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A decomposition method based on SQP for a class of multistage stochastic nonlinear programs

SIAM JOURNAL ON OPTIMIZATION 2003年第1期14卷 200-222页

作者： Liu, XW Zhao, GY Natl Univ Singapore Singapore MIT Alliance Singapore 117576 Singapore Natl Univ Singapore Dept Math Singapore 119260 Singapore

Multistage stochastic programming problems arise in many practical situations, such as production and manpower planning, portfolio selections, and so on. In general, the deterministic equivalents of these problems can be very large and may not be solvable directly by general-purpose optimization approaches. sequential quadratic programming (SQP) methods are very effective for solving medium-size nonlinear programming. By using the scenario analysis technique, a decomposition method based on SQP for solving a class of multistage stochastic nonlinear programs is proposed, which generates the search direction by solving parallelly a set of quadratic programming subproblems with much less size than the original problem at each iteration. Conjugate gradient methods can be introduced to derive the estimates of the dual multiplier associated with the nonanticipativity constraints. By selecting the step-size to reduce an exact penalty function sufficiently, the algorithm terminates finitely at an approximate optimal solution to the problem with any desirable accuracy. Some preliminary numerical results are reported.

关键词： multistage stochastic nonlinear programs sequential quadratic programming scenario analysis decomposition

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NONLINEAR MODEL BASED PREDICTIVE CONTROLLER OF A BUCK BOOST CONVERTER

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IFAC Proceedings Volumes 2005年第1期38卷 193-198页

作者： Martín J. Pomar García Julio E. Normey Rico Eduardo Camponogara Depto. de Automação e Sistemas Universidade Federal de Santa Catarina Cx.P. 476 88040-900 Florianópolis SC BRASIL

This paper presents a Nonlinear Model Based Predictive Controller (NMBPC) of a buck-boost converter (BBC). The NMBPC uses a nonlinear prediction of the system outputs based on a discretization of the average continuous model of the BBC, assuming the duty ratio as the control variable. A classical quadratic cost function J is minimized at each sample time using a sequential quadratic programming (SQP) optimization algorithm that guarantees that the obtained control action gives a local optimal value of J . The tuning of the controller parameters is defined to obtain a compromise between performance and robustness. Simulation results in a wide range of the output voltage show that the proposed control strategy yields very fast time responses even under varying load situations.

关键词： Model Based Predictive Control Nonlinear Systems Optimization sequential quadratic programming Buck-Boost Converter

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Predictive Cruise Control of Full Electric Vehicles: A Comparison of Different Solution Methods ⁎

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IFAC-PapersOnLine 2021年第10期54卷 120-125页

作者： Hongqing Chu Shiying Dong Jinlong Hong Hong Chen Bingzhao Gao School of Automotive Studies Tongji University Shanghai China Department of Control Science and Engineering Jilin university Chuangchun China

The integration of electrification and intelligence is of great significance to alleviating range anxiety of electric vehicles. Predictive cruise control (PCC), which optimizes the longitudinal driving strategies by using the upcoming road traffic information, can further improve the vehicle economy. The paper gives the comparison of different solution methods regarding PCC problem of electric vehicles. The car-following optimization problem is formulated as a constrained nonlinear optimization problem. For ease of presentation, the car-following optimization problem is reformulated as a standard form of the optimization problem in continuous time domain. Then, the standard form of the optimization problem is transformed from a continuous form to a discrete form by using Euler method and Gauss pseudospectral method. Two common solution methods, that is dynamic programming and sequential quadratic programming, are used to solve the optimization problem in discrete form. Simulations are performed to demonstrate the comparison of different solution schemes.

关键词： Predictive cruise control electric vehicle model predictive control Euler method Gauss pseudospectral method dynamic programming sequential quadratic programming

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A COMPARATIVE STUDY OF DETERMINISTIC AND STOCHASTIC OPTIMIZATION METHODS FOR INTEGRATED DESIGN OF PROCESSES

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IFAC Proceedings Volumes 2005年第1期38卷 335-340页

作者： Mario Francisco Silvana Revollar Pastora Vega Rosalba Lamanna Departamento de Informática y Automática. Universidad de Salamanca. Spain Universidad Simón Bolívar. Dpto. Procesos y Sistemas. Caracas 1081A Venezuela

This paper focuses on the application of stochastic (genetic algorithms, simulated annealing) and deterministic (sequential quadratic programming) optimization methods for the Integrated Design of processes considering dynamical non-linear models. Moreover, a hybrid methodology that combines both types of methods is proposed, showing an improvement on performance. Controllability indexes such as disturbance sensitivity gains, the H ∞ norm, and the ISE were considered to obtain optimum disturbance rejection. In order to illustrate and validate our proposal, an activated sludge process with PI schemes is taken. The problem is stated as a multiobjective non-linear optimization problem with non-linear constraints. The application of the mentioned strategies is discussed. The results are encouraging for future application of these techniques to solve synthesis MINLP problems.

关键词： Integrated Design sequential quadratic programming genetic algorithms stochastic optimization controllability

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An advanced heuristic approach for a nonlinear mathematical based medical smoking model

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RESULTS IN PHYSICS 2022年第0期32卷 105137-105137页

作者： Saeed, Tareq Sabir, Zulqurnain Alhodaly, Mohammed Sh. Alsulami, Hamed H. Sanchez, Yolana Guerrero Hazara Univ Dept Math & Stat Mansehra Pakistan King Abdulaziz Univ Fac Sci Dept Math Nonlinear Anal & Appl Math NAAM Res Grp POB 80203 Jeddah 21589 Saudi Arabia Univ Murcia Dept Anat & Psicobiol Murcia 30001 Spain

The present study is related to solve the nonlinear dynamics of a smoke model using artificial neural networks (ANNs) under the optimization procedures of global heuristic and local search scheme. The genetic algorithm (GA) and sequential quadratic programming (SQP), i.e., GA-SQP used as global-local search approaches. The smoke nonlinear medical model depends upon four categories named as potential smokers, temporary smokers, smokers and permanent smokers. For solving these categories of the smoke system, an error based objective function is designed using these nonlinear equations and the initial conditions of the model. The performance through optimization of the objective function is testified using the ANNs and the hybrid combination of the GASQP for solving the nonlinear dynamics of the smoke system. To check the perfection of the proposed stochastic approach, the obtained results through the hybrid of GA-SQP are compared with the Adams scheme. Moreover, the designed scheme through statistical performances using different operators authenticates the reliability and stability to solve the nonlinear smoke model.

关键词： Nonlinear smoke system Artificial neural networks Adams results sequential quadratic programming Genetic algorithms Statistical analysis

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Design of evolutionary cubic spline intelligent solver for nonlinear Painleve-I transcendent

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INTERNATIONAL JOURNAL OF MODERN PHYSICS B 2021年第29期35卷

作者： Ali, Sharafat Ahmad, Iftikhar Raja, Muhammad Asif Zahoor Ahmad, Siraj ul Islam Shoaib, Muhammad Univ Gujrat Dept Math Gujrat 50700 Pakistan Natl Yunlin Univ Sci & Technol Future Technol Res Ctr 123 Univ RdSect 3 Touliu 64002 Yunlin Taiwan COMSATS Univ Islamabad Dept Phys Islamabad 44000 Pakistan COMSATS Univ Islamabad Dept Math Attock Campus Attock 43600 Pakistan

In this research paper, an innovative bio-inspired algorithm based on evolutionary cubic splines method (CSM) has been utilized to estimate the numerical results of nonlinear ordinary differential equation Painleve-I. The computational mechanism is used to support the proposed technique CSM and optimize the obtained results with global search technique genetic algorithms (GAs) hybridized with sequential quadratic programming (SQP) for quick refinement. Painleve-I is solved by the proposed technique CSM-GASQP. In this process, variation of splines is implemented for various scenarios. The CSM-GASQP produces an interpolated function that is continuous upto its second derivative. Also, splines proved to be stable than a single polynomial fitted to all points, and reduce wiggles between the tabulated points. This method provides a reliable and excellent procedure for adaptation of unknown coefficients of splines by searching globally exploiting the performance of GA-SQP algorithms. The convergence, exactness and accuracy of the proposed scheme are examined through the statistical analysis for the several independent runs.

关键词： Painleve-I cubic splines method computational hybrid mechanism genetic algorithm sequential quadratic programming numerical computing

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Fast Intercept Trajectory Optimization for Multi-stage Air Defense Missile Using Hybrid Algorithm

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Procedia Engineering 2013年 67卷 447-456页

作者： F.B. Wang C.H. Dong School of Aeronautics Science and Engineering Beihang University Beijing 100191 China School of Astronautics Beihang University Beijing 100191 China

A hybridalgorithmconsists of particle swarm optimization (PSO) and sequential quadratic programming (SQP) is proposed, and appliesto solve the optimal trajectory with maximizing the terminal velocity at predict impact point (PIP) for multi-stage air defense missile. This hybrid optimization approach combines the advantages of PSO as a global optimizer and complemented with SQP to find the accurate local optima. A simple plane motion equation of multi-stage air defense is establishedwith respect to trajectory referenceframe firstly, and restrictions on path parameters and terminal conditions are *** task with given PIP, intercept trajectory optimization problem is a classical continuous optimal control problem. Then control of angle of attack (AOA) is parameterized according to empirical equations so that converting the continuousoptimal control problem into a parameters optimization ***, the hybrid algorithm is employed to solve this parameters optimization problem effectively with high accuracy. Several simulations and comparative cases are carried out, simulation results illustrate the hybrid method is feasible and it can fast converges to the optimal solution. Comparison results with the conventional optimization algorithm confirm that the proposed algorithm is more accurate and effective and more suited for missile trajectory profile optimization.

关键词： Trajectory optimization Air defense missile Hybrid algorithm Particle Swarm Optimization sequential quadratic programming

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A novel study of Morlet neural networks to solve the nonlinear HIV infection system of latently infected cells

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RESULTS IN PHYSICS 2021年 25卷 104235-104235页

作者： Umar, Muhammad Sabir, Zulqurnain Raja, Muhammad Asif Zahoor Baskonus, Haci Mehmet Yao, Shao-Wen Ilhan, Esin Hazara Univ Dept Math & Stat Mansehra Pakistan Natl Yunlin Univ Sci & Technol Future Technol Res Ctr 123 Univ RdSect 3 Touliu 64002 Yunlin Taiwan Harran Univ Dept Math & Sci Educ Sanliurfa Turkey Henan Polytech Univ Sch Math & Informat Sci Jiaozuo 454000 Henan Peoples R China Kirsehir Ahi Evran Univ Kirsehir Turkey

The aim of this study is to provide the numerical outcomes of a nonlinear HIV infection system of latently infected CD4+ T cells exists in bioinformatics using Morlet wavelet (MW) artificial neural networks (ANNs) optimized initially with global search of genetic algorithms (GAs) hybridized for speedy local search of sequential quadratic programming (SQP), i.e., MW-ANN-GA-SQP. The design of an error function is presented by designing the MW-ANN models for the differential equations along with the initial conditions that represent the HIV infection system involving latently infected CD4+ T cells. The precision and persistence of the presented approach MW-ANN-GA-SQP are recognized through comparative studies from the results of the Runge-Kutta numerical scheme for solving the HIV infection spread system in case of single and multiple trails of the MW-ANN-GA-SQP. Statistical estimates with 'Theil's inequality coefficient' and 'root mean square error' based indices further validate the sustainability and applicability of proposed MW-ANN-GA-SQP solver.

关键词： Morlet wavelets HIV infection models Genetic algorithms Neural networks sequential quadratic programming Bioinformatics

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Optimal designs for mixed continuous and binary responses with quantitative and qualitative factors

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JOURNAL OF MULTIVARIATE ANALYSIS 2021年 182卷 104712-104712页

作者： Kao, Ming-Hung Khogeer, Hazar Arizona State Univ Sch Math & Stat Sci Tempe AZ 85287 USA

This work is concerned with optimal designs for multivariate regression of responses of mixed variable types (continuous and binary) on quantitative and qualitative factors. New complete class results with respect to the Loewner ordering, and relevant Chebyshev systems are derived to identify a small class of designs, within which locally optimal designs can be found for a group of models and optimality criteria. The complete class results facilitate the search of optimal designs via some general-purpose optimization techniques. Extensions of some previous results for characterizing optimal designs are also provided. (C) 2020 Elsevier Inc. All rights reserved.

关键词： Approximate design Chebyshev system Complete class Optimality criteria sequential quadratic programming

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Application of Legendre polynomials based neural networks for the analysis of heat and mass transfer of a non-Newtonian fluid in a porous channel

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ADVANCES IN CONTINUOUS AND DISCRETE MODELS 2022年第1期2022卷 7-7页

作者： Khan, Naveed Ahmad Sulaiman, Muhammad Kumam, Poom Alarfaj, Fawaz Khaled Abdul Wali Khan Univ Mardan Dept Math Mardan 23200 KP Pakistan King Mongkuts Univ Technol Thonburi KMUTT Ctr Excellence Theoret & Computat Sci TaCS CoE Bangkok 10140 Thailand King Mongkuts Univ Technol Thonburi KMUTT Fac Sci Dept Math Bangkok 10140 Thailand China Med Univ China Med Univ Hosp Dept Med Res Taichung 40402 Taiwan Imam Mohammad Ibn Saud Islamic Univ Dept Comp & Informat Sci Riyadh 11564 Saudi Arabia

In this paper, the mathematical models for flow and heat-transfer analysis of a non-Newtonian fluid with axisymmetric channels and porous walls are analyzed. The governing equations of the problem are derived by using the basic concepts of continuity and momentum equations. Furthermore, artificial intelligence-based feedforward neural networks (ANNs) are utilized with hybridization of a generalized normal-distribution optimization (GNDO) algorithm and sequential quadratic programming (SQP) to study the heat-transfer equations and calculate the approximate solutions for the momentum of a non-Newtonian fluid. Legendre polynomials based Legendre neural networks (LNN) are used to develop a mathematical model for the governing equations, which are further exploited by the global search ability of GNDO and SQP for rapid localization convergence. The proposed technique is applied to study the effect of variations in Reynolds number Re on the velocity profile (f') and the temperature profile (q). The results obtained by the LeNN-GNDO-SQP algorithm are compared with the differential transformation method (DTM), which shows the stability of the results and the correctness of the technique. Extensive graphical and statistical analyses are conducted in terms of minimum, mean, and standard deviation based on fitness value, absolute errors, mean absolute deviation (MAD), error in the Nash-Sutcliffe efficiency (NSE), and root mean square error (RMSE).

关键词： Non-Newtonian fluid Porous media Heat and mass transfer Weighted Legendre neural networks Hybrid soft computing Generalized normal-distribution optimization sequential quadratic programming Machine learning

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