohtasham Dolatshahi

Abstract:

This paper investigates seismic soil-pile interaction using the Beam on Nonlinear Winkler Foundation (BNWF) approach. Three soil types are considered to cover all the possible responses, as well as nonlinear site response analysis using finite element method in OpenSees platform. Excitations at each elevation that are output of the site response analysis are used as the input excitation to the soil pile system implementing multi-support excitation method. Spectral intensities of acceleration show that the extent of the response in sand is more severe than that of clay, in addition, increasing the PGA of ground strong motion will affect the sandy soil more, in comparison with clayey medium, which is an indicator of the sensitivity of soil-pile systems in sandy soil.

Keywords: Beam on nonlinear Winkler foundation method, multi-support excitation, nonlinear site response analysis, seismic soil-pile interaction.

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Authors: C. Chitra, P. Subbaraj

Abstract:

The shortest path routing problem is a multiobjective nonlinear optimization problem with constraints. This problem has been addressed by considering Quality of service parameters, delay and cost objectives separately or as a weighted sum of both objectives. Multiobjective evolutionary algorithms can find multiple pareto-optimal solutions in one single run and this ability makes them attractive for solving problems with multiple and conflicting objectives. This paper uses an elitist multiobjective evolutionary algorithm based on the Non-dominated Sorting Genetic Algorithm (NSGA), for solving the dynamic shortest path routing problem in computer networks. A priority-based encoding scheme is proposed for population initialization. Elitism ensures that the best solution does not deteriorate in the next generations. Results for a sample test network have been presented to demonstrate the capabilities of the proposed approach to generate well-distributed pareto-optimal solutions of dynamic routing problem in one single run. The results obtained by NSGA are compared with single objective weighting factor method for which Genetic Algorithm (GA) was applied.

Keywords: Multiobjective optimization, Non-dominated Sorting Genetic Algorithm, Routing, Weighted sum.

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Authors: Sun Lim, Bong-Seok Kim

Abstract:

This paper presents an adaptive nonlinear position controller with velocity constraint, capable of combining the input-output linearization technique and Lyapunov stability theory. Based on the Lyapunov stability theory, the adaptation law of the proposed controller is derived along with the verification of the overall system-s stability. Computer simulation results demonstrate that the proposed controller is robust and it can ensure transient stability of BLDCM, under the occurrence of a large sudden fault.

Keywords: BLDC Motor Control, Backstepping Control, Adaptive nonlinear control

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Authors: M. Seguini, D. Nedjar

Abstract:

An accuracy nonlinear analysis of a deep beam resting on elastic perfectly plastic soil is carried out in this study. In fact, a nonlinear finite element modeling for large deflection and moderate rotation of Euler-Bernoulli beam resting on linear and nonlinear random soil is investigated. The geometric nonlinear analysis of the beam is based on the theory of von Kàrmàn, where the Newton-Raphson incremental iteration method is implemented in a Matlab code to solve the nonlinear equation of the soil-beam interaction system. However, two analyses (deterministic and probabilistic) are proposed to verify the accuracy and the efficiency of the proposed model where the theory of the local average based on the Monte Carlo approach is used to analyze the effect of the spatial variability of the soil properties on the nonlinear beam response. The effect of six main parameters are investigated: the external load, the length of a beam, the coefficient of subgrade reaction of the soil, the Young’s modulus of the beam, the coefficient of variation and the correlation length of the soil’s coefficient of subgrade reaction. A comparison between the beam resting on linear and nonlinear soil models is presented for different beam’s length and external load. Numerical results have been obtained for the combination of the geometric nonlinearity of beam and material nonlinearity of random soil. This comparison highlighted the need of including the material nonlinearity and spatial variability of the soil in the geometric nonlinear analysis, when the beam undergoes large deflections.

Keywords: Finite element method, geometric nonlinearity, material nonlinearity, soil-structure interaction, spatial variability.

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Authors: Abbas Al-Refaie

Abstract:

This study optimized the performance of plastic extrusion process of drip irrigation pipes using fuzzy goal programming. Two main responses were of main interest; roll thickness and hardness. Four main process factors were studied. The L₁₈ array was then used for experimental design. The individual-moving range control charts were used to assess the stability of the process, while the process capability index was used to assess process performance. Confirmation experiments were conducted at the obtained combination of optimal factor setting by fuzzy goal programming. The results revealed that process capability was improved significantly from -1.129 to 0.8148 for roll thickness and from 0.0965 to 0.714 and hardness. Such improvement results in considerable savings in production and quality costs.

Keywords: Fuzzy goal programming, extrusion process, process capability, irrigation plastic pipes.

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Authors: Hamid Abdi, Abolfazl Salami, Abolfazl Ahmadi

Abstract:

Programmable logic controllers are the main controllers in the today's industries; they are used for several applications in industrial control systems and there are lots of examples exist from the PLC applications in industries especially in big companies and plants such as refineries, power plants, petrochemical companies, steel companies, and food and production companies. In the PLCs there are some functions in the function library in software that can be used in PLC programs as basic program elements. The aim of this project are introducing and implementing a new function block of a neural network to the function library of PLC. This block can be applied for some control applications or nonlinear functions calculations after it has been trained for these applications. The implemented neural network is a Perceptron neural network with three layers, three input nodes and one output node. The block can be used in manual or automatic mode. In this paper the structure of the implemented function block, the parameters and the training method of the network are presented by considering the especial method of PLC programming and its complexities. Finally the application of the new block is compared with a classic simulated block and the results are presented.

Keywords: Programmable Logic Controller, PLC Programming, Neural Networks, Perception Network, Intelligent Control.

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Authors: Monica Hoedltke Pietruchinski, Andrey Ricardo Pimentel

Abstract:

The teaching of computer programming for beginners has been generally considered as a difficult and challenging task. Several methodologies and research tools have been developed, however, the difficulty of teaching still remains. Our work integrates the state of the art in teaching programming with game software and further provides metrics for the evaluation of student performance in a collaborative activity of playing games. This paper aims to present a multi-agent system architecture to be incorporated to the educational collaborative game software for teaching programming that monitors, evaluates and encourages collaboration by the participants. A literature review has been made on the concepts of Collaborative Learning, Multi-agents systems, collaborative games and techniques to teach programming using these concepts simultaneously.

Keywords: Architecture of multi-agent systems, collaborative evaluation, collaboration assessment, gamifying educational software.

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Authors: Mohammadsadegh Zanganehfar

Abstract:

Through the emergence of modern architecture, an aggressive desire for new design theories appeared through the works of architects and critics. The discourse of complexity and volumetric composition happened to be an important and controversial issue in the discipline of architecture which was discussed through a general point of view in Robert Venturi and Denise Scott Brown's book “Complexity and contradiction in architecture” in 1966, this paper attempts to identify chaos theory as a scientific model of complexity and its relation to architecture design theory by conducting a qualitative analysis and multidisciplinary critical approach through architecture and basic sciences resources. Accordingly, we identify chaotic architecture as the correlation between chaos theory and the discipline of architecture, and as an independent nonlinear design theory with specific characteristics and properties.

Keywords: Architecture complexity, chaos theory, fractals, nonlinear dynamic systems, nonlinear ontology.

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Authors: Anupma Bansal, Rajeev Budhiraja, Manoj Pandey

Abstract:

In this paper, we have investigated the nonlinear time-fractional hyperbolic partial differential equation (PDE) for its symmetries and invariance properties. With the application of this method, we have tried to reduce it to time-fractional ordinary differential equation (ODE) which has been further studied for exact solutions.

Keywords: Nonlinear time-fractional hyperbolic PDE, Lie Classical method, exact solutions.

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Authors: Shuangquan Liu, Jinwen Wang, Dada Wang

Abstract:

A case study of the generation scheduling optimization of the multi-hydroplants on the Yuan River Basin in China is reported in this paper. Concerning the uncertainty of the inflows, the long/mid-term generation scheduling (LMTGS) problem is solved by a stochastic model in which the inflows are considered as stochastic variables. For the short-term generation scheduling (STGS) problem, a constraint violation priority is defined in case not all constraints are satisfied. Provided the stage-wise separable condition and low dimensions, the hydroplant-based operational region schedules (HBORS) problem is solved by dynamic programming (DP). The coordination of LMTGS and STGS is presented as well. The feasibility and the effectiveness of the models and solution methods are verified by the numerical results.

Keywords: generation scheduling, multi-hydroplants, optimization.

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Authors: Md. Sayeed Salam

Abstract:

This paper presents an efficient emission constrained economic dispatch algorithm that deals with nonlinear cost function and constraints. It is then incorporated into the dynamic programming based hydrothermal coordination program. The program has been tested on a practical utility system having 32 thermal and 12 hydro generating units. Test results show that a slight increase in production cost causes a substantial reduction in emission.

Keywords: Emission constraint, Hydrothermal coordination, and Economic dispatch algorithm.

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