Analysis of strategies of circuit optimisation on basis of maximum principle

2018 ◽  
Vol 37 (1) ◽  
pp. 484-503
Author(s):  
Alexander Zemliak
Keyword(s):  
Maximum Principle ◽  
Dimensional Case ◽  
Processing Unit ◽  
Local Minima ◽  
Control Vector ◽  
Content Type ◽  
The Maximum Principle ◽  
Central Processing ◽  
Cpu Time ◽  
First Time

Purpose This paper aims to propose a new approach on the problem of circuit optimisation by using the generalised optimisation methodology presented earlier. This approach is focused on the application of the maximum principle of Pontryagin for searching the best structure of a control vector providing the minimum central processing unit (CPU) time. Design/methodology/approach The process of circuit optimisation is defined mathematically as a controllable dynamical system with a control vector that changes the internal structure of the equations of the optimisation procedure. In this case, a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. A practical approach for the realisation of the maximum principle is based on the analysis of the behaviour of a Hamiltonian for various strategies of optimisation and provides the possibility to find the optimum points of switching for the control vector. Findings It is shown that in spite of the fact that the maximum principle is not a sufficient condition for obtaining the global minimum for the non-linear problem, the decision can be obtained in the form of local minima. These local minima provide rather a low value of the CPU time. Numerical results were obtained for both a two-dimensional case and an N-dimensional case. Originality/value The possibility of the use of the maximum principle of Pontryagin to a problem of circuit optimisation is analysed systematically for the first time. The important result is the theoretical justification of formerly discovered effect of acceleration of the process of circuit optimisation.

A modified genetic algorithm for system optimization

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Alexander Zemliak
Keyword(s):  
Genetic Algorithm ◽  
Fitness Function ◽  
System Optimization ◽  
High Accuracy ◽  
Optimization Process ◽  
Processing Unit ◽  
Local Minima ◽  
Control Vector ◽  
Content Type ◽  
Cpu Time

Purpose In this paper, the previously developed idea of generalized optimization of circuits for deterministic methods has been extended to genetic algorithm (GA) to demonstrate new possibilities for solving an optimization problem that enhance accuracy and significantly reduce computing time. Design/methodology/approach The disadvantages of GAs are premature convergence to local minima and an increase in the computer operation time when setting a sufficiently high accuracy for obtaining the minimum. The idea of generalized optimization of circuits, previously developed for the methods of deterministic optimization, is built into the GA and allows one to implement various optimization strategies based on GA. The shape of the fitness function, as well as the length and structure of the chromosomes, is determined by a control vector artificially introduced within the framework of generalized optimization. This study found that changing the control vector that determines the method for calculating the fitness function makes it possible to bypass local minima and find the global minimum with high accuracy and a significant reduction in central processing unit (CPU) time. Findings The structure of the control vector is found, which makes it possible to reduce the CPU time by several orders of magnitude and increase the accuracy of the optimization process compared with the traditional approach for GAs. Originality/value It was demonstrated that incorporating the idea of generalized optimization into the body of a stochastic optimization method leads to qualitatively new properties of the optimization process, increasing the accuracy and minimizing the CPU time.

scholarly journals FEM using projection of physical properties suitable for movement modeling and optimization processes

2020 ◽  
Vol 39 (5) ◽  
pp. 1185-1199
Author(s):  
Baptiste Ristagno ◽  
Dominique Giraud ◽  
Julien Fontchastagner ◽  
Denis Netter ◽  
Noureddine Takorabet ◽  
...  
Keyword(s):  
Three Dimensional ◽  
Transient State ◽  
Mathematical Function ◽  
Processing Unit ◽  
Time Saving ◽  
Content Type ◽  
Central Processing ◽  
Cpu Time ◽  
Simple Geometry ◽  
Evaluation Time

Purpose Optimization processes and movement modeling usually require a high number of simulations. The purpose of this paper is to reduce global central processing unit (CPU) time by decreasing each evaluation time. Design Methodology Approach Remeshing the geometry at each iteration is avoided in the proposed method. The idea consists in using a fixed mesh on which functions are projected to represent geometry and supply. Findings Results are very promising. CPU time is reduced for three dimensional problems by almost a factor two, keeping a low relative deviation from usual methods. CPU time saving is performed by avoiding meshing step and also by a better initialization of iterative resolution. Optimization, movement modeling and transient-state simulation are very efficient and give same results as usual finite element method. Research Limitations Implications The method is restricted to simple geometry owing to the difficulty of finding spatial mathematical function describing the geometry. Moreover, a compromise between imprecision, caused by the boundary evaluation, and time saving must be found. Originality Value The method can be applied to optimize rotating machines design. Moreover, movement modeling is performed by shifting functions corresponding to moving parts.

scholarly journals Circuit Optimization Study According to the Maximum Principle

2021 ◽  
Vol 20 ◽  
pp. 362-371
Author(s):  
Alexander Zemliak
Keyword(s):  
Maximum Principle ◽  
Traditional Approach ◽  
Optimization Procedure ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
The Maximum Principle ◽  
Cpu Time ◽  
Optimization Study ◽  
Time Minimization

The minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behavior of a Hamiltonian for various strategies of optimization. The possibility of applying the maximum principle to the problem of optimization of electronic circuits is analyzed. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

Application of a collocation method based on linear barycentric interpolation for solving 2D and 3D Klein-Gordon-Schrödinger (KGS) equations numerically

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ömer Oruç
Keyword(s):  
Numerical Solutions ◽  
Interpolation Method ◽  
Processing Unit ◽  
Content Type ◽  
3 Dimensional ◽  
Central Processing ◽  
Barycentric Interpolation ◽  
Klein Gordon ◽  
2D And 3D ◽  
First Time

Purpose The purpose of this paper is to obtain accurate numerical solutions of two-dimensional (2-D) and 3-dimensional (3-D) Klein–Gordon–Schrödinger (KGS) equations. Design/methodology/approach The use of linear barycentric interpolation differentiation matrices facilitates the computation of numerical solutions both in 2-D and 3-D space within reasonable central processing unit times. Findings Numerical simulations corroborate the efficiency and accuracy of the proposed method. Originality/value Linear barycentric interpolation method is applied to 2-D and 3-D KGS equations for the first time, and good results are obtained.

scholarly journals Computer Time Minimizing for the Circuit Optimization

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Maximum Principle ◽  
Dynamic System ◽  
Traditional Approach ◽  
Optimization Procedure ◽  
Computer Time ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
The Maximum Principle ◽  
Cpu Time

The solution of a problem of analogue circuit optimization is mathematically defined as a controllable dynamic system. In this context the minimization of the processor time of designing can be formulated as a problem of time minimization for transitional process of dynamic system. A special control vector that changes the internal structure of the equations of optimization procedure serves as a principal tool for searching the best strategies with the minimal CPU time. In this case a well-known maximum principle of Pontryagin is the best theoretical approach for finding of the optimum structure of control vector. Practical approach for realization of the maximum principle is based on the analysis of behaviour of a Hamiltonian for various strategies of optimization. It is shown that in spite of the fact that the problem of optimization is formulated as a nonlinear task, and the maximum principle in this case isn't a sufficient condition for obtaining a minimum of the functional, it is possible to obtain the decision in the form of local minima. The relative acceleration of the CPU time for the best strategy found by means of maximum principle compared with the traditional approach is equal two to three orders of magnitude.

PRACTICAL PERFORMANCE ASSESSMENT OF ACCOMPANYING COORDINATE EXPANSION RECURRENCE RELATION ALGORITHM FOR COMPUTATION OF ELECTRON REPULSION INTEGRALS

2005 ◽  
Vol 04 (01) ◽  
pp. 139-149 ◽  
Author(s):  
MICHIO KATOUDA ◽  
MASATO KOBAYASHI ◽  
HIROMI NAKAI ◽  
SHIGERU NAGASE
Keyword(s):  
Computer Program ◽  
Recurrence Relation ◽  
Basis Set ◽  
Basis Sets ◽  
Processing Unit ◽  
Central Processing ◽  
Cpu Time ◽  
Electron Repulsion ◽  
Electron Repulsion Integrals ◽  
Practical Performance

We have developed a computer program for evaluation of electron repulsion integrals (ERIs) based on the accompanying coordinate expansion recurrence relation (ACE-RR) algorithm, which has been recently developed as an efficient algorithm for computation of ERIs using Pople-type basis sets (STO-3G and 6-31G, for example) and derivatives of ERIs [Kobayashi and Nakai, J Chem Phys121:4050 2004]. The computer program can be linked to GAMESS ab initio quantum chemistry program. The practical performance of the ACE-RR method is assessed by means of the central processing unit (CPU) time for the first direct self-consistent field cycle on a model system (4 × 4 × 4 cubic hydrogen lattice), taxol ( C 47 H 51 NO 14), and valinomycin ( C 54 H 90 N 6 O 18) using Pople-type basis sets. The considerable efficiency of the present ACE-RR method is demonstrated by measuring the CPU time. The present ACE-RR method is comparable to or at most 30% faster than the Pople–Hehre method which is also designed for efficient computation of ERIs using Pople-type basis sets. Furthermore, the ACE-RR method is drastically faster than the Dupuis–Rys–King method in the case where the degree of contraction of Pople-type basis sets is high: 7.5 times faster in the case of valinomycin using STO-6G basis set, for example.

scholarly journals Scheduling Two Identical Parallel Machines Subjected to Release Times, Delivery Times and Unavailability Constraints

Processes ◽  
2020 ◽  
Vol 8 (9) ◽  
pp. 1025
Author(s):  
Adel M. Al-Shayea ◽  
Mustafa Saleh ◽  
Moath Alatefi ◽  
Mageed Ghaleb
Keyword(s):  
Parallel Machines ◽  
Release Time ◽  
Processing Unit ◽  
Scheduling Problem ◽  
Identical Parallel Machines ◽  
Central Processing ◽  
Cpu Time ◽  
Release Times ◽  
Delivery Times ◽  
Input Variables

This paper proposes a genetic algorithm (GA) for scheduling two identical parallel machines subjected to release times and delivery times, where the machines are periodically unavailable. To make the problem more practical, we assumed that the machines are undergoing periodic maintenance rather than making them always available. The objective is to minimize the makespan (Cmax). A lower bound (LB) of the makespan for the considered problem was proposed. The GA performance was evaluated in terms of the relative percentage deviation (RPD) (the relative distance to the LB) and central processing unit (CPU) time. Response surface methodology (RSM) was used to optimize the GA parameters, namely, population size, crossover probability, mutation probability, mutation ratio, and pressure selection, which simultaneously minimize the RPD and CPU time. The optimized settings of the GA parameters were used to further analyze the scheduling problem. Factorial design of the scheduling problem input variables, namely, processing times, release times, delivery times, availability and unavailability periods, and number of jobs, was used to evaluate their effects on the RPD and CPU time. The results showed that increasing the release time intervals, decreasing the availability periods, and increasing the number of jobs increase the RPD and CPU time and make the problem very difficult to reach the LB.

Analysis of the structure of different optimization strategies

2020 ◽  
Vol 39 (3) ◽  
pp. 583-593
Author(s):  
Alexander Zemliak ◽  
Jorge Espinosa-Garcia
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Optimal Structure ◽  
Optimization Process ◽  
Main Element ◽  
Circuit Optimization ◽  
Control Vector ◽  
Processor Time ◽  
Content Type ◽  
Cpu Time

Purpose In this paper, on the basis of a previously developed approach to circuit optimization, the main element of which is the control vector that changes the form of the basic equations, the structure of the control vector is determined, which minimizes CPU time. Design/methodology/approach The circuit optimization process is defined as a controlled dynamic system with a special control vector. This vector serves as the main tool for generalizing the problem of circuit optimization and produces a huge number of different optimization strategies. The task of finding the best optimization strategy that minimizes processor time can be formulated. There is a need to find the optimal structure of the control vector that minimizes processor time. A special function, which is a combination of the Lyapunov function of the optimization process and its time derivative, was proposed to predict the optimal structure of the control vector. The found optimal positions of the switching points of the control vector give a large gain in CPU time in comparison with the traditional approach. Findings The optimal positions of the switching points of the components of the control vector were calculated. They minimize processor time. Numerical results are obtained for various circuits. Originality/value The Lyapunov function, which is one of the main characteristics of any dynamic system, is used to determine the optimal structure of the control vector, which minimizes the time of the circuit optimization process.

Acceleration of the numerical solution for the radiative transfer equation using a modified relaxation factor

2020 ◽  
Vol 37 (5) ◽  
pp. 1823-1847 ◽  
Author(s):  
Carlos Enrique Torres-Aguilar ◽  
Jesús Xamán ◽  
Pedro Moreno-Bernal ◽  
Iván Hernández-Pérez ◽  
Ivett Zavala-Guillén ◽  
...  
Keyword(s):  
Radiative Transfer ◽  
Numerical Solution ◽  
Transfer Equation ◽  
Radiative Transfer Equation ◽  
Boundary Surface ◽  
Processing Unit ◽  
Content Type ◽  
Cpu Time ◽  
Relaxation Factor ◽  
Factor Method

Purpose The purpose of this study is to propose a novel relaxation modified factor to accelerate the numerical solution of the radiative transfer equation (RTE) with several high-resolution total variation diminishing schemes. The methodology proposed is denoted as the X-factor method. Design/methodology/approach The X-factor method was compared with the technique deferred-correction (DC) for the calculations of a two-dimensional cavity with absorting-emiting-scatteting gray media using the discrete ordinates method. Four parameters were considered to evaluate: the absorption coefficient, the emissivity of boundary surface, the scattering albedo and under-relaxation factor. Findings The results showed the central processing unit (CPU) time of X-factor method was lower than DC. The reductions of CPU time with the X-factor method were observed from 0.6 to 75.4%. Originality/value The superiority of the X-factor method over DC was showed with the reduction of CPU time of the numerical solution of RTE for evaluated cases.

scholarly journals Microbial Community Analysis with Ribosomal Gene Fragments from Shotgun Metagenomes

2015 ◽  
Vol 82 (1) ◽  
pp. 157-166 ◽  
Author(s):  
Jiarong Guo ◽  
James R. Cole ◽  
Qingpeng Zhang ◽  
C. Titus Brown ◽  
James M. Tiedje
Keyword(s):  
Community Analysis ◽  
Rrna Genes ◽  
Metagenomic Data ◽  
Rrna Gene ◽  
Processing Unit ◽  
Metagenomic Sequencing ◽  
Ssu Rrna ◽  
Variable Regions ◽  
Content Type ◽  
Central Processing

ABSTRACTShotgun metagenomic sequencing does not depend on gene-targeted primers or PCR amplification; thus, it is not affected by primer bias or chimeras. However, searching rRNA genes from large shotgun Illumina data sets is computationally expensive, and no approach exists for unsupervised community analysis of small-subunit (SSU) rRNA gene fragments retrieved from shotgun data. We present a pipeline, SSUsearch, to achieve the faster identification of short-subunit rRNA gene fragments and enabled unsupervised community analysis with shotgun data. It also includes classification and copy number correction, and the output can be used by traditional amplicon analysis platforms. Shotgun metagenome data using this pipeline yielded higher diversity estimates than amplicon data but retained the grouping of samples in ordination analyses. We applied this pipeline to soil samples with paired shotgun and amplicon data and confirmed bias againstVerrucomicrobiain a commonly used V6-V8 primer set, as well as discovering likely bias againstActinobacteriaand forVerrucomicrobiain a commonly used V4 primer set. This pipeline can utilize all variable regions in SSU rRNA and also can be applied to large-subunit (LSU) rRNA genes for confirmation of community structure. The pipeline can scale to handle large amounts of soil metagenomic data (5 Gb memory and 5 central processing unit hours to process 38 Gb [1 lane] of trimmed Illumina HiSeq2500 data) and is freely available athttps://github.com/dib-lab/SSUsearchunder a BSD license.

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