Search results for: time optimization

Authors: María L. Jalón, Feargal Brennan

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A non-stationary stochastic optimization methodology is applied to an OWC (oscillating water column) to find the design that maximizes the wave energy extraction. Different temporal cycles are considered to represent the long-term variability of the wave climate at the site in the optimization problem. The results of the non-stationary stochastic optimization problem are compared against those obtained by a stationary stochastic optimization problem. The comparative analysis reveals that the proposed non-stationary optimization provides designs with a better fit to reality. However, the stationarity assumption can be adequate when looking at averaged system response.

Keywords: non-stationary stochastic optimization, oscillating water, temporal variability, wave energy

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Authors: Liudmyla Koliechkina, Olena Dvirna

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The statement of the multi-objective optimization problem on combinatorial configurations is formulated, and the approach to its solution is proposed. The problem is of interest as a combinatorial optimization one with many criteria, which is a model of many applied tasks. The approach to solving the multi-objective optimization problem on combinatorial configurations consists of two stages; the first is the reduction of the multi-objective problem to the single criterion based on existing multi-objective optimization methods, the second stage solves the directly replaced single criterion combinatorial optimization problem by the horizontal combinatorial method. This approach provides the optimal solution to the multi-objective optimization problem on combinatorial configurations, taking into account additional restrictions for a finite number of steps.

Keywords: discrete set, linear combinatorial optimization, multi-objective optimization, Pareto solutions, partial permutation set, structural graph

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Authors: Saeed Kamarian, Mahmoud Shakeri

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Sandwich structures are used in a variety of engineering applications including aircraft, construction and transportation where strong, stiff and light structures are required. In this paper, frequency maximization of Functionally Graded Sandwich (FGS) beams resting on Pasternak foundations is investigated. A generalized power-law distribution with four parameters is considered for material distribution through the thicknesses of face layers. Since the search space is large, the optimization processes becomes so complicated and too much time consuming. Thus a novel meta–heuristic called Imperialist Competitive Algorithm (ICA) which is a socio-politically motivated global search strategy is implemented to improve the speed of optimization process. Results show the success of applying ICA for engineering problems especially for design optimization of FGM sandwich beams.

Keywords: sandwich beam, functionally graded materials, optimization, imperialist competitive algorithm

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Authors: Alireza Lavaei, Alireza Lohrasbi, Mohammadali M. Shahlaei

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To reduce the overall time of structural optimization for earthquake loads two strategies are adopted. In the first strategy, a neural system consisting self-organizing map and radial basis function neural networks, is utilized to predict the time history responses. In this case, the input space is classified by employing a self-organizing map neural network. Then a distinct RBF neural network is trained in each class. In the second strategy, an improved genetic algorithm is employed to find the optimum design. A 72-bar space truss is designed for optimal weight using exact and approximate analysis for the El Centro (S-E 1940) earthquake loading. The numerical results demonstrate the computational advantages and effectiveness of the proposed method.

Keywords: optimization, genetic algorithm, neural networks, self-organizing map

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Authors: Joseph Bostick

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A method of decreasing the heating load of HVAC systems in a single-dwelling model of a multifamily building, by controlling movable insulation through the optimization of flux, time, surface incident solar radiation, and temperature thresholds. Simulations are completed using a co-simulation between EnergyPlus and MATLAB as an optimization tool to find optimal control thresholds. Optimization of the control thresholds leads to a significant decrease in total heating energy expenditure.

Keywords: energy plus, MATLAB, simulation, energy efficiency

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Authors: R. M. Rizk-Allah

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This paper presents co-evolutionary fruit fly optimization algorithm based on firefly algorithm (CFOA-FA) for solving unconstrained optimization problems. The proposed algorithm integrates the merits of fruit fly optimization algorithm (FOA), firefly algorithm (FA) and elite strategy to refine the performance of classical FOA. Moreover, co-evolutionary mechanism is performed by applying FA procedures to ensure the diversity of the swarm. Finally, the proposed algorithm CFOA- FA is tested on several benchmark problems from the usual literature and the numerical results have demonstrated the superiority of the proposed algorithm for finding the global optimal solution.

Keywords: firefly algorithm, fruit fly optimization algorithm, unconstrained optimization problems

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Authors: Thomas Weber, Nina Strobel, Thomas Kohne, Eberhard Abele

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In context of the energy transition in Germany, the importance of so-called virtual power plants in the energy supply continues to increase. The progressive dismantling of the large power plants and the ongoing construction of many new decentralized plants result in great potential for optimization through synergies between the individual plants. These potentials can be exploited by mathematical optimization algorithms to calculate the optimal application planning of decentralized power and heat generators and storage systems. This also includes linear or linear mixed integer optimization. In this paper, procedures for reducing the number of decision variables to be calculated are explained and validated. On the one hand, this includes combining n similar installation types into one aggregated unit. This aggregated unit is described by the same constraints and target function terms as a single plant. This reduces the number of decision variables per time step and the complexity of the problem to be solved by a factor of n. The exact operating mode of the individual plants can then be calculated in a second optimization in such a way that the output of the individual plants corresponds to the calculated output of the aggregated unit. Another way to reduce the number of decision variables in an optimization problem is to reduce the number of time steps to be calculated. This is useful if a high temporal resolution is not necessary for all time steps. For example, the volatility or the forecast quality of environmental parameters may justify a high or low temporal resolution of the optimization. Both approaches are examined for the resulting calculation time as well as for optimality. Several optimization models for virtual power plants (combined heat and power plants, heat storage, power storage, gas turbine) with different numbers of plants are used as a reference for the investigation of both processes with regard to calculation duration and optimality.

Keywords: CHP, Energy 4.0, energy storage, MILP, optimization, virtual power plant

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Authors: P. Parthiban, Sonu Rajak, R. Dhanalakshmi

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This paper presents an Ant Colony Optimization (ACO) approach, combined with a Speed Optimization Algorithm (SOA) to solve the Vehicle Routing Problem (VRP) with environmental considerations, which is well known as Pollution-Routing Problem (PRP). It consists of routing a number of vehicles to serve a set of customers, and determining fuel consumption, driver wages and their speed on each route segment, while respecting the capacity constraints and time windows. Since VRP is NP-hard problem, so PRP also a NP-hard problem, which requires metaheuristics to solve this type of problems. The proposed solution method consists of two stages. Stage one is to solve a Vehicle Routing Problem with Time Window (VRPTW) using ACO and in the second stage, a SOA is run on the resulting VRPTW solution. Given a vehicle route, the SOA consists of finding the optimal speed on each arc of the route to minimize an objective function comprising fuel consumption costs and driver wages. The proposed algorithm tested on benchmark problem, the preliminary results show that the proposed algorithm can provide good solutions within reasonable computational time.

Keywords: ant colony optimization, CO2 emissions, speed optimization, vehicle routing

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Authors: Arya Prakash Padhi, Anupam Chakrabarti, Rajib Chowdhury

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Topology or layout optimization often gives better performing economic structures and is very helpful in the conceptual design phase. But traditionally it is being done in finite element-based optimization schemes which, although gives a good result, is very time-consuming especially in 3D structures. Among other alternatives machine learning, especially deep learning-based methods, have a very good potential in resolving this computational issue. Here convolutional neural network (3D-CNN) based variational auto encoder (VAE) is trained using a dataset generated from commercially available topology optimization code ABAQUS Tosca using solid isotropic material with penalization (SIMP) method for compliance minimization. The encoded data in latent space is then fed to a 3D generative adversarial network (3D-GAN) to generate the outcome in 64x64x64 size. Here the network consists of 3D volumetric CNN with rectified linear unit (ReLU) activation in between and sigmoid activation in the end. The proposed network is seen to provide almost optimal results with significantly reduced computational time, as there is no iteration involved.

Keywords: 3D generative adversarial network, deep learning, structural topology optimization, variational auto encoder

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Authors: Fatemeh Sadat Miri, Morteza Ehsani, Seyed Farshid Hosseini

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The present research is concerned with the optimization of extrusion parameters of ABS sheets by the Taguchi experimental design method. In this design method, three parameters of % recycling ABS, processing temperature and degassing time on mechanical properties, hardness, HDT, and color matching of ABS sheets were investigated. The variations of this research are the dosage of recycling ABS, processing temperature, and degassing time. According to experimental test data, the highest level of tensile strength and HDT belongs to the sample with 5% recycling ABS, processing temperature of 230°C, and degassing time of 3 hours. Additionally, the minimum level of MFI and color matching belongs to this sample, too. The present results are in good agreement with the Taguchi method. Based on the outcomes of the Taguchi design method, degassing time has the most effect on the mechanical properties of ABS sheets.

Keywords: ABS, process optimization, Taguchi, mechanical properties

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Authors: Soudabeh Shemehsavar

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In this paper, we consider the situation under a life test, in which the failure time of the test units are not related deterministically to an observable stochastic time varying covariate. In such a case, the joint distribution of failure time and a marker value would be useful for modeling the step stress life test. The problem of accelerating such an experiment is considered as the main aim of this paper. We present a step stress accelerated model based on a bivariate Wiener process with one component as the latent (unobservable) degradation process, which determines the failure times and the other as a marker process, the degradation values of which are recorded at times of failure. Parametric inference based on the proposed model is discussed and the optimization procedure for obtaining the optimal time for changing the stress level is presented. The optimization criterion is to minimize the approximate variance of the maximum likelihood estimator of a percentile of the products’ lifetime distribution.

Keywords: bivariate normal, Fisher information matrix, inverse Gaussian distribution, Wiener process

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Authors: Pham Van Nha, Le Cam Binh

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Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm. PSO was inspired by the natural behavior of birds and fish in migration and foraging for food. PSO is considered as a multidisciplinary optimization model that can be applied in various optimization problems. PSO’s ideas are simple and easy to understand but PSO is only applied in simple model problems. We think that in order to expand the applicability of PSO in complex problems, PSO should be described more explicitly in the form of a mathematical model. In this paper, we represent PSO in a mathematical model and apply in the multivariate data classification. First, PSOs general mathematical model (MPSO) is analyzed as a universal optimization model. Then, Model of Optimal Centroids (MOC) is proposed for the multivariate data classification. Experiments were conducted on some benchmark data sets to prove the effectiveness of MOC compared with several proposed schemes.

Keywords: analysis of optimization, artificial intelligence based optimization, optimization for learning and data analysis, global optimization

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Authors: Kalpana Dahiya

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This paper discusses a two-level hierarchical time minimization transportation problem, which is an important class of transportation problems arising in industries. This problem has been studied by various researchers, and a number of polynomial time iterative algorithms are available to find its solution. All the existing algorithms, though efficient, have some shortcomings. The current study proposes an alternate solution algorithm for the problem that is more efficient in terms of computational time than the existing algorithms. The results justifying the underlying theory of the proposed algorithm are given. Further, a detailed comparison of the computational behaviour of all the algorithms for randomly generated instances of this problem of different sizes validates the efficiency of the proposed algorithm.

Keywords: global optimization, hierarchical optimization, transportation problem, concave minimization

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Authors: Sait Ali Uymaz, Gülay Tezel

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This paper presents the comparison results on the performance of the Cuckoo Search (CS) algorithm for constrained optimization problems. For constraint handling, CS algorithm uses penalty method. CS algorithm is tested on thirteen well-known test problems and the results obtained are compared to Particle Swarm Optimization (PSO) algorithm. Mean, best, median and worst values were employed for the analyses of performance.

Keywords: cuckoo search, particle swarm optimization, constrained optimization problems, penalty method

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Authors: Emad Askar, Eldesoky Elsoaly, Mohamed Kamel, Hisham Kamel

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The objective of this article is to improve the passive vibration damping of solar array (SA) used in space structures, by the effective application of numerical optimization. A case study of a SA is used for demonstration. A finite element (FE) model was created and verified by experimental testing. Optimization was then conducted by implementing the FE model with the genetic algorithm, to find the optimal placement of aluminum circular patches, to suppress the first two bending mode shapes. The results were verified using experimental testing. Finally, a parametric study was conducted using the FE model where patch locations, material type, and shape were varied one at a time, and the results were compared with the optimal ones. The results clearly show that through the proper application of FE modeling and numerical optimization, passive vibration damping of space structures has been successfully achieved.

Keywords: damping optimization, genetic algorithm optimization, passive vibration damping, solar array vibration damping

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Authors: Arbnor Pajaziti, Hasan Cana

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In this paper, the structural genetic algorithm is used to optimize the neural network to control the joint movements of robotic arm. The robotic arm has also been modeled in 3D and simulated in real-time in MATLAB. It is found that Neural Networks provide a simple and effective way to control the robot tasks. Computer simulation examples are given to illustrate the significance of this method. By combining Genetic Algorithm optimization method and Neural Networks for the given robotic arm with 5 D.O.F. the obtained the results shown that the base joint movements overshooting time without controller was about 0.5 seconds, while with Neural Network controller (optimized with Genetic Algorithm) was about 0.2 seconds, and the population size of 150 gave best results.

Keywords: robotic arm, neural network, genetic algorithm, optimization

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Authors: Rahul Paul, Kedar Nath Das

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The field of machine learning (ML) is experiencing rapid development, resulting in a multitude of theoretical advancements and extensive practical implementations across various disciplines. The objective of ML is to facilitate the ability of machines to perform cognitive tasks by leveraging knowledge gained from prior experiences and effectively addressing complex problems, even in situations that deviate from previously encountered instances. Reinforcement Learning (RL) has emerged as a prominent subfield within ML and has gained considerable attention in recent times from researchers. This surge in interest can be attributed to the practical applications of RL, the increasing availability of data, and the rapid advancements in computing power. At the same time, optimization algorithms play a pivotal role in the field of ML and have attracted considerable interest from researchers. A multitude of proposals have been put forth to address optimization problems or improve optimization techniques within the domain of ML. The necessity of a thorough examination and implementation of optimization algorithms within the context of ML is of utmost importance in order to provide guidance for the advancement of research in both optimization and ML. This article provides a comprehensive overview of the application of metaheuristic evolutionary optimization algorithms in conjunction with RL to address a diverse range of scientific challenges. Furthermore, this article delves into the various challenges and unresolved issues pertaining to the optimization of RL models.

Keywords: machine learning, reinforcement learning, loss function, evolutionary optimization techniques

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Authors: Badr M. Alshammari, T. Guesmi

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In this paper, the concept of a non-dominated sorting multi-objective particle swarm optimization with local search (NSPSO-LS) is presented for the optimal design of multimachine power system stabilizers (PSSs). The controller design is formulated as an optimization problem in order to shift the system electromechanical modes in a pre-specified region in the s-plan. A composite set of objective functions comprising the damping factor and the damping ratio of the undamped and lightly damped electromechanical modes is considered. The performance of the proposed optimization algorithm is verified for the 3-machine 9-bus system. Simulation results based on eigenvalue analysis and nonlinear time-domain simulation show the potential and superiority of the NSPSO-LS algorithm in tuning PSSs over a wide range of loading conditions and large disturbance compared to the classic PSO technique and genetic algorithms.

Keywords: multi-objective optimization, particle swarm optimization, power system stabilizer, low frequency oscillations

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Authors: Takahiro Hino, Michiharu Maeda

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Particle swarm optimization (PSO) is an optimization approach that achieves the social model of bird flocking and fish schooling. PSO works in continuous space and can solve continuous optimization problem with high quality. Set-based particle swarm optimization (SPSO) functions in discrete space by using a set. SPSO can solve combinatorial optimization problem with high quality and is successful to apply to the large-scale problem. In this paper, we present an algorithm of SPSO with status memory to decide the position based on the previous position for solving traveling salesman problem (TSP). In order to show the effectiveness of our approach. We examine SPSOSM for TSP compared to the existing algorithms.

Keywords: combinatorial optimization problems, particle swarm optimization, set-based particle swarm optimization, traveling salesman problem

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Authors: Michal Kopcek, Tomas Skulavik, Michal Kebisek, Gabriela Krizanova

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The operation of nuclear power plants involves continuous monitoring of the environment in their area. This monitoring is performed using a complex data acquisition system, which collects status information about the system itself and values of many important physical variables e.g. temperature, humidity, dose rate etc. This paper describes a proposal and optimization of communication that takes place in teledosimetric system between the central control server responsible for the data processing and storing and the decentralized measuring stations, which are measuring the physical variables. Analyzes of ongoing communication were performed and consequently the optimization of the system architecture and communication was done.

Keywords: communication protocol, transmission optimization, data acquisition, system architecture

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Authors: Seyed Abbas Tabatabaei, Marjan Naderan Tahan, Arman Kadkhodai

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An efficient optimization approach, called feasible gate (FG), is developed to enhance the computation efficiency and solution quality of the previously developed highway alignment optimization (HAO) model. This approach seeks to realistically represent various user preferences and environmentally sensitive areas and consider them along with geometric design constraints in the optimization process. This is done by avoiding the generation of infeasible solutions that violate various constraints and thus focusing the search on the feasible solutions. The proposed method is simple, but improves significantly the model’s computation time and solution quality. On the other, highway alignment optimization through Feasible Gates, eventuates only economic model by considering minimum design constrains includes minimum reduce of circular curves, minimum length of vertical curves and road maximum gradient. This modelling can reduce passenger comfort and road safety. In most of highway optimization models, by adding penalty function for each constraint, final result handles to satisfy minimum constraint. In this paper, we want to propose a safety-function solution by introducing gift function.

Keywords: safety, highway geometry, optimization, alignment

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Authors: Zair Firdaous, Fourka Mohamed, Elfelsoufi Zoubir

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The arrival of e-commerce has changed the supply chain management on the operational level as well as on the organization and strategic and even tactical decisions of the companies. The optimization of resources is an issue that is needed on the tactical and operational strategic plan. This work considers the allocation of resources in the case of pure players that have launched online sales. The aim is to improve the level of customer satisfaction and maintaining the benefits of e-retailer and of its cooperators and reducing costs and risks. We first modeled the B2C chain with all operations that integrates and possible scenarios since online retailers offer a wide selection of personalized service. The personalized services that online shopping companies offer to the clients can be embodied in many aspects, such as the customizations of payment, the distribution methods, and after-sales service choices. Every aspect of customized service has several modes. At that time, we analyzed the optimization problems of supply chain resource in customized online shopping service mode. Then, we realized an optimization model and algorithm for the development based on the analysis of the of the B2C supply chain resources. It is a multi-objective optimization that considers the collaboration of resources in operations, time and costs but also the risks and the quality of services as well as dynamic and uncertain characters related to the request.

Keywords: supply chain resource, e-commerce, pure-players, optimization

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Authors: H. Hentati, R. Abdelmoula, Li Jia, A. Maalej

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In this work, we present numerical simulations of the quasi-static crack propagation based on the variation approach. We perform numerical simulations of a piece of brittle material without initial crack. An alternate minimization algorithm is used. Based on these numerical results, we determine the influence of numerical parameters on the location of crack. We show the importance of trying to optimize the time of numerical computation and we present the first attempt to develop a simple numerical method to optimize this time.

Keywords: fracture mechanics, optimization, variation approach, mechanic

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Authors: Imen Boudali, Marwa Ragmoun

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The Vehicle Routing Problem with Hard Time Windows (VRPHTW) is a basic distribution management problem that models many real-world problems. The objective of the problem is to deliver a set of customers with known demands on minimum-cost vehicle routes while satisfying vehicle capacity and hard time windows for customers. In this paper, we propose to deal with our optimization problem by using a new hybrid stochastic algorithm based on two metaheuristics: Chemical Reaction Optimization (CRO) and Greedy Randomized Adaptive Search Procedure (GRASP). The first method is inspired by the natural process of chemical reactions enabling the transformation of unstable substances with excessive energy to stable ones. During this process, the molecules interact with each other through a series of elementary reactions to reach minimum energy for their existence. This property is embedded in CRO to solve the VRPHTW. In order to enhance the population diversity throughout the search process, we integrated the GRASP in our method. Simulation results on the base of Solomon’s benchmark instances show the very satisfactory performances of the proposed approach.

Keywords: Benchmark Problems, Combinatorial Optimization, Vehicle Routing Problem with Hard Time Windows, Meta-heuristics, Hybridization, GRASP, CRO

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Authors: G. Rajyalakhmi, C. Karthik, Gerson Desouza, Rimmie Duraisamy

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In this present work, metal matrix composites with combination of aluminium with (Sic/Al2O3) were fabricated using stir casting technique. The objective of the present work is to optimize the process parameters of Wire Electric Discharge Machining (WEDM) composites. Pulse ON Time, Pulse OFF Time, wire feed and sensitivity are considered as input process parameters with responses Material Removal Rate (MRR), Surface Roughness (SR) for optimization of WEDM process. Taguchi L18 Orthogonal Array (OA) is used for experimentation. Grey Relational Analysis (GRA) is coupled with Taguchi technique for multiple process parameters optimization. ANOVA (Analysis of Variance) is used for finding the impact of process parameters individually. Finally confirmation experiments were carried out to validate the predicted results.

Keywords: parametric optimization, particulate reinforced metal matrix composites, Taguchi-grey relational analysis, WEDM

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Authors: Deepa Das, Susmita Das

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Cognitive Radio (CR) is an emerging technology to combat the spectrum scarcity issues. This is achieved by consistently sensing the spectrum, and detecting the under-utilized frequency bands without causing undue interference to the primary user (PU). In soft decision fusion (SDF) based cooperative spectrum sensing, various evolutionary algorithms have been discussed, which optimize the weight coefficient vector for maximizing the detection performance. In this paper, we propose the hybrid invasive weed optimization and particle swarm optimization (IWO/PSO) algorithm as a fast and global optimization method, which improves the detection probability with a lesser sensing time. Then, the efficiency of this algorithm is compared with the standard invasive weed optimization (IWO), particle swarm optimization (PSO), genetic algorithm (GA) and other conventional SDF based methods on the basis of convergence and detection probability.

Keywords: cognitive radio, spectrum sensing, soft decision fusion, GA, PSO, IWO, hybrid IWO/PSO

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Authors: A. Ramalho, L. Romeiro, R. Ventura, A. Suleman

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A real-time path planning framework for Unmanned Air Vehicles, and in particular multi-rotors is proposed. The framework is designed to provide feasible trajectories from the current UAV position to a goal state, taking into account constraints such as obstacle avoidance, problem kinematics, and vehicle limitations such as maximum speed and maximum acceleration. The framework computes feasible paths online, allowing to avoid new, unknown, dynamic obstacles without fully re-computing the trajectory. These features are achieved using an iterative process in which the robot computes and optimizes the trajectory while performing the mission objectives. A first trajectory is computed using a modified Rapidly-Exploring Random Tree (RRT) algorithm, that provides trajectories that respect a maximum curvature constraint. The trajectory optimization is accomplished using the Interior Point Optimizer (IPOPT) as a solver. The framework has proven to be able to compute a trajectory and optimize to a locally optimal with computational efficiency making it feasible for real-time operations.

Keywords: interior point optimization, multi-rotors, online path planning, rapidly exploring random trees, trajectory optimization

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Authors: O. Mohamed Amine, A. Khireddine

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Telecoms operators are always looking to meet their share of the other customers, they try to gain optimum utilization of the deployed equipment and network optimization has become essential. This project consists of optimizing UMTS network, and the study area is an urban area situated in the center of Algiers. It was initially questions to become familiar with the different communication systems (3G) and the optimization technique, its main components, and its fundamental characteristics radios were introduced.

Keywords: UMTS, UTRAN, WCDMA, optimization

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Authors: A. K. M. Kamrul Islam, Abdelhamid Bouchachia, Suang Cang, Hongnian Yu

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Forecasting model has a great impact in terms of prediction and continues to do so into the future. Although many forecasting models have been studied in recent years, most researchers focus on different forecasting methods based on fuzzy time series to solve forecasting problems. The forecasted models accuracy fully depends on the two terms that are the length of the interval in the universe of discourse and the content of the forecast rules. Moreover, a hybrid forecasting method can be an effective and efficient way to improve forecasts rather than an individual forecasting model. There are different hybrids forecasting models which combined fuzzy time series with evolutionary algorithms, but the performances are not quite satisfactory. In this paper, we proposed a hybrid forecasting model which deals with the first order as well as high order fuzzy time series and particle swarm optimization to improve the forecasted accuracy. The proposed method used the historical enrollments of the University of Alabama as dataset in the forecasting process. Firstly, we considered an automatic clustering algorithm to calculate the appropriate interval for the historical enrollments. Then particle swarm optimization and fuzzy time series are combined that shows better forecasting accuracy than other existing forecasting models.

Keywords: fuzzy time series (fts), particle swarm optimization, clustering algorithm, hybrid forecasting model

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Authors: Khodamorad Nabaki, Jianhu Shen, Xiaodong Huang

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This paper develops a method for considering the critical fatigue stress as a constraint in the Bi-directional Evolutionary Structural Optimization (BESO) method. Our aim is to reach an optimal design in which high cycle fatigue failure does not occur for a specific life time. The critical fatigue stress is calculated based on modified Goodman criteria and used as a stress constraint in our topology optimization problem. Since fatigue generally does not occur for compressive stresses, we use the p-norm approach of the stress measurement that considers the highest tensile principal stress in each point as stress measure to calculate the sensitivity numbers. The BESO method has been extended to minimize volume an object subjected to the critical fatigue stress constraint. The optimization results are compared with the results from the compliance minimization problem which shows clearly the merits of our newly developed approach.

Keywords: topology optimization, BESO method, p-norm, fatigue constraint

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