Search results for: morphology optimization

Authors: Soumitra Satapathi, Anubhav Raghav

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Perovskite solar cell technology has passed through a phase of unprecedented growth in the efficiency scale from 3.8% to above 22% within a half decade. This technology has drawn tremendous research interest. It has been observed that performances of perovskite based solar cells are extremely dependent on the morphology and crystallinity of the perovskite layer. It has also been observed that device lifetime depends on the perovskite morphology; devices with larger perovskite grains degrade slowly than those of the smaller ones. Various methods of perovskite growth have been applied to achieve the most appropriate morphology necessary for high efficient solar cells. The recent progress in morphology optimization by various methods emphasizing on grain sizes, stoichiometry, and ambient compatibility as well as photophysics study in air-processed perovskite solar cells will be discussed.

Keywords: perovskite solar cells, morphology optimization, photophysics study, air-processed solar cells

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Authors: E. R. Jimenez Barron, M. Castillo Morales, D. F. Ramírez Morales

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The study of the morphology (shape change) in wings leads to the optimization of aerodynamic characteristics in an aircraft, so for the development and implementation of a change in the structure and shape of an airfoil, in this case the extrados, helps to increase the aerodynamic performance of an aircraft at different operating velocities, according to the required mission profile. A previous work on morphology is continued where the 'initial' profile is the NACA 4415 and as a new profile 'objective' the FUSION. The objective of this work is the dimensioning of the elements of the mechanism used to achieve the required changes. We consulted the different materials used in the aeronautics industry, as well as new materials in this area that could contribute to the good performance of the mechanism without negatively affecting the aerodynamics. These results allow evaluating the performance of a wing with variable extrados with respect to the defined morphology.

Keywords: numerical analysis, mechanisms, morphing airfoil, morphing wings

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Authors: Fawzi Srairi, Abderrahmane Dib

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Recently, the desire for a self-powered micro and nanodevices has attracted a great interest of using sustainable energy sources. Further, the ultimate goal of nanogenerator is to harvest energy from the ambient environment in which a self-powered device based on these generators is needed. With the development of nanogenerator-based circuits design and optimization, the building of new device simulator is necessary for the study and the synthesis of electromechanical parameters of this type of models. In the present article, both numerical modeling and optimization of piezoelectric nanogenerator based on zinc oxide have been carried out. They aim to improve the electromechanical performances, robustness, and synthesis process for nanogenerator. The proposed model has been developed for a systematic study of the nanowire morphology parameters in stretching mode. In addition, heuristic optimization technique, namely, particle swarm optimization has been implemented for an analytic modeling and an optimization of nanogenerator-based process in stretching mode. Moreover, the obtained results have been tested and compared with conventional model where a good agreement has been obtained for excitation mode. The developed nanogenerator model can be generalized, extended and integrated into simulators devices to study nanogenerator-based circuits.

Keywords: electrical potential, heuristic algorithms, numerical modeling, nanogenerator

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Authors: Mitat Uysal

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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: Mojdeh Mohseni

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In the context of tissue engineering, the effect of microtopography as afforded by scaffold morphology is an important design parameter. Since the morphology of pores can effect on cell behavior, in this study, porous Chitosan (CHIT) - Gelatin (GEL)- Alginate (ALG) scaffolds with microtubule orientation structure were manufactured by unidirectional freeze-drying method and the effect of pore morphology on differentiation of Mesenchymal Stem Cells (MSCs) was investigated. This study showed that, the provided scaffold with natural polymer had good properties for cell behavior and the pores with highest orientation rate have produced appropriate substrate for the differentiation of stem cells.

Keywords: Chitosan, gelatin, Alginate, pore morphology, stem cell differentiation

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Authors: Fabio Salvador Aparecido Santos, Spencer Chainey, Richard Wortley

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Urban morphology can be understood as the study of the physical form of cities through its elements. Crime, at this turn, can be oversimplified as an action that breaks the rules established in a certain society. This study involves these two subjects through the relationship between elements of urban morphology and density of crime occurrences. We consider that there is a research gap about the influence of urban features on crime occurrences using statistic methods and mapping techniques on Geographic Information Systems. The investigation will comprehend three main phases. The first phase involves examining how theoretical principles associated with urban morphology can be viewed in terms of their influence on crime patterns. The second phase involves the development of tools to be used to model elements of urban morphology, and measure the relationship between these urban morphological elements and patterns of crime. The third phase involves determining the extent to which elements of the urban environment can contribute to crime reduction. Understanding the relationship between urban morphology and crime patterns in a Latin American context will help highlight the influence urban planning has on the crime problems that emerge in these settings, and how effectively urban planning can contribute to reducing crime.

Keywords: Agent-based Modelling, Environmental Criminology, Geographic Information System, Urban Morphology

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Authors: Kostas Metaxiotis

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Portfolio optimization is one of the most important topics in finance. This paper proposes a mean–variance–skewness (MVS) portfolio optimization model. Traditionally, the portfolio optimization problem is solved by using the mean–variance (MV) framework. In this study, we formulate the proposed model as a three-objective optimization problem, where the portfolio's expected return and skewness are maximized whereas the portfolio risk is minimized. For solving the proposed three-objective portfolio optimization model we apply an adapted version of the non-dominated sorting genetic algorithm (NSGAII). Finally, we use a real dataset from FTSE-100 for validating the proposed model.

Keywords: evolutionary algorithms, portfolio optimization, skewness, stock selection

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Authors: Serges Mendomo Meye, Li Guowei, Shen Zhenzhong, Gan Lei, Xu Liqun

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Given the limitations of the original whale optimization algorithm (WAO) in local optimum and low convergence accuracy in truss structure optimization problems, based on the fundamental whale algorithm, an improved whale optimization algorithm (SWAO) based on information entropy is proposed. The information entropy itself is an uncertain measure. It is used to control the range of whale searches in path selection. It can overcome the shortcomings of the basic whale optimization algorithm (WAO) and can improve the global convergence speed of the algorithm. Taking truss structure as the optimization research object, the mathematical model of truss structure optimization is established; the cross-sectional area of truss is taken as the design variable; the objective function is the weight of truss structure; and an improved whale optimization algorithm (SWAO) is used for optimization design, which provides a new idea and means for its application in large and complex engineering structure optimization design.

Keywords: information entropy, structural optimization, truss structure, whale algorithm

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Authors: Ramin Javadzadeh

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The particle swarm optimization are Meta heuristic optimization method, which are used for clustering and pattern recognition applications are abundantly. These algorithms in multimodal optimization problems are more efficient than genetic algorithms. A major drawback in these algorithms is their slow convergence to global optimum and their weak stability can be considered in various running of these algorithms. In this paper, improved Particle swarm optimization is introduced for the first time to overcome its problems. The fuzzy cellular automata is used for improving the algorithm efficiently. The credibility of the proposed approach is evaluated by simulations, and it is shown that the proposed approach achieves better results can be achieved compared to the Particle swarm optimization algorithms.

Keywords: cellular automata, cellular learning automata, local search, optimization, particle swarm optimization

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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: 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: 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: Hema Lattupalli

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Introduction: The palate forms a partition between the oral cavity and nasal cavity. The palate is made up of two parts hard palate and soft palate. The Hard palate forms the anterior part of the palate, the soft palate forms a movable muscular fold covered by mucous membrane that is suspended from the posterior border of a hard palate. Aim and Objectives: Soft palate morphological variations have a great paucity in the literature. It’s also believed that the soft palate has no such important anatomical variations. There is a variable presentation of the soft palate morphology in the lateral cephalograms. The aim of this study is to identify the velar morphology. Materials and Methods: 100 normal subjects between the age group of 20 – 35 were taken for the study. Method: Lateral Cephalogram (radiologic study). Results: Different shapes of the soft palate were observed in the lateral cephalograms. The morphology of soft palate was classified into six types 1.Leaf like (50 cases) most common type, 2.Straight line (20 cases), 3.S shaped (4 cases) very rare, 4.Butt like (10 cases), 5. Rat tail (6 cases), 6. Hook shaped (10 cases). Conclusion: This classification helps us to understand the better diversity of the velar morphology in mid-sagittal plane. These findings help us to understand the etiology of OSAS.

Keywords: soft palate, cephalometric radiographs, morphology, cleft palate, obstructive sleep apnoea syndrome

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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: Mohammad Saber Eslamlou

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Morphology of Islamic cities has been extensively studied by researchers of Islamic cities and different theories could be found about it. In this regard, there exist much difference in method of analysis, classification, recognition, confrontation and comparative method of urban morphology. The present paper aims to examine the previous methods, approaches and insights and that how Dr. Giulia Annalinda Neglia dealt with the analysis of morphology of Islamic cities. Neglia is assistant professor in University of Bari, Italy (UNIBA) who has published numerous papers and books on Islamic cities. I introduce her works in the field of morphology of Islamic cities. And then, her thoughts, insights and research methodologies are presented and analyzed in critical perspective. This is a qualitative research on her written works, which have been classified in three major categories. The first category consists mainly of her works on morphology and physical shape of Islamic cities. The results of her works’ review suggest that she has used Moratoria typology in investigating morphology of Islamic cities. Moreover, overall structure of the cities under investigation is often described linear; however, she’s against to define a single framework for the recognition of morphology in Islamic cities. She states that ‘to understand the physical complexity and irregularities in Islamic cities, it is necessary to study the urban fabric by typology method, focusing on transformation processes of the buildings’ form and their surrounding open spaces’ and she believes that fabric of each region in the city follows from the principles of an specific period or urban pattern, in particular, Hellenistic and Roman structures. Furthermore, she believes that it is impossible to understand the morphology of a city without taking into account the obvious and hidden developments associated with it, because form of building and their surrounding open spaces are written history of the city.

Keywords: city, Islamic city, Giulia Annalinda Neglia, morphology

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Authors: B. Afsari, M. Hassanpour, M. Shabani

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This study aimed to investigate the phase morphology of ternary blends comprising PP, PA6, and a blend of EPDM and EPDM-g-MA in a 70/15/15 ratio. Varying ratios of EPDM to EPDM-g-MA were examined. As the proportion of EPDM-g-MA increased, an interlayer phase formed between the dispersed PA6 domains and the PP matrix. This resulted in the development of a core-shell encapsulation morphology within the blends. The concentration of the EPDM-g-MA component is inversely correlated with the average size of PA6 particles. Additionally, blends containing higher proportions of the EPDM-g-MA rubbery phase exhibited an aggregated structure of the modifier particles. Notably, as the concentration of EPDM-g-MA increased from 0% to 15% in the blend, there was a consistent monotonic reduction in the size of PA6 particles.

Keywords: phase morphology, rubbery phase, rubber functionality, ternary blends

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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: D. Li

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Optical thin films are used in a wide variety of optical components and there are many software tools programmed for advancing multilayer thin film design. The available software packages for designing the thin film structure may not provide optimum designs. Normally, almost all current software programs obtain their final designs either from optimizing a starting guess or by technique, which may or may not involve a pseudorandom process, that give different answers every time, depending upon the initial conditions. With the increasing power of personal computers, functional methods in optimization and synthesis of optical multilayer systems have been developed such as DGL Optimization, Simulated Annealing, Genetic Algorithms, Needle Optimization, Inductive Optimization and Flip-Flop Optimization. Among these, DGL Optimization has proved its efficiency in optical thin film designs. The application of the DGL optimization technique to the design of optical coating is presented. A DGL optimization technique is provided, and its main features are discussed. Guidelines on the application of the DGL optimization technique to various types of design problems are given. The innovative global optimization strategies used in a software tool, OnlyFilm, to optimize multilayer thin film designs through different filter designs are outlined. OnlyFilm is a powerful, versatile, and user-friendly thin film software on the market, which combines optimization and synthesis design capabilities with powerful analytical tools for optical thin film designers. It is also the only thin film design software that offers a true global optimization function.

Keywords: optical coatings, optimization, design software, thin film design

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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: Risti Suryantari, Flaviana

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The aim of this research is to design calibration method of Thermochromic Liquid Crystal for temperature distribution measurement based on mathematical morphology of hue image A glass of water is placed on the surface of sample TLC R25C5W at certain temperature. We use scanner for image acquisition. The true images in RGB format is converted to HSV (hue, saturation, value) by taking of hue without saturation and value. Then the hue images is processed based on mathematical morphology using Matlab2013a software to get better images. There are differences on the final images after processing at each temperature variation based on visualization observation and the statistic value. The value of maximum and mean increase with rising temperature. It could be parameter to identify the temperature of the human body surface like hand or foot surface.

Keywords: thermochromic liquid crystal, TLC, mathematical morphology, hue image

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Authors: Wu Qinglong, Zhou Qicai, Xiong Xiaolei, Zhang Richeng

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In order to achieve the layout and size optimization of the web members of tower crane boom, a truss topology and cross section size optimization method based on continuum is proposed considering three typical working conditions. Firstly, the optimization model is established by replacing web members with web plates. And the web plates are divided into several sub-domains so that periodic soft kill option (SKO) method can be carried out for topology optimization of the slender boom. After getting the optimized topology of web plates, the optimized layout of web members is formed through extracting the principal stress distribution. Finally, using the web member radius as design variable, the boom compliance as objective and the material volume of the boom as constraint, the cross section size optimization mathematical model is established. The size optimization criterion is deduced from the mathematical model by Lagrange multiplier method and Kuhn-Tucker condition. By comparing the original boom with the optimal boom, it is identified that this optimization method can effectively lighten the boom and improve its performance.

Keywords: tower crane boom, topology optimization, size optimization, periodic, SKO, optimization criterion

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Authors: Mohammad Khodaei, Mahmood Meratien, Alireza Valanezhad, Serdar Pazarlioglu, Serdar Salman, Ikuya Watanabe

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Pore size and morphology plays a crucial role on mechanical properties of porous scaffolds. In this research, titanium scaffold was prepared using space holder technique. Sodium chloride and ammonium bicarbonate were utilized as spacer agent separately. The effect of the hardness of spacer on the cell morphology was investigated using scanning electron microscopy (SEM) and optical stereo microscopy. Image analyzing software was used to interpret the microscopic images quantitatively. It was shown that sodium chloride, due to its higher hardness, maintain its morphology during cold compaction, and cause better replication in porous scaffolds.

Keywords: Spacer, Titanium Scaffold, Pore Morphology, Space Holder Technique

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Authors: Mengxiao Li, Johnson Zhang

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Currently, topology optimization technique is widely used to define the layout design of structures that are presented as truss-like topologies. However, due to the difficulty in combining optimization technique with more realistic material models where their nonlinear properties should be considered, the achieved optimized topologies are commonly unable to apply straight towards the practical design problems. This study presented an optimization procedure of composite structures where different elastic stiffness, yield criteria, and hardening models are assumed for the candidate materials. From the results, it can be concluded that a more explicit modeling has the significant influence on the resulting topologies. Also, the isotropic or kinematic hardening is important for elastoplastic structural optimization design. The capability of the proposed optimization procedure is shown through several cases.

Keywords: topology optimization, material composition, nonlinear modeling, hardening rules

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Authors: S. Adhirai, R. P. Mahapatra, Paramjit Singh

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Optimization is an important tool in making decisions and in analysing physical systems. In mathematical terms, an optimization problem is the problem of finding the best solution from among the set of all feasible solutions. The paper discusses the Whale Optimization Algorithm (WOA), and its applications in different fields. The algorithm is tested using MATLAB because of its unique and powerful features. The benchmark functions used in WOA algorithm are grouped as: unimodal (F1-F7), multimodal (F8-F13), and fixed-dimension multimodal (F14-F23). Out of these benchmark functions, we show the experimental results for F7, F11, and F19 for different number of iterations. The search space and objective space for the selected function are drawn, and finally, the best solution as well as the best optimal value of the objective function found by WOA is presented. The algorithmic results demonstrate that the WOA performs better than the state-of-the-art meta-heuristic and conventional algorithms.

Keywords: optimization, optimal value, objective function, optimization problems, meta-heuristic optimization algorithms, Whale Optimization Algorithm, implementation, MATLAB

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Authors: Amirhosein Rostampour, Mehdi Sharif

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In this article, a series of high impact polystyrene/graphene (HIPS/Gr) nanocomposites were prepared by solution mixing method and their morphology and dynamic mechanical properties were investigated as a function of graphene content. SEM images and X-Ray diffraction data confirm that the graphene platelets are well dispersed in HIPS matrix for the nanocomposites with Gr contents up to 5.0 wt%. Mechanical properties analysis demonstrates that yielding strength and initial modulus of HIPS/Gr nanocomposites are highly improved with the increment of Gr content compared to pure HIPS.

Keywords: nanocomposite, graphene, dynamic mechanical properties, morphology

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Authors: Shrikaant Kulkarni, Akshata Naik Nimbalkar

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In this worki a method protocol has been developed for the synthesis of innovative Co3O4 material by using a method of chemical synthesis followed by calcination. The effect of calcination temperature on the morphology, structure and catalytic performance on material in question is investigated by using characterization tools like scanning electron microscopy (SEM), X-ray diffraction (XRD) spectroscopy and electrochemical techniques. The SEM images reveal that the morphology of the Co3O4 material undergoes a change from the rod to a beadlike shape on calcination at temperature of 700 °C. The XRD image shows that although the morphology of synthesized Co3O4 material exhibits a cubic phase but it differs in crystallinity depending upon morphology. Similarly spherical beadlike Co3O4 material has exhibited better activity than its rodlike counterpart which is reflected from electrochemical findings. Further, its performance in terms of bifunctional nature and hlods a lot much of promise as a excellent electrode material in the next generation batteries and fuel cells.

Keywords: bifunctional, next generation material, Co3O4, XRD

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Authors: Mazura Mokhtar, Adibah Shuib, Daud Mohamad

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Portfolio optimization problem has received a lot of attention from both researchers and practitioners over the last six decades. This paper provides an overview of the current state of research in portfolio optimization with the support of mathematical programming techniques. On top of that, this paper also surveys the solution algorithms for solving portfolio optimization models classifying them according to their nature in heuristic and exact methods. To serve these purposes, 40 related articles appearing in the international journal from 2003 to 2013 have been gathered and analyzed. Based on the literature review, it has been observed that stochastic programming and goal programming constitute the highest number of mathematical programming techniques employed to tackle the portfolio optimization problem. It is hoped that the paper can meet the needs of researchers and practitioners for easy references of portfolio optimization.

Keywords: portfolio optimization, mathematical programming, multi-objective programming, solution approaches

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Authors: Elham Kazemi

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Quadratic Assignment Problem (QAP) is one the combinatorial optimization problems about which research has been done in many companies for allocating some facilities to some locations. The issue of particular importance in this process is the costs of this allocation and the attempt in this problem is to minimize this group of costs. Since the QAP’s are from NP-hard problem, they cannot be solved by exact solution methods. Cuckoo Optimization Algorithm is a Meta-heuristicmethod which has higher capability to find the global optimal points. It is an algorithm which is basically raised to search a continuous space. The Quadratic Assignment Problem is the issue which can be solved in the discrete space, thus the standard arithmetic operators of Cuckoo Optimization Algorithm need to be redefined on the discrete space in order to apply the Cuckoo Optimization Algorithm on the discrete searching space. This paper represents the way of discretizing the Cuckoo optimization algorithm for solving the quadratic assignment problem.

Keywords: Quadratic Assignment Problem (QAP), Discrete Cuckoo Optimization Algorithm (DCOA), meta-heuristic algorithms, optimization algorithms

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Authors: Amit Kamra, V. K. Jain, Pragya

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Mammography is widely used technique for breast cancer screening. There are various other techniques for breast cancer screening but mammography is the most reliable and effective technique. The images obtained through mammography are of low contrast which causes problem for the radiologists to interpret. Hence, a high quality image is mandatory for the processing of the image for extracting any kind of information from it. Many contrast enhancement algorithms have been developed over the years. In the present work, an efficient morphology based technique is proposed for contrast enhancement of masses in mammographic images. The proposed method is based on Multiscale Morphology and it takes into consideration the scale of the structuring element. The proposed method is compared with other state-of-the-art techniques. The experimental results show that the proposed method is better both qualitatively and quantitatively than the other standard contrast enhancement techniques.

Keywords: enhancement, mammography, multi-scale, mathematical morphology

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