Search results for: routing algorithm

Authors: Bircan Demiral

Abstract:

Cognitive radio (CR) is the promising technology that addresses the spectrum scarcity problem for future wireless communications. Orthogonal Frequency Division Multiplexing (OFDM) technology provides more power band ratios for cognitive radio networks (CRNs). While CR is a solution to the spectrum scarcity, it also brings up the capacity problem. In this paper, a novel power allocation algorithm that aims at maximizing the sum capacity in the OFDM based cognitive radio networks is proposed. Proposed allocation algorithm is based on the previously developed water-filling algorithm. To reduce the computational complexity calculating in water filling algorithm, proposed algorithm allocates the total power according to each subcarrier. The power allocated to the subcarriers increases sum capacity. To see this increase, Matlab program was used, and the proposed power allocation was compared with average power allocation, water filling and general power allocation algorithms. The water filling algorithm performed worse than the proposed algorithm while it performed better than the other two algorithms. The proposed algorithm is better than other algorithms in terms of capacity increase. In addition the effect of the change in the number of subcarriers on capacity was discussed. Simulation results show that the increase in the number of subcarrier increases the capacity.

Keywords: cognitive radio network, OFDM, power allocation, water filling

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Authors: Majid Khalili

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This paper deals with a bi-objective hybrid no-wait flowshop scheduling problem minimizing the makespan and total weighted tardiness, in which we consider transportation times between stages. Obtaining an optimal solution for this type of complex, large-sized problem in reasonable computational time by using traditional approaches and optimization tools is extremely difficult. This paper presents a new multi-objective variable neighborhood algorithm (MOVNS). A set of experimental instances are carried out to evaluate the algorithm by advanced multi-objective performance measures. The algorithm is carefully evaluated for its performance against available algorithm by means of multi-objective performance measures and statistical tools. The related results show that a variant of our proposed MOVNS provides sound performance comparing with other algorithms.

Keywords: no-wait hybrid flowshop scheduling; multi-objective variable neighborhood algorithm; makespan; total weighted tardiness

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Authors: Duckyong Kim, Jong Kang Park, Jong Tae Kim

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DOA (Direction of Arrival) estimation is an important method in array signal processing and has a wide range of applications such as direction finding, beam forming, and so on. In this paper, we briefly introduce the MUSIC (Multiple Signal Classification) Algorithm, one of DOA estimation methods for analyzing several targets. Then we apply the MUSIC algorithm to the two-dimensional antenna array to analyze DOA estimation in 3D space through MATLAB simulation. We also analyze the design factors that can affect the accuracy of DOA estimation through simulation, and proceed with further consideration on how to apply the system.

Keywords: DOA estimation, MUSIC algorithm, spatial spectrum, array signal processing

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Authors: Alaa Allakany, Koji Okamura

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Multicast technology is an efficient and scalable technology for data distribution in order to optimize network resources. However, in the IP network, the responsibility for management of multicast groups is distributed among network routers, which causes some limitations such as delays in processing group events, high bandwidth consumption and redundant tree calculation. Software Defined Networking (SDN) represented by OpenFlow presented as a solution for many problems, in SDN the control plane and data plane are separated by shifting the control and management to a remote centralized controller, and the routers are used as a forwarder only. In this paper we will proposed fast switching mechanism for solving the problem of link failure in multicast tree based on Tabu Search heuristic algorithm and modifying the functions of OpenFlow switch to fasts switch to the pack up sub tree rather than sending to the controller. In this work we will implement multicasting OpenFlow controller, this centralized controller is a core part in our multicasting approach, which is responsible for 1- constructing the multicast tree, 2- handling the multicast group events and multicast state maintenance. And finally modifying OpenFlow switch functions for fasts switch to pack up paths. Forwarders, forward the multicast packet based on multicast routing entries which were generated by the centralized controller. Tabu search will be used as heuristic algorithm for construction near optimum multicast tree and maintain multicast tree to still near optimum in case of join or leave any members from multicast group (group events).

Keywords: multicast tree, software define networks, tabu search, OpenFlow

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Authors: Archit Yajnik

Abstract:

Part of Speech Tagging has always been a challenging task in the era of Natural Language Processing. This article presents POS tagging for Nepali text using Hidden Markov Model and Viterbi algorithm. From the Nepali text, annotated corpus training and testing data set are randomly separated. Both methods are employed on the data sets. Viterbi algorithm is found to be computationally faster and accurate as compared to HMM. The accuracy of 95.43% is achieved using Viterbi algorithm. Error analysis where the mismatches took place is elaborately discussed.

Keywords: hidden markov model, natural language processing, POS tagging, viterbi algorithm

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Authors: Hussain K. Chaiel

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The development in the field of the digital signal processing (DSP) and the microelectronics technology reduces the complexity of the iterative algorithms that need large number of arithmetic operations. Virtex-Field Programmable Gate Arrays (FPGAs) are programmable silicon foundations which offer an important solution for addressing the needs of high performance DSP designer. In this work, Virtex-7 FPGA technology is used to implement an iterative algorithm to estimate the earthquake location. Simulation results show that an implementation based on block RAMB36E1 and DSP48E1 slices of Virtex-7 type reduces the number of cycles of the clock frequency. This enables the algorithm to be used for earthquake prediction.

Keywords: DSP, earthquake, FPGA, iterative algorithm

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Authors: A. Andreasyan, C. Connors

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The Elliptic Curve Digital Signature algorithm-based X509v3 certificates are becoming more popular due to their short public and private key sizes. Moreover, these certificates can be stored in Internet of Things (IoT) devices, with limited resources, using less memory and transmitted in network security protocols, such as Internet Key Exchange (IKE), Transport Layer Security (TLS) and Secure Shell (SSH) with less bandwidth. The proposed method gives another advantage, in that it increases the performance of the above-mentioned protocols in terms of key exchange by saving one scalar multiplication operation.

Keywords: cryptography, elliptic curve digital signature algorithm, key exchange, network security protocol

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Authors: Meng Wu

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Motion planning is a common task required to be fulfilled by robots. A strategy combining Ant Colony Optimization (ACO) and gravity gradient inversion algorithm is proposed for motion planning of mobile robots. In this paper, in order to realize optimal motion planning strategy, the cost function in ACO is designed based on gravity gradient inversion algorithm. The obstacles around mobile robot can cause gravity gradient anomalies; the gradiometer is installed on the mobile robot to detect the gravity gradient anomalies. After obtaining the anomalies, gravity gradient inversion algorithm is employed to calculate relative distance and orientation between mobile robot and obstacles. The relative distance and orientation deduced from gravity gradient inversion algorithm is employed as cost function in ACO algorithm to realize motion planning. The proposed strategy is validated by the simulation and experiment results.

Keywords: motion planning, gravity gradient inversion algorithm, ant colony optimization

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Authors: Sofiane Bououden, Ilyes Boulkaibet

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In terms of security of the information signal, the meta-heuristic Penguins Search Optimization Algorithm (PeSOA) is applied to synchronize chaotic encryption communications in the case of sensitive dependence on initial conditions in chaotic generator oscillator. The objective of this paper is the use of the PeSOA algorithm to exploring search space with random and iterative processes for synchronization of symmetric keys in both transmission and reception. Simulation results show the effectiveness of the PeSOA algorithm in generating symmetric keys of the encryption process and synchronizing.

Keywords: meta-heuristic, PeSOA, chaotic systems, encryption, synchronization optimization

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Authors: Watchara Songserm, Teeradej Wuttipornpun

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This paper presents a genetic algorithm based permutation and non-permutation scheduling heuristics (GAPNP) to solve a multi-stage finite capacity material requirement planning (FCMRP) problem in automotive assembly flow shop with unrelated parallel machines. In the algorithm, the sequences of orders are iteratively improved by the GA characteristics, whereas the required operations are scheduled based on the presented permutation and non-permutation heuristics. Finally, a linear programming is applied to minimize the total cost. The presented GAPNP algorithm is evaluated by using real datasets from automotive companies. The required parameters for GAPNP are intently tuned to obtain a common parameter setting for all case studies. The results show that GAPNP significantly outperforms the benchmark algorithm about 30% on average.

Keywords: capacitated MRP, genetic algorithm, linear programming, automotive industries, flow shop, application in industry

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Authors: Shreya Pare, Parvin Akhter

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Remotely sensing image classification becomes a very challenging task owing to the high dimensionality of hyperspectral images. The pixel-wise classification methods fail to take the spatial structure information of an image. Therefore, to improve the performance of classification, spatial information can be integrated into the classification process. In this paper, the multilevel thresholding algorithm based on a modified fuzzy entropy function is used to perform the segmentation of hyperspectral images. The fuzzy parameters of the MFE function have been optimized by using a new meta-heuristic algorithm based on the Tree-Search algorithm. The segmented image is classified by a large distribution machine (LDM) classifier. Experimental results are shown on a hyperspectral image dataset. The experimental outputs indicate that the proposed technique (MFE-TSA-LDM) achieves much higher classification accuracy for hyperspectral images when compared to state-of-art classification techniques. The proposed algorithm provides accurate segmentation and classification maps, thus becoming more suitable for image classification with large spatial structures.

Keywords: classification, hyperspectral images, large distribution margin, modified fuzzy entropy function, multilevel thresholding, tree search algorithm, hyperspectral image classification using tree search algorithm

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Authors: Ioannis P. Panapakidis, Marios N. Moschakis

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With the continuous increment of smart meter installations across the globe, the need for processing of the load data is evident. Clustering-based load profiling is built upon the utilization of unsupervised machine learning tools for the purpose of formulating the typical load curves or load profiles. The most commonly used algorithm in the load profiling literature is the K-means. While the algorithm has been successfully tested in a variety of applications, its drawback is the strong dependence in the initialization phase. This paper proposes a novel modified form of the K-means that addresses the aforementioned problem. Simulation results indicate the superiority of the proposed algorithm compared to the K-means.

Keywords: clustering, load profiling, load modeling, machine learning, energy efficiency and quality

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Authors: Nevena Jakovčević Stor, Ivan Slapničar

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Any polynomial can be expressed as a characteristic polynomial of a complex symmetric arrowhead matrix. This expression is not unique. If the polynomial is real with only real distinct roots, the matrix can be chosen as real. By using accurate forward stable algorithm for computing eigen values of real symmetric arrowhead matrices we derive a forward stable algorithm for computation of roots of such polynomials in O(n^2 ) operations. The algorithm computes each root to almost full accuracy. In some cases, the algorithm invokes extended precision routines, but only in the non-iterative part. Our examples include numerically difficult problems, like the well-known Wilkinson’s polynomials. Our algorithm compares favorably to other method for polynomial root-finding, like MPSolve or Newton’s method.

Keywords: roots of polynomials, eigenvalue decomposition, arrowhead matrix, high relative accuracy

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Authors: Aydin Teymourifar, Gurkan Ozturk

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In this paper, a new hybrid particle swarm optimization algorithm is proposed for the multi-objective flexible job shop scheduling problem that is very important and hard combinatorial problem. The Pareto approach is used for solving the multi-objective problem. Several new local search heuristics are integrated into an algorithm based on the critical block concept to enhance the performance of the algorithm. The algorithm is compared with the recently published multi-objective algorithms based on benchmarks selected from the literature. Several metrics are used for quantifying performance and comparison of the achieved solutions. The algorithms are also compared based on the Weighting summation of objectives approach. The proposed algorithm can find the Pareto solutions more efficiently than the compared algorithms in less computational time.

Keywords: swarm-based optimization, local search, Pareto optimality, flexible job shop scheduling, multi-objective optimization

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Authors: Y. Wang

Abstract:

The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem

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Authors: Zhe Li, Aihua Cai

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Aiming at the problem of high-density clutter and interference affecting radar detection target track initiation in ECM and complex radar mission, the traditional radar target track initiation method has been difficult to adapt. To this end, we propose a multi-algorithm fusion learning track initiation algorithm, which transforms the track initiation problem into a true-false track discrimination problem, and designs an algorithm based on 1DCNN(One-Dimensional CNN)combined with Bi-LSTM (Bi-Directional Long Short-Term Memory )for fusion classification. The experimental dataset consists of real trajectories obtained from a certain type of three-coordinate radar measurements, and the experiments are compared with traditional trajectory initiation methods such as rule-based method, logical-based method and Hough-transform-based method. The simulation results show that the overall performance of the multi-algorithm fusion learning track initiation algorithm is significantly better than that of the traditional method, and the real track initiation rate can be effectively improved under high clutter density with the average initiation time similar to the logical method.

Keywords: track initiation, multi-algorithm fusion, 1DCNN, Bi-LSTM

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Authors: Manjula Sutagundar, B. G. Sheeparamatti, D. S. Jangamshetti

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Micro Electro Mechanical Systems (MEMS) resonators have shown the potential of replacing quartz crystal technology for sensing and high frequency signal processing applications because of inherent advantages like small size, high quality factor, low cost, compatibility with integrated circuit chips. This paper presents the optimization and modelling and simulation of the optimized micro cantilever resonator. The objective of the work is to optimize the dimensions of a micro cantilever resonator for a specified range of resonant frequency and specific quality factor. Optimization is carried out using genetic algorithm. The genetic algorithm is implemented using MATLAB. The micro cantilever resonator is modelled in CoventorWare using the optimized dimensions obtained from genetic algorithm. The modeled cantilever is analysed for resonance frequency.

Keywords: MEMS resonator, genetic algorithm, modelling and simulation, optimization

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Authors: Sarah Abdourraziq, Rachid Elbachtiri

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The use of solar energy as a source for pumping water is one of the promising areas in the photovoltaic (PV) application. The energy of photovoltaic pumping systems (PVPS) can be widely improved by employing an MPPT algorithm. This will lead consequently to maximize the electrical motor speed of the system. This paper presents a modified incremental conductance (IncCond) MPPT algorithm with direct control method applied to a standalone PV pumping system. The influence of the algorithm parameters on system behavior is investigated and compared with the traditional (INC) method. The studied system consists of a PV panel, a DC-DC boost converter, and a PMDC motor-pump. The simulation of the system by MATLAB-SIMULINK is carried out. Simulation results found are satisfactory.

Keywords: photovoltaic pumping system (PVPS), incremental conductance (INC), MPPT algorithm, boost converter

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Authors: Khaled Salah

Abstract:

Model order reduction has been one of the most challenging topics in the past years. In this paper, a hybrid solution of genetic algorithm (GA) and simulated annealing algorithm (SA) are used to approximate high-order transfer functions (TFs) to lower-order TFs. In this approach, hybrid algorithm is applied to model order reduction putting in consideration improving accuracy and preserving the properties of the original model which are two important issues for improving the performance of simulation and computation and maintaining the behavior of the original complex models being reduced. Compared to conventional mathematical methods that have been used to obtain a reduced order model of high order complex models, our proposed method provides better results in terms of reducing run-time. Thus, the proposed technique could be used in electronic design automation (EDA) tools.

Keywords: genetic algorithm, simulated annealing, model reduction, transfer function

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Authors: Tesnim Charrad, Kaouther Nouira, Ahmed Ferchichi

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In order to reduce the number of deaths due to heart problems, we propose the use of Hierarchical Temporal Memory Algorithm (HTM) which is a real time anomaly detection algorithm. HTM is a cortical learning algorithm based on neocortex used for anomaly detection. In other words, it is based on a conceptual theory of how the human brain can work. It is powerful in predicting unusual patterns, anomaly detection and classification. In this paper, HTM have been implemented and tested on ECG datasets in order to detect cardiac anomalies. Experiments showed good performance in terms of specificity, sensitivity and execution time.

Keywords: cardiac anomalies, ECG, HTM, real time anomaly detection

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Authors: Aishwarya Talapuru, Sri Silpa Padmanabhuni, B. Jyoshna

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Cryptography helps in preventing threats to information security by providing various algorithms. This study introduces a new symmetric key encryption algorithm for information security which is linked with the "raagas" which means Indian traditional scale and pattern of music notes. This algorithm takes the plain text as input and starts its encryption process. The algorithm then randomly selects a raaga from the list of raagas that is assumed to be present with both sender and the receiver. The plain text is associated with the thus selected raaga and an intermediate cipher-text is formed as the algorithm converts the plain text characters into other characters, depending upon the rules of the algorithm. This intermediate code or cipher text is arranged in various patterns in three different rounds of encryption performed. The total number of rounds in the algorithm is equal to the multiples of 3. To be more specific, the outcome or output of the sequence of first three rounds is again passed as the input to this sequence of rounds recursively, till the total number of rounds of encryption is performed. The raaga selected by the algorithm and the number of rounds performed will be specified at an arbitrary location in the key, in addition to important information regarding the rounds of encryption, embedded in the key which is known by the sender and interpreted only by the receiver, thereby making the algorithm hack proof. The key can be constructed of any number of bits without any restriction to the size. A software application is also developed to demonstrate this process of encryption, which dynamically takes the plain text as input and readily generates the cipher text as output. Therefore, this algorithm stands as one of the strongest tools for information security.

Keywords: cipher text, cryptography, plaintext, raaga

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Authors: Shaimaa M. Mohamed, Haitham S. Hamza, Imane A. Saroit

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Many wireless sensor network applications require K-coverage of the monitored area. In this paper, we propose a scalable harmony search based algorithm in terms of execution time, K-Coverage Enhancement Algorithm (KCEA), it attempts to enhance initial coverage, and achieve the required K-coverage degree for a specific application efficiently. Simulation results show that the proposed algorithm achieves coverage improvement of 5.34% compared to K-Coverage Rate Deployment (K-CRD), which achieves 1.31% when deploying one additional sensor. Moreover, the proposed algorithm is more time efficient.

Keywords: Wireless Sensor Networks (WSN), harmony search algorithms, K-Coverage, Mobile WSN

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Authors: Mehmet Hakan Karaata

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In this paper, we first coin a new graph theocratic problem with numerous applications. Second, we provide two algorithms for the problem. The first solution is using a brute-force techniques, whereas the second solution is based on an initial identification of the cycles in the given graph. We then provide a correctness proof of the algorithm. The applications of the problem include graph analysis, graph drawing and network structuring.

Keywords: algorithm, cycle, graph algorithm, graph theory, network structuring

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Authors: Wael M. Bazzi, Amir Rastegarnia, Azam Khalili

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In this paper we consider the issue of reliability of measurements in distributed adaptive estimation problem. To this aim, we assume a sensor network with different observation noise variance among the sensors and propose new estimation method based on incremental distributed least mean-square (IDLMS) algorithm. The proposed method contains two phases: I) Estimation of each sensors observation noise variance, and II) Estimation of the desired parameter using the estimated observation variances. To deal with the reliability of measurements, in the second phase of the proposed algorithm, the step-size parameter is adjusted for each sensor according to its observation noise variance. As our simulation results show, the proposed algorithm considerably improves the performance of the IDLMS algorithm in the same condition.

Keywords: adaptive filter, distributed estimation, sensor network, IDLMS algorithm

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Authors: Cheng-Lin Liu, Fei Liu

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For the multi-agent systems with agent's dynamics described by high-order integrator, and usual consensus algorithm composed of the state coordination control parts is proposed. Under communication delay, consensus algorithm in asynchronously-coupled form just can make the agents achieve a stationary consensus, and sufficient consensus condition is obtained based on frequency-domain analysis. To recover the original consensus state of the high-order agents without communication delay, besides, a predictor-based consensus algorithm is constructed via multiplying the delayed neighboring agents' states by a delay-related compensation part, and sufficient consensus condition is also obtained. Simulation illustrates the correctness of the results.

Keywords: high-order dynamic agents, communication delay, consensus, predictor-based algorithm

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Authors: Ludovic Favre, Thibaut M. Schafer, Jean-Luc Robyr, Elena-Lavinia Niederhäuser

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This paper presents an optimization method based on genetic algorithm for the energy management inside buildings developed in the frame of the project Smart Living Lab (SLL) in Fribourg (Switzerland). This algorithm optimizes the interaction between renewable energy production, storage systems and energy consumers. In comparison with standard algorithms, the innovative aspect of this project is the extension of the smart regulation over three simultaneous criteria: the energy self-consumption, the decrease of greenhouse gas emissions and operating costs. The genetic algorithm approach was chosen due to the large quantity of optimization variables and the non-linearity of the optimization function. The optimization process includes also real time data of the building as well as weather forecast and users habits. This information is used by a physical model of the building energy resources to predict the future energy production and needs, to select the best energetic strategy, to combine production or storage of energy in order to guarantee the demand of electrical and thermal energy. The principle of operation of the algorithm as well as typical output example of the algorithm is presented.

Keywords: building's energy, control system, energy management, energy storage, genetic optimization algorithm, greenhouse gases, modelling, renewable energy

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Authors: Mitat Uysal

Abstract:

A new met heuristic optimization algorithm called as Migrating Birds Optimization is used for curve fitting by rational cubic Bezier Curves. This requires solving a complicated multivariate optimization problem. In this study, the solution of this optimization problem is achieved by Migrating Birds Optimization algorithm that is a powerful met heuristic nature-inspired algorithm well appropriate for optimization. The results of this study show that the proposed method performs very well and being able to fit the data points to cubic Bezier Curves with a high degree of accuracy.

Keywords: algorithms, Bezier curves, heuristic optimization, migrating birds optimization

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Authors: E. Tandis, E. Assareh

Abstract:

Designing the optimal shape of MW wind turbine blades is provided in a number of cases through evolutionary algorithms associated with mathematical modeling (Blade Element Momentum Theory). Evolutionary algorithms, among the optimization methods, enjoy many advantages, particularly in stability. However, they usually need a large number of function evaluations. Since there are a large number of local extremes, the optimization method has to find the global extreme accurately. The present paper introduces a new population-based hybrid algorithm called Genetic-Based Bees Algorithm (GBBA). This algorithm is meant to design the optimal shape for MW wind turbine blades. The current method employs crossover and neighborhood searching operators taken from the respective Genetic Algorithm (GA) and Bees Algorithm (BA) to provide a method with good performance in accuracy and speed convergence. Different blade designs, twenty-one to be exact, were considered based on the chord length, twist angle and tip speed ratio using GA results. They were compared with BA and GBBA optimum design results targeting the power coefficient and solidity. The results suggest that the final shape, obtained by the proposed hybrid algorithm, performs better compared to either BA or GA. Furthermore, the accuracy and speed convergence increases when the GBBA is employed

Keywords: Blade Design, Optimization, Genetic Algorithm, Bees Algorithm, Genetic-Based Bees Algorithm, Large Wind Turbine

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Authors: Farzaneh Rajabighamchi, Stan van Hoesel, Christof Defryn

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The generalized traveling salesman problem (GTSP) is an extension of the traveling salesman problem (TSP) where the set of nodes is partitioned into clusters, and the salesman must visit exactly one node per cluster. In this research, we apply the definition of the GTSP to an order picker routing problem with multiple locations per product. As such, each product represents a cluster and its corresponding nodes are the locations at which the product can be retrieved. To pick a certain product item from the warehouse, the picker needs to visit one of these locations during its pick tour. As all products are scattered throughout the warehouse, the product clusters not separated geographically. We propose an exact LP model as well as heuristic and meta-heuristic solution algorithms for the order picking problem with multiple product locations.

Keywords: warehouse optimization, order picking problem, generalised travelling salesman problem, heuristic algorithm

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Authors: Yulong Jia, Xiang Zhang, Ziyuan Wu, Shiji Hu

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The calculation of bilinear pairing is the core of the SM9 algorithm, which relies on the underlying prime domain algorithm and the quadratic extension domain algorithm. Among the field algorithms, modular multiplication operation is the most time-consuming part. Therefore, the underlying modular multiplication algorithm is optimized to maximize the operation speed of bilinear pairings. This paper uses a modular multiplication method based on non-least positive (NLP) combined with Karatsuba and schoolbook multiplication to improve the Montgomery algorithm. At the same time, according to the characteristics of multiplication operation in the quadratic extension domain, a quadratic extension domain FP2-NLP modular multiplication algorithm for bilinear pairings is proposed, which effectively reduces the operation time of modular multiplication in the quadratic extension domain. The sub-expanded domain Fp₂ -NLP modular multiplication algorithm effectively reduces the operation time of modular multiplication under the second-expanded domain. The multiplication unit in the quadratic extension domain is implemented using SMIC55nm process, and two different implementation architectures are designed to cope with different application scenarios. Compared with the existing related literature, The output latency of this design can reach a minimum of 15 cycles. The shortest time for calculating the (AB+CD)r⁻¹ mod form is 37.5ns, and the comprehensive area-time product (AT) is 11400. The final R-ate pairing algorithm hardware accelerator consumes 2670k equivalent logic gates and 1.8ms computing time in 55nm process.

Keywords: sm9, hardware, NLP, Montgomery

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