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.

scholarly journals Selection of Control Vector Switching Points for Circuit Optimization

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Lyapunov Function ◽  
Dynamic System ◽  
Design Process ◽  
Time Derivative ◽  
Computational Cost ◽  
Optimal Structure ◽  
Control Vector ◽  
Processor Time ◽  
Design Algorithm ◽  
Cpu Time

The process of optimizing the circuit is formulated as a controlled dynamic system. A special control vector has been defined to redistribute the computational cost between circuit analysis and parametric optimization. This redistribution will help solve the task of optimizing the circuit for minimum CPU time. In this case, the task of optimizing the circuit with minimal CPU time can be formulated as the classical optimal control problem for minimizing some functional. The concept of the Lyapunov function of a controlled dynamic system is used to analyze the main characteristics of the design process. An analysis of the Lyapunov function and its time derivative makes it possible to predict the optimal structure of the control vector for constructing an optimal or quasi-optimal circuit design algorithm. The results are based on the previously discovered effect of accelerating the design process. In this case, the optimal structure of the control vector is determined, which minimizes processor time.

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.

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.

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.

Study of different optimization strategies for analogue circuits

2016 ◽  
Vol 35 (3) ◽  
Author(s):  
Alexander Zemliak ◽  
Fernando Reyes ◽  
Sergio Vergara
Keyword(s):  
Dynamical System ◽  
Optimal Control ◽  
Lyapunov Function ◽  
Optimal Control Theory ◽  
Design Methodology ◽  
Initial Part ◽  
Circuit Optimization ◽  
Optimization Strategy ◽  
Analogue Circuit ◽  
Cpu Time

Purpose In this paper, we propose further development of the generalized methodology for analogue circuit optimization. This methodology is based on optimal control theory. This approach generates many different circuit optimization strategies. We lead the problem of minimizing the CPU time needed for circuit optimization to the classical problem of minimizing a functional in optimal control theory. Design/methodology/approach The process of analogue circuit optimization is defined mathematically as a controllable dynamical system. In this context, we can formulate the problem of minimizing the CPU time as the minimization problem of a transitional process of a dynamical system. To analyse the properties of such a system, we propose to use the concept of the Lyapunov function of a dynamical system. This function allows us to analyse the stability of the optimization trajectories and to predict the CPU time for circuit optimization by analysing the characteristics of the initial part of the process. Findings We present numerical results that show that we can compare the CPU time for different circuit optimization strategies by analysing the behaviour of a special function. We establish that, for any optimization strategy, there is a correlation between the behaviour of this function and the CPU time that corresponds to that strategy. Originality/value The analysis shows that Lyapunov function of optimization process and its time derivative can be informative sources for searching a strategy, which has minimal processor time expense. This permits to predict the best optimization strategy by analyzing only initial part of the optimization process.

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.

scholarly journals Study of the Dynamic Characteristics of Some Circuit Optimization Strategies

2020 ◽  
Vol 19 ◽  
Keyword(s):  
Optimal Control ◽  
Lyapunov Function ◽  
Design Process ◽  
Analog Circuits ◽  
Analog Circuit ◽  
Time Derivative ◽  
Computational Cost ◽  
Design Strategies ◽  
Processor Time ◽  
Cpu Time

The work explores the possibility of a significant reduction in processor time required to optimize analog circuits. For this, we can reformulate and generalize the problem of chain optimization based on the approaches of optimal control theory. The analog circuit design process is formulated as a dynamic controlled system. A special control vector has been defined to redistribute the computational cost between circuit analysis and parametric optimization. This redistribution significantly reduces CPU time. The task of designing a circuit for the minimum processor time can be formulated as a classical optimal control problem while minimizing some functional. The introduction of the concept of the Lyapunov function of a controlled dynamic system made it possible to use it to analyse the main characteristics of the design process. An analysis of the behaviour of a special function, which is a combination of the Lyapunov function and its time derivative, made it possible to compare various design strategies and select the best ones that are executed in minimal CPU time.

Transient elastodynamic analysis with a combination of convolution quadrature method and pseudo-initial condition method

2018 ◽  
Vol 36 (1) ◽  
pp. 334-355
Author(s):  
Yuan Li ◽  
J. Zhang ◽  
Yudong Zhong ◽  
Xiaomin Shu ◽  
Yunqiao Dong
Keyword(s):  
Initial Conditions ◽  
Initial Condition ◽  
Quadrature Method ◽  
Memory Requirement ◽  
Content Type ◽  
Convolution Quadrature ◽  
Force Method ◽  
Cpu Time ◽  
Condition Method ◽  
Convolution Quadrature Method

Purpose The Convolution Quadrature Method (CQM) has been widely applied to solve transient elastodynamic problems because of its stability and generality. However, the CQM suffers from the problems of huge memory requirement in case of direct implementation in time domain or CPU time in case of its reformulation in Laplace domain. The purpose of this paper is to combine the CQM with the pseudo-initial condition method (PICM) to achieve a good balance between memory requirement and CPU time. Design/methodology/approach The combined methods first subdivide the whole analysis into a few sub-analyses, which is dealt with the PICM, namely, the results obtained by previous sub-analysis are used as the initial conditions for the next sub-analysis. In each sub-analysis, the time interval is further discretized into a number of sub-steps and dealt with the CQM. For non-zero initial conditions, the pseudo-force method is used to transform them into equivalent body forces. The boundary face method is employed in the numerical implementation. Three examples are analyzed. Results are compared with analytical solutions or FEM results and the results of reformulated CQM. Findings Results demonstrate that the computation time and the storage requirement can be reduced significantly as compared to the CQM, by using the combined approach. Originality/value The combined methods can be successfully applied to the problems of long-time dynamic response, which requires a large amount of computer memory when CQM is applied, while preserving the CQM stability. If the number of time steps is high, then the accuracy of the proposed approach can be deteriorated because of the pseudo-force method.

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