Search results for: numerical optimization

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: Fuzhang Zhao

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Particle swarm optimization (PSO) is becoming one of the most important swarm intelligent paradigms for solving global optimization problems. Although some progress has been made to improve PSO algorithms over the last two decades, additional work is still needed to balance parameters to achieve better numerical properties of accuracy, efficiency, and stability. In the optimal PSO algorithm, the optimal weightings of (√ 5 − 1)/2 and (3 − √5)/2 are used for the cognitive factor and the social factor, respectively. By the same token, the same optimal weightings have been applied for intensification searches and diversification searches, respectively. Perturbation and constriction effects are optimally balanced. Simulations of the de Jong, the Rosenbrock, and the Griewank functions show that the optimal PSO algorithm indeed achieves better numerical properties and outperforms the canonical PSO algorithm.

Keywords: diversification search, intensification search, optimal weighting, particle swarm optimization

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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: 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: Yue-Tzu Yang, Shu-Ching Liao

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This study presents the numerical simulation of three-dimensional incompressible steady and laminar fluid flow and conjugate heat transfer of a trapezoidal microchannel heat sink using water as a cooling fluid in a silicon substrate. Navier-Stokes equations with conjugate energy equation are discretized by finite-volume method. We perform numerical computations for a range of 50 ≦ Re ≦ 600, 0.05W ≦ P ≦ 0.8W, 20W/cm2 ≦ ≦ 40W/cm2. The present study demonstrates the numerical optimization of a trapezoidal microchannel heat sink design using the response surface methodology (RSM) and the genetic algorithm method (GA). The results show that the average Nusselt number increases with an increase in the Reynolds number or pumping power, and the thermal resistance decreases as the pumping power increases. The thermal resistance of a trapezoidal microchannel is minimized for a constant heat flux and constant pumping power.

Keywords: microchannel heat sinks, conjugate heat transfer, optimization, genetic algorithm method

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Authors: Belloufi Mohammed, Sellami Badreddine

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Conjugate gradient methods have played a special role for solving large scale optimization problems due to the simplicity of their iteration, convergence properties and their low memory requirements. In this work, we propose a new class of conjugate gradient methods which ensures sufficient descent. Moreover, we propose a new search direction with the Wolfe line search technique for solving unconstrained optimization problems, a global convergence result for general functions is established provided that the line search satisfies the Wolfe conditions. Our numerical experiments indicate that our proposed methods are preferable and in general superior to the classical conjugate gradient methods in terms of efficiency and robustness.

Keywords: unconstrained optimization, conjugate gradient method, sufficient descent property, numerical comparisons

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Authors: F. Rahimi Dehgolan, M. Behzadi, J. Fathi Sola

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In this article, the Johnson-Cook material model’s constants for structural steel ST.37 have been determined by a method which integrates experimental tests, numerical simulation, and optimization. In the first step, a quasi-static test was carried out on a plain specimen. Next, the constants were calculated for it by minimizing the difference between the results acquired from the experiment and numerical simulation. Then, a quasi-static tension test was performed on three notched specimens with different notch radii. At last, in order to verify the results, they were used in numerical simulation of notched specimens and it was observed that experimental and simulation results are in good agreement. Changing the diameter size of the plain specimen in the necking area was set as the objective function in the optimization step. For final validation of the proposed method, diameter variation was considered as a parameter and its sensitivity to a change in any of the model constants was examined and the results were completely corroborating.

Keywords: constants, Johnson-Cook material model, notched specimens, quasi-static test, sensitivity

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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: Dongkyu Lee, Thanh Banh Thien, Soomi Shin

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In the present study, the isogeometric topology optimization is proposed for cracked structures through using Solid Isotropic Material with Penalization (SIMP) as a design model. Design density variables defined in the variable space are used to approximate the element analysis density by the bivariate B-spline basis functions. The mathematical formulation of topology optimization problem solving minimum structural compliance is an alternating active-phase algorithm with the Gauss-Seidel version as an optimization model of optimality criteria. Stiffness and adjoint sensitivity formulations linked to strain energy of cracked structure are proposed in terms of design density variables. Numerical examples demonstrate interactions of topology optimization to structures design with cracks.

Keywords: topology optimization, isogeometric, NURBS, design

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Authors: Yue-Tzu Yang, Peng-Jen Chen

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The present study deals with the numerical optimization of wavy channel with the help of genetic algorithm (GA). Three design variables related to the wave amplitude (A), the wavelength (λ) and the channel aspect ratio (α) are chosen and their ranges are decided through preliminary calculations of three-dimensional Navier-stokes and energy equations. A parametric study is also performed to show the effects of different design variables on the overall performance of the wavy channel. Objective functions related to the heat transfer and pressure drop, performance factor (PF) is formulated to analyze the performance of the wavy channel. The numerical results show that the wave amplitude and the channel aspect ratio have significant effects on the thermal performance. It can improve the performance of the wavy channels by increasing wave amplitude or decreasing the channel aspect ratio. Increasing wavelengths have no significant effects on the heat transfer performance.

Keywords: wavy channel, genetic algorithm, optimization, numerical simulation

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Authors: Kawser Ahmed, K. Bousson, Milca F. Coelho

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4D flight trajectory optimization is one of the key ingredients to improve flight efficiency and to enhance the air traffic capacity in the current air traffic management (ATM). The present paper explores the iterative dynamic programming (IDP) as a potential numerical optimization method for 4D flight trajectory optimization. IDP is an iterative version of the Dynamic programming (DP) method. Due to the numerical framework, DP is very suitable to deal with nonlinear discrete dynamic systems. The 4D waypoint representation of the flight trajectory is similar to the discretization by a grid system; thus DP is a natural method to deal with the 4D flight trajectory optimization. However, the computational time and space complexity demanded by the DP is enormous due to the immense number of grid points required to find the optimum, which prevents the use of the DP in many practical high dimension problems. On the other hand, the IDP has shown potentials to deal successfully with high dimension optimal control problems even with a few numbers of grid points at each stage, which reduces the computational effort over the traditional DP approach. Although the IDP has been applied successfully in chemical engineering problems, IDP is yet to be validated in 4D flight trajectory optimization problems. In this paper, the IDP has been successfully used to generate minimum length 4D optimal trajectory avoiding any obstacle in its path, such as a no-fly zone or residential areas when flying in low altitude to reduce noise pollution.

Keywords: 4D waypoint navigation, iterative dynamic programming, obstacle avoidance, trajectory optimization

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Authors: David Lindström

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We evaluate the performance of a numerical method for global optimization of expensive functions. The method is using a response surface to guide the search for the global optimum. This metamodel could be based on radial basis functions, kriging, or a combination of different models. We discuss how to set the cycling parameters of the optimization method to get a balance between local and global search. We also discuss the eventual problem with Runge oscillations in the response surface.

Keywords: expensive function, infill sampling criterion, kriging, global optimization, response surface, Runge phenomenon

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Authors: Adel Sabry Eesa, Adnan Mohsin Abdulazeez Brifcani, Zeynep Orman

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This paper presents a new meta-heuristic bio-inspired optimization algorithm which is called Cuttlefish Algorithm (CFA). The algorithm mimics the mechanism of color changing behavior of the cuttlefish to solve numerical global optimization problems. The colors and patterns of the cuttlefish are produced by reflected light from three different layers of cells. The proposed algorithm considers mainly two processes: reflection and visibility. Reflection process simulates light reflection mechanism used by these layers, while visibility process simulates visibility of matching patterns of the cuttlefish. To show the effectiveness of the algorithm, it is tested with some other popular bio-inspired optimization algorithms such as Genetic Algorithms (GA), Particle Swarm Optimization (PSO) and Bees Algorithm (BA) that have been previously proposed in the literature. Simulations and obtained results indicate that the proposed CFA is superior when compared with these algorithms.

Keywords: Cuttlefish Algorithm, bio-inspired algorithms, optimization, global optimization problems

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Authors: H. Ghodbane, A. A. Taleb, O. Kraa

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This paper presents geometric design of induction heating system. The objective of this design is to improve the temperature distribution in the load. The study of such a device requires the use of models or modeling representation, physical, mathematical, and numerical. This modeling is the basis of the understanding, the design, and optimization of these systems. The optimization technique is to find values of variables that maximize or minimize the objective function.

Keywords: optimization, modeling, geometric design system, temperature increase

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Authors: Fares Senouci, Bachir Imine

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This document provides numerical and experimental optimization of the aerodynamic performance of a drone equipped with three types of horizontal stabilizer. To build this optimal configuration, an experimental and numerical study was conducted on three parameters: the geometry of the stabilizer (horizontal form or reverse V form), the position of the horizontal stabilizer (up or down), and the landing gear position (closed or open). The results show that up-stabilizer position with respect to the horizontal plane of the fuselage provides better aerodynamic performance, and that the landing gear increases the lift in the zone of stability, that is to say where the flow is not separated.

Keywords: aerodynamics, drag, lift, turbulence model, wind tunnel

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Authors: D. K. Lee, S. M. Shin, J. H. Lee

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Topology optimization technique utilizes constant element densities as design parameters. Finally, optimal distribution contours of the material densities between voids (0) and solids (1) in design domain represent the determination of topology. It means that regions with element density values become occupied by solids in design domain, while there are only void phases in regions where no density values exist. Therefore the void regions of topology optimization results provide design information to decide appropriate depositions of web-opening in structure. Contrary to the basic objective of the topology optimization technique which is to obtain optimal topology of structures, this present study proposes a new idea that topology optimization results can be also utilized for decision of proper web-opening’s position. Numerical examples of linear elastostatic structures demonstrate efficiency of methodological design processes using topology optimization in order to determinate the proper deposition of web-openings.

Keywords: topology optimization, web-opening, structure, element density, material

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Authors: R. Kanmaniraja, R. Freshipali, J. Abdullah, K. Niranjan, K. Balasubramani, V. R. Sanal Kumar

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The present environmental issues have made aircraft jet noise reduction a crucial problem in aero-acoustics research. Acoustic studies reveal that addition of chevrons to the nozzle reduces the sound pressure level reasonably with acceptable reduction in performance. In this paper comprehensive numerical studies on acoustic characteristics of different types of chevron nozzles have been carried out with non-reacting flows for the shape optimization of chevrons in supersonic nozzles for aerospace applications. The numerical studies have been carried out using a validated steady 3D density based, k-ε turbulence model. In this paper chevron with sharp edge, flat edge, round edge and U-type edge are selected for the jet acoustic characterization of supersonic nozzles. We observed that compared to the base model a case with round-shaped chevron nozzle could reduce 4.13% acoustic level with 0.6% thrust loss. We concluded that the prudent selection of the chevron shape will enable an appreciable reduction of the aircraft jet noise without compromising its overall performance. It is evident from the present numerical simulations that k-ε model can predict reasonably well the acoustic level of chevron supersonic nozzles for its shape optimization.

Keywords: supersonic nozzle, Chevron, acoustic level, shape optimization of Chevron nozzles, jet noise suppression

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Authors: Mohamed Abdelwahed

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We propose an optimization algorithm for the geometric control of fluid flow. The used approach is based on the topological sensitivity analysis method. It consists in studying the variation of a cost function with respect to the insertion of a small obstacle in the domain. Some theoretical and numerical results are presented in 2D and 3D.

Keywords: sensitivity analysis, topological gradient, shape optimization, stokes equations

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Authors: Mohammad Sadeghian, Mohsen Sadeghian

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In this paper, planning catamaran and mono-hull vessels resistance and trim in calm waters were considered. Hydrodynamic analysis of fast mono-hull planning vessel was also investigated. For hull form geometry optimization, numerical methods of different parameters were used for this type of vessels. Hull material was selected as carbon fiber composite. Exact architectural aspects were specified and stability calculations were performed, as well. Hydrodynamic calculations to extract the resistance force using semi-analytical methods and numerical modeling were carried out. Free surface numerical analysis of vessel in designed draft using finite volume method and double phase were evaluated and verified by experimental tests.

Keywords: fast vessel, hydrostatic and hydrodynamic optimization, free surface flow, computational fluid dynamics

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Authors: Mohammad Ali Badri, Pouya Molana, Amin Rezvanpour

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In this paper, planning catamaran and mono-hull vessels resistance and trim in calm waters were considered. Hydrodynamic analysis of fast mono-hull planning vessel was also investigated. In order to hull form geometry optimization, numerical methods of different parameters were used for this type of vessels. Hull material was selected in carbon fiber composite. Exact architectural aspects were specified and stability calculations were performed as well. Hydrodynamic calculations to extract the resistance force using semi-analytical methods and numerical modeling were carried out. Free surface numerical analysis of vessel in designed draft using finite volume method and double phase were evaluated and verified by experimental tests.

Keywords: fast vessel, hydrostatic and hydrodynamic optimization, free surface flow, computational fluid dynamics

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Authors: Mohammed Belloufi, Rachid Benzine, Badreddine Sellami

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Conjugate gradient methods is useful for solving large scale optimization problems in scientific and engineering computation, characterized by the simplicity of their iteration and their low memory requirements. It is well known that the search direction plays a main role in the line search method. In this paper, we propose a search direction with the Wolfe line search technique for solving unconstrained optimization problems. Under the above line searches and some assumptions, the global convergence properties of the given methods are discussed. Numerical results and comparisons with other CG methods are given.

Keywords: unconstrained optimization, conjugate gradient method, strong Wolfe line search, global convergence

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Authors: M. Chen, S-Q. Zhang, X. Wang, D. Tate

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This paper presents a numerical solution, namely limit and shakedown analysis, to predict the safety state of smart structures made of heterogeneous materials under unknown cyclic loadings, for instance, the flexure hinge in the micro-positioning stage driven by piezoelectric actuator. In combination of homogenization theory and finite-element method (FEM), the safety evaluation problem is converted to a large-scale nonlinear optimization programming for an acceptable bounded loading as the design reference. Furthermore, a general numerical scheme integrated with the FEM and interior-point-algorithm based optimization tool is developed, which makes the practical application possible.

Keywords: limit state, shakedown analysis, homogenization, heterogeneous structure

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Authors: H. Nikzad, S. Yoshitomi

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In this paper, an optimization procedure is applied for 3D Reinforced concrete building structure with shear wall.  In the optimization problem, cross sections of beams, columns and shear wall dimensions are considered as design variables and the optimal cross sections can be derived to minimize the total cost of the structure. As for final design application, the most suitable sections are selected to satisfy ACI 318-14 code provision based on static linear analysis. The validity of the method is examined through numerical example of 15 storied 3D RC building with shear wall.  This optimization method is expected to assist in providing a useful reference in design early stage, and to be an effective and powerful tool for structural design of RC shear wall structures.

Keywords: structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures

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Authors: Mounir Adal, Baalal Azeddine, Afifi Moulay Larbi

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Numerical analysis is a branch of mathematics devoted to the development of iterative matrix calculation techniques. We are searching for operations optimization as objective to calculate and solve systems of equations of order n with time and energy saving for computers that are conducted to calculate and analyze big data by solving matrix equations. Furthermore, this scientific discipline is producing results with a margin of error of approximation called rates. Thus, the results obtained from the numerical analysis techniques that are held on computer software such as MATLAB or Simulink offers a preliminary diagnosis of the situation of the environment or space targets. By this we can offer technical procedures needed for engineering or scientific studies exploitable by engineers for water.

Keywords: numerical analysis methods, obstacles solving, engineering, simulation, numerical modeling, iteration, computer, MATLAB, water, underground, velocity

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Authors: Emery A. Coppola Jr., Suna Cinar, Ferenc Szidarovszky

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Over-pumping of groundwater resources is a serious problem world-wide. In addition to depleting this valuable resource, hydraulically connected sensitive ecological resources like wetlands and surface water bodies are often impacted and even destroyed by over-pumping. Effectively managing groundwater in a way that satisfy human demand while preserving natural resources is a daunting challenge that will only worsen with growing human populations and climate change. As presented in this paper, a numerical flow model developed for a hypothetical but realistic groundwater/surface water system was combined with formal optimization. Response coefficients were used in an optimization management model to maximize groundwater pumping in a complex, multi-layered aquifer system while protecting against groundwater over-draft, streamflow depletion, and wetland impacts. Pumping optimization was performed for different constraint sets that reflect different resource protection preferences, yielding significantly different optimal pumping solutions. A sensitivity analysis on the optimal solutions was performed on select response coefficients to identify differences between wet and dry periods. Stochastic optimization was also performed, where uncertainty associated with changing irrigation demand due to changing weather conditions are accounted for. One of the strengths of this optimization approach is that it can efficiently and accurately identify superior management strategies that minimize risk and adverse environmental impacts associated with groundwater pumping under different hydrologic conditions.

Keywords: numerical groundwater flow modeling, water management optimization, groundwater overdraft, streamflow depletion

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Authors: Mohamed Rahal, Djaouida Guetta

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In this paper, the one-dimensional unconstrained global optimization problem of continuous functions satifying a Hölder condition is considered. We extend the algorithm of sequential covering SCA for Lipschitz functions to a large class of Hölder functions. The convergence of the method is studied and the algorithm can be applied to systems of nonlinear equations. Finally, some numerical examples are presented and illustrate the efficiency of the present approach.

Keywords: global optimization, Hölder functions, sequential covering method, systems of nonlinear equations

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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: K. Djellabi, M. E. H. Latreche

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Induction heating computer simulation is a powerful tool for process design and optimization, induction coil design, equipment selection, as well as education and business presentations. The authors share their vast experience in the practical use of computer simulation for different induction heating and heat treating processes. In this paper deals with mathematical modeling and numerical simulation of induction heating furnaces with axisymmetric geometries. For the numerical solution, we propose finite element methods combined with boundary (FEM) for the electromagnetic model using COMSOL® Multiphysics Software. Some numerical results for an industrial furnace are shown with high frequency.

Keywords: numerical methods, induction furnaces, induction heating, finite element method, Comsol multiphysics software

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Authors: Zahid Ullah, Atlas Khan

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This abstract focuses on the advancements in mathematical modeling and optimization techniques that play a crucial role in enhancing the efficiency, reliability, and performance of these systems. In this era of rapidly evolving technology, mathematical modeling and optimization offer powerful tools to tackle the complex challenges faced by control, signal processing, and energy systems. This abstract presents the latest research and developments in mathematical methodologies, encompassing areas such as control theory, system identification, signal processing algorithms, and energy optimization. The abstract highlights the interdisciplinary nature of mathematical modeling and optimization, showcasing their applications in a wide range of domains, including power systems, communication networks, industrial automation, and renewable energy. It explores key mathematical techniques, such as linear and nonlinear programming, convex optimization, stochastic modeling, and numerical algorithms, that enable the design, analysis, and optimization of complex control and signal processing systems. Furthermore, the abstract emphasizes the importance of addressing real-world challenges in control, signal processing, and energy systems through innovative mathematical approaches. It discusses the integration of mathematical models with data-driven approaches, machine learning, and artificial intelligence to enhance system performance, adaptability, and decision-making capabilities. The abstract also underscores the significance of bridging the gap between theoretical advancements and practical applications. It recognizes the need for practical implementation of mathematical models and optimization algorithms in real-world systems, considering factors such as scalability, computational efficiency, and robustness. In summary, this abstract showcases the advancements in mathematical modeling and optimization techniques for control, signal processing, and energy systems. It highlights the interdisciplinary nature of these techniques, their applications across various domains, and their potential to address real-world challenges. The abstract emphasizes the importance of practical implementation and integration with emerging technologies to drive innovation and improve the performance of control, signal processing, and energy.

Keywords: mathematical modeling, optimization, control systems, signal processing, energy systems, interdisciplinary applications, system identification, numerical algorithms

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Authors: Geetanjali Panda, Suvrakanti Chakraborty

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In this paper, Newton-like descent methods are proposed for unconstrained optimization problems, which use q-derivatives of the gradient of an objective function. First, a local scheme is developed with alternative sufficient optimality condition, and then the method is extended to a global scheme. Moreover, a variant of practical Newton scheme is also developed introducing a real sequence. Global convergence of these schemes is proved under some mild conditions. Numerical experiments and graphical illustrations are provided. Finally, the performance profiles on a test set show that the proposed schemes are competitive to the existing first-order schemes for optimization problems.

Keywords: Descent algorithm, line search method, q calculus, Quasi Newton method

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