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Efficient MILP formulations for AC optimal power flow to reduce computational effort

INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2020年第8期30卷 1-18页

作者： Nozarian, Mahdi Nikoofard, Amir Hossein Fereidunian, Alireza KN Toosi Univ Technol Fac Elect Engn POB 15875-4416 Tehran Iran

AC optimal power flow (ACOPF) is a nonlinear and non-convex problem that might include various constraints. The methods in the literature for solving this problem may suffer from premature convergence and high computational effort. In this study, ACOPF is formulated as a mixed-integer linear programming (MILP) that allows problem modeling with a closer look at the limitations of actual operating conditions along with other common constraints. This article contributes to literature by presenting efficient MILP methods of the ACOPF problem in terms of various actual constraints, such as valve loading cost, prohibited operating zones, and the multi-fuel units. The proposed methods aim at reducing the computational effort with a sufficient improvement in finding the optimal solution. Effectiveness and accuracy of the proposed methods are evaluated on the standard IEEE 30-bus, 118-bus, and the polish 2746-bus test systems. Numerical results confirm the validity and quality of the proposed MILP methods with convexified various actual constraints (MILP_CVAC) for the ACOPF problem. A significant reduction is found in computing time to solve the ACOPF problem with the proposed MILP_CVAC methods due to the use of strong MILP solvers and the convexity of the model, without affecting the accuracy. In some cases, the results show several hundred times shorter computation time compared to nonclassical methods.

关键词： AC optimal power flow (ACOPF) actual constraints computational effort MILP methods with convexified various actual constraints (MILP_CVAC) mixed-integer linear programming (MILP)

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The Reliability of Confidence Intervals for computational effort Comparisons 07

The Reliability of Confidence Intervals for Computational Ef...

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Annual Conference of Genetic and Evolutionary Computation Conference

作者： Walker, Matthew Edwards, Howard Messom, Chris Massey Univ Inst Informat & Math Sci Auckland New Zealand

ISBN: (纸本)9781595936974

This paper analyses the reliability of confidence intervals for Koza's computational effort statistic. First. we conclude that dependence between the observed minimum generation and the observed cumulative probability of success leads to the production of more reliable confidence intervals for our preferred method. Second, we show that confidence intervals front 80% to 95% have appropriate levels of performance. Third. simulated data is used to consider the effect of large minimum generations and the confidence intervals are again found to be reliable. Finally, results from four large datasets collected from real genetic programming experiments are used to provide even more empirical evidence that, the method for producing confidence intervals is reliable.

关键词： Genetic Programming computational effort Confidence Intervals Wilson's Method

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A Comparative Study of One-Step and Multi-Step Numerical Methods for Solving Ordinary Differential Equations in Water Tank Drainage Systems

ENGINEERING REPORTS

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ENGINEERING REPORTS 2025年第3期7卷

作者： Alemu Wendimu, Abebe Matusu, Radek Gazdos, Frantisek Shaikh, Ibrahim Tomas Bata Univ Zlin Fac Appl Informat Dept Automat & Control Engn Zlin Czech Republic

Numerical methods are essential for solving differential equations in applications such as water drainage systems, where precise water level control is critical for industrial and environmental processes. This study compares one-step numerical methods naming explicit Euler, implicit Euler, implicit midpoint, modified Euler, and fourth-order Runge-Kutta (RK4) with multi-step numerical methods, including Adams-Bashforth, Adams-Moulton, and Predictor-corrector schemes, to solve ordinary differential equations for water tank drainage systems. The analysis focuses on accuracy, stability, computational efficiency, and optimal step size selection. MATLAB scripts and Python (Google Colab) were used to evaluate each method's performance by calculating local and global errors, with detailed analyses of error versus step size, error versus computational effort, and computational effort versus step size. The results reveal that multi-step numerical methods provide superior accuracy and stability for long-term simulations but require greater memory resources, whereas one-step numerical methods are computationally faster but sensitive to step size selection, significantly influencing solution accuracy. This study offers practical recommendations for selecting numerical methods based on application-specific requirements, providing insights into optimizing numerical approaches for systems requiring precise water level control and balancing accuracy with computational efficiency.

关键词： accuracy computational effort explicit and implicit multi-step methods nonlinear ODEs one-step methods stability region step size

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Choice of the hypothesis matrix for using the Anova-type-statistic

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STATISTICS & PROBABILITY LETTERS 2025年 219卷

作者： Sattler, Paavo Rosenbaum, Manuel Tech Univ Dortmund Inst Math Stat & Ind Applicat Fac Stat Joseph Von Fraunhofer Str 2-4 D-44221 Dortmund Germany Ulm Univ Inst Stat Helmholtzstr 20 D-89081 Ulm Germany

Initially developed in Brunner et al. (1997), the Anova-type-statistic (ATS) is one of the most used quadratic forms for testing multivariate hypotheses for a variety of different parameter vectors B is an element of R d . Tests based on a version of the ATS are usually preferable over those based on other quadratic forms, like the Wald-type-statistic. However, the same null hypothesis HB = y can be expressed by various hypothesis matrices H is an element of R m x d and corresponding vectors y is an element of R m , yielding different values of the test statistic. Since this can entail differing test decisions, we investigate under which conditions certain tests using different hypothesis matrices coincide. In this manuscript, we show that for several versions of the Anova-typestatistic, for each hypothesis HB = y a companion matrix with a minimal number of rows can be constructed, testing the same hypothesis but also always yielding the same test decisions. This can substantially reduce computation time, as demonstrated in several conducted simulations.

关键词： Multivariate statistic computational effort Hypothesis matrix Anova-type-statistic Quadratic-forms

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Genetic Programming Using Dynamic Population Variation for computational efforts Reduction in System Modeling

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Journal of Shanghai Jiaotong university(Science) 2012年第2期17卷 190-196页

作者：陶砚蕴曹健李明禄 Department of Computer Science and Engineering Shanghai Jiaotong University Shanghai Key Laboratory of Scalable Computing and System

In this paper,we propose genetic programming(GP) using dynamic population variation(DPV) with four innovations for reducing computational efforts.A new stagnation phase definition and characteristic measure are defined for our *** exponential pivot function is proposed to our DPV method in conjunction with the new stagnation phase *** appropriate population variation formula is suggested to accelerate *** efficacy of these innovations in our DPV is examined using six benchmark *** among the difierent characteristic measures has been conducted for regression problems and the new proposed measure outperformed other *** is proved that our DPV has the capacity to provide solutions at a lower computational effort compared with previously proposed DPV methods and standard genetic programming in most ***,our DPV approach introduced in GP could also rapidly find an excellent solution as well as standard GP in system modeling problems.

关键词： dynamic population variation(DPV) stagnation phase exponential pivot function computational effort average number of evaluation diversity

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A study on Koza's performance measures

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GENETIC PROGRAMMING AND EVOLVABLE MACHINES 2015年第3期16卷 327-349页

作者： Barrero, David F. Castano, Bonifacio R-Moreno, Maria D. Camacho, David Univ Alcala de Henares Dept Automat Madrid Spain Univ Alcala de Henares Dept Matemat Madrid Spain Univ Autonoma Madrid Dept Informat Madrid Spain

John R. Koza defined several metrics to measure the performance of an Evolutionary Algorithm that have been widely used by the Genetic Programming community. Despite the importance of these metrics, and the doubts that they have generated in many authors, their reliability has attracted little research attention, and is still not well understood. The lack of knowledge about these metrics has likely contributed to the decline in their usage in the last years. This paper is an attempt to increase the knowledge about these measures, exploring in which circumstances they are more reliable, providing some clues to improve how they are used, and eventually making their use more justifiable. Specifically, we investigate the amount of uncertainty associated with the measures, taking an analytical and empirical approach and reaching theoretical boundaries to the error. Additionally, a new method to calculate Koza's performance measures is presented. It is shown that these metrics, under common experimental configurations, have an unacceptable error, which can be arbitrary large in certain conditions.

关键词： Genetic Programming computational effort Performance measures Experimental methods Measurement error

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Fast EMC Analysis of Systems Consisting of PCBs and Metallic Antenna Structures by a Hybridization of PEEC and MoM

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IEEE TRANSACTIONS ON ELECTROMAGNETIC COMPATIBILITY 2010年第4期52卷 962-973页

作者： Vahrenholt, Volker Bruens, Heinz-Dietrich Singer, Hermann Hamburg Univ Technol TUHH Inst Electromagnet Theory D-21079 Hamburg Germany

This paper presents hybridization approaches of the method of moments (MoMs) and the partial-element equivalent-circuit (PEEC) method in order to achieve a significant reduction of numerical complexity. The MoMs is applied as a full-wave method-only where it is necessary-to 3-D metallic scatterers such as antennas. Furthermore, the PEEC method is applied to single-layer printed circuit boards combined with an effective dielectric constant assuming an infinite dielectric in order to avoid discretization of the substrate. In the hybrid approaches of the MoMs and the PEEC method, both techniques are applied consecutively compared to a full-wave MoMs model. The validity of the hybrid approaches and the gain in numerical computation time are demonstrated by three numerical examples, which are related to electromagnetic compatibility. The results are verified by full-wave MoMs reference calculations and by a measurement.

关键词： computational effort dielectric hybridization method of moments (MoMs) partial element equivalent circuit (PEEC)

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Stochastic Runge-Kutta Rosenbrock type methods for SDE systems

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APPLIED NUMERICAL MATHEMATICS 2017年 115卷 1-15页

作者： Amiri, Sadegh Hosseini, S. Mohammad Tarbiat Modares Univ Dept Appl Math Fac Math Sci POB 14115-175 Tehran Iran Shahid Sattari Univ Fac Basic Sci Tehran IR Iran

In this paper we introduce a family of stochastic Runge-Kutta Rosenbrock (SRKR) type methods for multi-dimensional Ito stochastic differential equations (SDEs). The presented class of semi-implicit methods need less computational effort in comparison with some implicit ones. General order conditions for the coefficients and the random variables of the SRKR methods are obtained. Then a set of order conditions for a subclass of stochastic weak second order is given. Numerical examples are presented to demonstrate the efficiency and accuracy of the new schemes. (c) 2016 IMACS. Published by Elsevier B.V. All rights reserved.

关键词： Stochastic Runge-Kutta Rosenbrock type methods Stochastic differential equations Stochastic B-series computational effort

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A Simplified Feedforward Carrier Recovery Algorithm for Coherent Optical QAM System

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JOURNAL OF LIGHTWAVE TECHNOLOGY 2011年第5期29卷 801-807页

作者： Li, Xin Cao, Yinwen Yu, Song Gu, Wanyi Ji, Yuefeng Beijing Univ Posts & Telecommun Key Lab Informat Photon & Opt Commun Beijing 10086 Peoples R China

A simplified quadrature amplitude modulation (QAM) feedforward carrier recovery algorithm is proposed. By introducing a new two-stage estimation structure and sliding-block approach, the required computational effort can be significantly reduced with a tolerable performance deterioration compared with the original algorithm. In order to choose the size of the sliding block properly, an analytical model is proposed that takes the optical SNR (OSNR) and the laser-linewidth-times symbol-rate product into account. The model reveals different influence of OSNR and the laser-linewidth-times symbol-rate product on the performance of any carrier recovery algorithm. The performance of the simplified algorithm is evaluated by Monte Carlo simulations for square 16-, 64-, and 256-QAM. The simulation results show that the computational effort for each symbol can be significantly reduced at the cost of a 11% reduction of laser linewidth tolerance.

关键词： computational effort feedforward carrier recovery (FFCR) quadrature amplitude modulation (QAM) sliding block

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Frequency Stability Enhancement of Low-Inertia Large-Scale Power System Based on Grey Wolf Optimization

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IEEE ACCESS 2022年 10卷 11657-11668页

作者： Lim, Sunghoon Choi, Donghee Lee, Soo Hyoung Kang, Chongqing Park, Jung-Wook Yonsei Univ Sch Elect & Elect Engn Seoul 03722 South Korea Cheongju Univ Div Converged Elect Engn Cheongju 28503 South Korea Mokpo Natl Univ Dept Elect & Control Engn Jeollanam Do 58554 South Korea Tsinghua Univ Dept Elect Engn Beijing 100084 Peoples R China

The high penetration of converter-based distributed generations (DGs) to power system can give rise to the lack of rotational inertia while replacing the conventional synchronous generators (SGs), which provide the primary frequency reserve (PFR) in power systems. As the result, the decrease in PFR aggravates the frequency stability. To overcome this problem, the droop coefficients of governors in the remaining conventional SGs must be re-determined newly and properly. This paper proposes a new solution based on the grey wolf optimization (GWO) method to optimally select the droop coefficients of SG governors in the low-inertia large-scale power system due to the high penetration of renewables. The proposed solution is very effective for reducing the computational effort significantly, and it is able to recover not only the steady-state but also the transient frequency stability. To verify the effectiveness of proposed optimization solution based on the GWO method, several case studies are carried out on the practical Korea electric power system with the penetration of wind power plants of 4 GW.

关键词： Power system stability Optimization Transient analysis Frequency response Steady-state Stability criteria Renewable energy sources computational effort distributed generations droop coefficients frequency stability grey wolf optimization large-scale power system

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