scholarly journals Fractal algorithm for the modeling of consumption in COVID-19

2020 ◽  
pp. 1-7
Author(s):  
María Ramos-Escamilla
Keyword(s):  
Objective Function ◽  
Iterative Methods ◽  
Initial Function ◽  
Economies Of Scale ◽  
Absolute Convergence ◽  
Optimization Algorithms ◽  
Stochastic Method ◽  
Final Solution ◽  
Exogenous Factors

We present an analysis of the exogenous factors of consumption, we simulate it in a fractal algorithm whose objective is the Brownian equilibrium through the iterative multiplication of assumptions of an initial function at current prices whose values are constant and positive that will derive in the final solution that is characterized by non-negativity and does not denote absolute convergence, only relative to their economies of scale compared to iterative methods, we find other procedures derived from the stochastic method but formulated strictly as mathematical developments, they are fractal optimization algorithms, which are based on search of an objective function that minimizes the distance between the initial function and the expected iterations of the candidate functions to be a solution, verifying the corresponding restrictions.

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation

Processes ◽  
2018 ◽  
Vol 6 (8) ◽  
pp. 130 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation is implicitly given in respect to the unknown flow friction factor λ; λ = ζ ( R e , ε * , λ ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. A common approach to solve it is through the Newton–Raphson iterative procedure or through the fixed-point iterative procedure. Both require in some cases, up to seven iterations. On the other hand, numerous more powerful iterative methods such as three- or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require, in the worst case, only two iterations to reach the final solution. The recommended representatives are Sharma–Guha–Gupta, Sharma–Sharma, Sharma–Arora, Džunić–Petković–Petković; Bi–Ren–Wu, Chun–Neta based on Kung–Traub, Neta, and the Jain method based on the Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between the iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

Electromagnetic and thermal parameter identification method for best prediction of temperature distribution on transformer tank covers

2015 ◽  
Vol 34 (2) ◽  
pp. 485-495 ◽  
Author(s):  
Patricia Penabad Durán ◽  
Paolo Di Barba ◽  
Xose Lopez-Fernandez ◽  
Janusz Turowski
Keyword(s):  
Temperature Distribution ◽  
Measurement Error ◽  
Parameter Identification ◽  
Objective Function ◽  
Measurement Errors ◽  
Optimization Algorithms ◽  
Identification Problem ◽  
Content Type ◽  
Identification Method ◽  
Wide Range

Purpose – The purpose of this paper is to describe a parameter identification method based on multiobjective (MO) deterministic and non-deterministic optimization algorithms to compute the temperature distribution on transformer tank covers. Design/methodology/approach – The strategy for implementing the parameter identification process consists of three main steps. The first step is to define the most appropriate objective function and the identification problem is solved for the chosen parameters using single-objective (SO) optimization algorithms. Then sensitivity to measurement error of the computational model is assessed and finally it is included as an additional objective function, making the identification problem a MO one. Findings – Computations with identified/optimal parameters yield accurate results for a wide range of current values and different conductor arrangements. From the numerical solution of the temperature field, decisions on dimensions and materials can be taken to avoid overheating on transformer covers. Research limitations/implications – The accuracy of the model depends on its parameters, such as heat exchange coefficients and material properties, which are difficult to determine from formulae or from the literature. Thus the goal of the presented technique is to achieve the best possible agreement between measured and numerically calculated temperature values. Originality/value – Differing from previous works found in the literature, sensitivity to measurement error is considered in the parameter identification technique as an additional objective function. Thus, solutions less sensitive to measurement errors at the expenses of a degradation in accuracy are identified by means of MO optimization algorithms.

A Comparison Study on Algorithms in Reservoir Automatic History Matching

2012 ◽  
Vol 518-523 ◽  
pp. 4376-4379
Author(s):  
Bao Yi Jiang ◽  
Zhi Ping Li
Keyword(s):  
Objective Function ◽  
Reservoir Simulation ◽  
History Matching ◽  
Optimization Algorithms ◽  
Reservoir Engineering ◽  
Comparison Study ◽  
Automatic History Matching ◽  
Numerical Reservoir Simulation ◽  
Computational Capability ◽  
Matching Procedure

With the increase in computational capability, numerical reservoir simulation has become an essential tool for reservoir engineering. To minimize the objective function involved in the history matching procedure, we need to apply the optimization algorithms. This paper is based on the optimization algorithms used in automatic history matching.

scholarly journals COMPARISON OF GLOBAL SEARCH OPTIMIZATION ALGORITHMS TO PERFORM THE VELOCITY ANALYSIS WITH A CONVERTED WAVE MOVEOUT EQUATION

2019 ◽  
Vol 7 (6) ◽  
pp. 1-9
Author(s):  
Nelson Ricardo Coelho Flores Zuniga
Keyword(s):  
Objective Function ◽  
Travel Time ◽  
Optimization Algorithm ◽  
Processing Time ◽  
Optimization Algorithms ◽  
Global Search ◽  
Velocity Analysis ◽  
Converted Wave ◽  
Search Optimization ◽  
Deep Reservoir

Even with previous works having studied about the accuracy and objective function of several nonhyperbolic multiparametric travel-time approximations for velocity analysis, they lack tests concerning different optimization algorithms and how they influence the accuracy and processing time. Once many approximations were tested and found the multimodal one which presented the best accuracy results, it is possible to perform a velocity analysis with different global search optimization algorithms. The minimization of the curve calculated with the converted wave moveout equation to the observed curve can be done for each optimization algorithm selected in this work. The travel-time curves tested here are the PP and PS reflection events coming from the interface of the top of an offshore ultra-deep reservoir. After the inversion routine have been performed, it is possible to define the processing time and the accuracy of each optimization algorithm for this kind of problem.

scholarly journals Strong error analysis for stochastic gradient descent optimization algorithms

2020 ◽  
Author(s):  
Arnulf Jentzen ◽  
Benno Kuckuck ◽  
Ariel Neufeld ◽  
Philippe von Wurstemberger
Keyword(s):  
Error Analysis ◽  
Objective Function ◽  
Optimization Algorithm ◽  
Gradient Descent ◽  
Convergence Rates ◽  
Optimization Algorithms ◽  
Stochastic Gradient ◽  
Stochastic Gradient Descent ◽  
Induction Argument ◽  
Machine Learning Applications

Abstract Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analysis for SGD optimization algorithms. In particular, we prove for every arbitrarily small $\varepsilon \in (0,\infty )$ and every arbitrarily large $p{\,\in\,} (0,\infty )$ that the considered SGD optimization algorithm converges in the strong $L^p$-sense with order $1/2-\varepsilon $ to the global minimum of the objective function of the considered stochastic optimization problem under standard convexity-type assumptions on the objective function and relaxed assumptions on the moments of the stochastic errors appearing in the employed SGD optimization algorithm. The key ideas in our convergence proof are, first, to employ techniques from the theory of Lyapunov-type functions for dynamical systems to develop a general convergence machinery for SGD optimization algorithms based on such functions, then, to apply this general machinery to concrete Lyapunov-type functions with polynomial structures and, thereafter, to perform an induction argument along the powers appearing in the Lyapunov-type functions in order to achieve for every arbitrarily large $ p \in (0,\infty ) $ strong $ L^p $-convergence rates.

A Nondifferentiable Optimization Algorithm for Constrained Minimax Linkage Function Generation

1993 ◽  
Vol 115 (4) ◽  
pp. 978-987 ◽  
Author(s):  
K. Kurien Issac
Keyword(s):  
Objective Function ◽  
Optimization Algorithm ◽  
Nondifferentiable Optimization ◽  
Optimization Algorithms ◽  
Necessary Condition ◽  
Function Generation ◽  
Smooth Optimization ◽  
Constrained Minimax ◽  
Linkage Synthesis

This paper describes a nondifferentiable optimization (NDO) algorithm for solving constrained minimax linkage synthesis. Use of a proper characterization of minima makes the algorithm superior to the smooth optimization algorithms for minimax linkage synthesis and the concept of following the curved ravines of the objective function makes it very effective. The results obtained are superior to some of the reported solutions and demonstrate the algorithm’s ability to consistently arrive at actual minima from widely separated starting points. The results indicate that Chebyshev’s characterization is not a necessary condition for minimax linkages, while the characterization used in the algorithm is a proper necessary condition.

On: “Application of Gauss’s method to magnetic anomalies of dipping dikes” by I. J. Won (GEOPHYSICS, 46, 211–215, February, 1981).

Geophysics ◽  
1986 ◽  
Vol 51 (8) ◽  
pp. 1691-1691
Author(s):  
C. V. Rao
Keyword(s):  
Least Squares ◽  
Absolute Convergence ◽  
Iterative Scheme ◽  
Final Solution ◽  
Rapid Convergence ◽  
Differential Correction ◽  
The Subject ◽  
Magnetic Profile ◽  
The One ◽  
Initial Choice

Dr. Won chose to comment on some of the earlier computerized interpretation schemes on the “inversion of a magnetic profile across a dipping dike” where he remarked that the schemes are often susceptible to (1) difficulty in absolute convergence, and (2) dependence of the final solution on the initially assumed model. Dr. Won described an iterative scheme which combines the differential correction and least‐squares methods, and he claimed rapid convergence to minimum rms error. The scheme he proposed seems to be substantially the same as the one described by Rao et al. (1973), who also employed differential correction and least‐squares criteria for the convergence of the solution. The flow chart given by Rao et al. (p. 714) clearly shows this. The only difference I could observe in the subject paper from that of Rao et al. is the imposition of certain allowable limits on each parameter of the dike to be determined so that the solution does not diverge. This is outside the principle of the method. Furthermore, no new scheme has been developed to eliminate the dependence of the final solution of the dike on the initial model; without such a scheme the conclusion arrived at in the paper, “that the final solution is independent of the initial choice of the model,” is not realistic.

An Advanced Optimization Procedure for the Thermodynamic Selection of Centrifugal Compressors Stages

2008 ◽  
Author(s):  
Simone Pazzi ◽  
Marco Giachi ◽  
Ashraf Al Musleh ◽  
Massimo Pusceddu ◽  
Nidal Ghizawi
Keyword(s):  
Objective Function ◽  
Performance Optimization ◽  
Optimization Algorithms ◽  
Optimization Procedure ◽  
Optimization Process ◽  
Performance Parameters ◽  
Centrifugal Compressors ◽  
Operating Range ◽  
Size Constraints ◽  
Selection Of

The present paper deals with the application of optimization algorithms to the selection of centrifugal stages for industrial compressors. The optimization procedure has been developed allowing an automatic stage selection to meet a mathematically stated target including the most relevant performance parameters and machine operating and size constraints. The thermodynamic selection is assessed by means of an internal-use CCS (Centrifugal Compressors Selector) that computes compressor flange-to-flange performance with a given sequence of stages. The CCS has been coupled to an internally used optimization code (“PEZ”, Perl Version of Easy Optimizer) using the CCS as the performance evaluator. The user indicates which flange variables must be matched as well as the stages parameters that the optimizer is allowed to alter, with their respective ranges of acceptable variation. The optimization objective reflects the job specifications and can be stated as a combination of several performance parameters. Constraints are enforced through appropriate penalty terms added to the objective function. The performance optimization process includes an automatic rotordynamic analysis that checks the rotor mechanical acceptability. The optimization of two different in-line barrel compressors, originally configured manually, brought a remarkable 2% flange-to-flange performance increase and a 5% gain in operating range respectively. Each case required about 10 hours windows desktop workstation.

scholarly journals Performance analysis of selected metaheuristic optimization algorithms applied in the solution of an unconstrained task

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Łukasz Knypiński
Keyword(s):  
Performance Analysis ◽  
Objective Function ◽  
Permanent Magnet ◽  
Optimization Algorithm ◽  
Search Algorithm ◽  
Optimization Algorithms ◽  
Bat Algorithm ◽  
Statistical Efficiency ◽  
Comparative Performance ◽  
Content Type

Purpose The purpose of this paper is to execute the efficiency analysis of the selected metaheuristic algorithms (MAs) based on the investigation of analytical functions and investigation optimization processes for permanent magnet motor. Design/methodology/approach A comparative performance analysis was conducted for selected MAs. Optimization calculations were performed for as follows: genetic algorithm (GA), particle swarm optimization algorithm (PSO), bat algorithm, cuckoo search algorithm (CS) and only best individual algorithm (OBI). All of the optimization algorithms were developed as computer scripts. Next, all optimization procedures were applied to search the optimal of the line-start permanent magnet synchronous by the use of the multi-objective objective function. Findings The research results show, that the best statistical efficiency (mean objective function and standard deviation [SD]) is obtained for PSO and CS algorithms. While the best results for several runs are obtained for PSO and GA. The type of the optimization algorithm should be selected taking into account the duration of the single optimization process. In the case of time-consuming processes, algorithms with low SD should be used. Originality/value The new proposed simple nondeterministic algorithm can be also applied for simple optimization calculations. On the basis of the presented simulation results, it is possible to determine the quality of the compared MAs.

scholarly journals Choosing the Optimal Multi-Point Iterative Method for the Colebrook Flow Friction Equation – Numerical Validation

2018 ◽  
Author(s):  
Pavel Praks ◽  
Dejan Brkić
Keyword(s):  
Iterative Method ◽  
Iterative Methods ◽  
Iterative Procedure ◽  
Accurate Solution ◽  
Final Solution ◽  
Worst Case ◽  
Flow Friction ◽  
One Step ◽  
Newton Raphson ◽  
Number Of Iterations

The Colebrook equation ζ is implicitly given in respect to the unknown flow friction factor λ ;  λ=ζ(Re,ε*,λ) which cannot be expressed explicitly in exact way without simplifications and use of approximate calculus. Common approach to solve it is through the Newton-Raphson iterative procedure or through the fixed-point iterative procedure. Both requires in some case even eight iterations. On the other hand numerous more powerful iterative methods such as three-or two-point methods, etc. are available. The purpose is to choose optimal iterative method in order to solve the implicit Colebrook equation for flow friction accurately using the least possible number of iterations. The methods are thoroughly tested and those which require the least possible number of iterations to reach the accurate solution are identified. The most powerful three-point methods require in worst case only two iterations to reach final solution. The recommended representatives are Sharma-Guha-Gupta, Sharma-Sharma, Sharma-Arora, Džunić-Petković-Petković; Bi-Ren-Wu, Chun-Neta based on Kung-Traub, Neta, and Jain method based on Steffensen scheme. The recommended iterative methods can reach the final accurate solution with the least possible number of iterations. The approach is hybrid between iterative procedure and one-step explicit approximations and can be used in engineering design for initial rough, but also for final fine calculations.

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