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Global Convergence and Asymptotic Optimality of the Heavy Bell Method for a Class of Nonconvex optimization Problems

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IEEE CONTROL SYSTEMS LETTERS 2022年 6卷 2449-2454页

作者： Ugrinovskii, V Petersen, I. R. Shames, I Australian Natl Univ Res Sch Engn Canberra ACT 2601 Australia Australian Natl Univ Sch Engn CIICADA Lab Canberra ACT 2601 Australia

In this letter we revisit the famous heavy ball method and study its global convergence for a class of non-convex problems with sector-bounded gradient. We characterize the parameters that render the method globally convergent and yield the best R-convergence factor. We show that for this family of functions, this convergence factor is superior to the factor obtained from the triple momentum method.

关键词： optimization algorithms robust control

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QPALM-OCP: A Newton-Type Proximal Augmented Lagrangian Solver Tailored for Quadratic Programs Arising in Model Predictive Control

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 1349-1354页

作者： Lowenstein, Kristoffe Fink Bernardini, Daniele Patrinos, Panagiotis Politecn Milan Dipartimento Elettron Informaz & Bioingn I-20133 Milan Italy ODYS Srl I-20159 Milan Italy Katholieke Univ Leuven Dept Elect Engn ESAT STADIUS B-3001 Leuven Belgium

In model predictive control fast and reliable quadratic programming solvers are of fundamental importance. The inherent structure of the subsequent optimal control problems can lead to substantial performance improvements if exploited. Therefore, we present a structure-exploiting solver based on proximal augmented Lagrangian, extending the general-purpose quadratic programming solver QPALM. Our solver relies on semismooth Newton iterations to solve the inner sub-problem while directly accounting for the optimal control problem structure via efficient and sparse matrix factorizations. The matrices to be factorized depend on the active-set and therefore low-rank factorization updates can be employed like in active-set methods resulting in cheap iterates. We compare our solver with QPALM and other well-known solvers and show its benefits in a numerical example.

关键词： optimization algorithms optimal control predictive control for nonlinear systems

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Accelerated algorithms for Constrained Nonconvex-Nonconcave Min-Max optimization and Comonotone Inclusion

arXiv

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arXiv 2022年

作者： Cai, Yang Oikonomou, Argyris Zheng, Weiqiang Department of Computer Science Yale University New Haven United States

We study constrained comonotone min-max optimization, a structured class of nonconvex-nonconcave min-max optimization problems, and their generalization to comonotone inclusion. In our first contribution, we extend the Extra Anchored Gradient (EAG) algorithm, originally proposed by Yoon & Ryu (2021) for unconstrained min-max optimization, to constrained comonotone min-max optimization and comonotone inclusion, achieving an optimal convergence rate of O T1 among all first-order methods. Additionally, we prove that the algorithm’s iterations converge to a point in the solution set. In our second contribution, we extend the Fast Extra Gradient (FEG) algorithm, as developed by Lee & Kim (2021), to constrained comonotone min-max optimization and comonotone inclusion, achieving the same O T1 convergence rate. This rate is applicable to the broadest set of comonotone inclusion problems yet studied in the literature. Our analyses are based on simple potential function arguments, which might be useful for analyzing other accelerated algorithms. Copyright © 2022, The Authors. All rights reserved.

关键词： optimization algorithms

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Enhanced efficiency and quality in wind turbine gearbox assembly: a new parallel assembly sequence planning (PASP) model

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INTERNATIONAL JOURNAL OF SUSTAINABLE ENGINEERING 2024年第1期17卷 1048-1065页

作者： Mutale, Sydney Wang, Yong Yasir, Jan North China Elect Power Univ Sch New Energy Changping Beijing Peoples R China Univ Zambia Sch Engn Lusaka Zambia

This paper presents two major advances in parallel assembly sequence planning (PASP) for complex systems, specifically wind turbine gearboxes. The proposed time-cost-quality PASP hybrid model (PASP-TCQ) aims to enhance efficiency, reduce costs, and improve quality by aligning optimisation parameters with real-world demands. This model is designed to optimise complex assembly processes by addressing constraints on time, cost, and quality effectively. Additionally, we introduce a particle swarm-bacteria foraging optimisation (PSBFO) algorithm that integrates the global search capability of particle swarm optimisation (PSO) with the local optimisation strengths of bacteria foraging optimisation (BFO). Integrating PSBFO into PASP-TCQ achieves significant improvements: a 17% reduction in assembly time to 100 hours, a 10% cost reduction to $94,500, and a quality index improvement to 0.93. Statistical tests, including analysis of variance (ANOVA) and tukey's honest significant difference (HSD), confirmed the PSBFO's superiority, with significant gains of 8.44 units over BFO and 13.02 units over PSO in objective function values (p < 0.05). Extensive simulations on a 10 MW wind turbine gearbox validate the effectiveness of the PASP-TCQ and PSBFO, demonstrating their potential to enhance efficiency and productivity in industrial assembly operations.

关键词： Parallel assembly sequence planning time-cost-quality hybrid model particle swarm-bacteria foraging optimisation optimization algorithms industrial assembly efficiency wind turbine gearboxes

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Sequential Linear Programming With Adaptive Linearization Error Limits for All-Time Feasibility

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 3051-3056页

作者： Leko, Dorijan Vasak, Mario Univ Zagreb Fac Elect Engn & Comp Dept Control & Comp Engn Zagreb 10000 Croatia

This letter presents an enhanced Trust Region Method (TRM) for Sequential Linear Programming (SLP) designed to improve the initial feasible solution to a constrained nonlinear programming problem while maintaining the interim solutions feasibility throughout the SLP iterations. The method employs a polytopic sub-approximation of the feasible region, defined around the interim solution as a level set based on variable limits for the linearization error. This polytopic feasible region is established by using a trust region that ensures that maximum limits of the linearization errors are respected. The method adaptively adjusts the size of the feasible region during iterations to achieve convergence to a local optimum by employing variable linearization error limits. Local convergence is attained by reducing the size of the trust radius. A case study illustrates the effectiveness of the proposed method, which is compared to the benchmark TRM that uses heuristic limits on the permissible changes in manipulated variables.

关键词： Transmission line measurements Benchmark testing Level set Convergence Navigation Linear programming Heuristic algorithms Vectors Taylor series Programming optimization algorithms optimization computational methods

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Evaluation Of Fracture Energy Of Concrete By Hybrid SVR Analysis

JOURNAL OF APPLIED SCIENCE AND ENGINEERING

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JOURNAL OF APPLIED SCIENCE AND ENGINEERING 2024年第12期27卷 3645-3661页

作者： Jiang, Pan Ge, Nan Hebei Univ Water Resources & Elect Engn Dept Civil Engn Cangzhou 061001 Peoples R China North China Univ Sci & Technol Coll Civil & Architectural Engn Tangshan 063210 Peoples R China

Regression techniques were developed to determine the concrete initial (Gf) and total (GF) fracture energy based on prior data using mechanical features and mixed design elements. There were 264 samples retrieved from prior investigations in all. Research contributes to the field by improving the accuracy of predicting concrete fracture energy, offering a methodology for optimizing hyperparameters, and providing a model comparison that demonstrates the practical value of the new approach. These findings can benefit the construction and engineering industries by enhancing the accuracy of material property predictions and improving the quality and safety of constructed structures. This study merged support vector regression (SVR) assessment with arithmetic optimization algorithm (AOA) and whale optimization algorithm (WOA) to predict the Gf and GFF of concrete. The aim of combining the optimization algorithms with SVR analysis was to determine the optimal values of hyperparameters that play pivotal role in developed models' accuracy. The computation and analysis for Gf and GF using five criteria shows that optimized SVR-AOA and SVR-WOA analyses can do admirably well throughout the forecasting model. When the outperforming SVR analysis was compared to the library, it was discovered that the newly constructed SVR-AOA also present a small raise in accuracy, with modification in all metrics. In conclusion, while the SVR-WOA demonstrates its effectiveness in the forecasting outline, the SVR-AOA analysis appears to be a reliable approach for determining accurate Gf values (R2train = 0.921, and R2test = 0.9853) and GF values (R2train = 0.9281, and R2test = 0.9236, as supported by the arguments and feasibility of the models.

关键词： Concrete Fracture energy Support vector regression optimization algorithms

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Prediction of shallow foundation settlement: usage of hybridized support vector regression model

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MULTISCALE AND MULTIDISCIPLINARY MODELING EXPERIMENTS AND DESIGN 2024年第1期7卷 281-290页

作者： Yang, Xiaochuan Chongqing Coll Finance & Econ Coll Appl Technol Chongqing 402160 Peoples R China

Because of the intricacy of cohesion soil texture, settlement simulation in cohesion materials is a critical subject to address. According to the literature study, shallow foundation prediction did not much considered, so developing optimized models can enhance the forecast accuracy in this field. It is the focus of this research to put newly developed machine learning models, such as hybridized support vector regression (SVR) with firefly algorithm (FFA) and cuckoo optimization algorithm (COA), into practice as efficient approaches to predict settlement (S-m) of shallow foundations over cohesion soil properties. The footing width, footing pressure, footing geometry, count of SPT blow, and footing embedment ratio are chosen as estimation parameters. The use of optimization techniques served the aim of determining the ideal value for the major variables of the investigated model. In the COA-SVR system, the values of R-2 and RMSE in the learning phase are 0.9649 and 4.7693, suitable than ANFIS-PSO by 0.9025 and 8.09, and in the examining phase are 0.9937 and 2.5485, considerably proper compared to ANFIS-PSO at 0.739 and 14.10, respectively. By considering another metric-like PI index, the COA-SVR network results more properly than the FFA-SVR model, with a decline of 0.0206 and 0.0717 in the learning and examining data sets, respectively. Furthermore, VAF index also depicts the same trend with outperforming the COA-SVR to FFA-SVR, especially in the examining stage, with a rise of about 3.2%. In conclusion, it is clear that the COA-SVR system could perform better than those integrated with FFA, as well as ANFI-PSO, where the proposed system can be known as the proposed system in the estimation procedure of shallow foundation S-m.

关键词： Shallow foundation Settlement Estimation Hybrid SVR optimization algorithms

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Learning to Optimize With Convergence Guarantees Using Nonlinear System Theory

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 1355-1360页

作者： Martin, Andrea Furieri, Luca Ecole Polytech Fed Lausanne Inst Mech Engn CH-1015 Lausanne Switzerland

The increasing reliance on numerical methods for controlling dynamical systems and training machine learning models underscores the need to devise algorithms that dependably and efficiently navigate complex optimization landscapes. Classical gradient descent methods offer strong theoretical guarantees for convex problems;however, they demand meticulous hyperparameter tuning for non-convex ones. The emerging paradigm of learning to optimize (L2O) automates the discovery of algorithms with optimized performance leveraging learning models and data - yet, it lacks a theoretical framework to analyze convergence of the learned algorithms. In this letter, we fill this gap by harnessing nonlinear system theory. Specifically, we propose an unconstrained parametrization of all convergent algorithms for smooth non-convex objective functions. Notably, our framework is directly compatible with automatic differentiation tools, ensuring convergence by design while learning to optimize.

关键词： Machine learning nonlinear optimal control optimization algorithms system theory

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A Dual Bisection Approach to Economic Dispatch of Generators With Prohibited Operating Zones

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IEEE CONTROL SYSTEMS LETTERS 2024年 8卷 1547-1552页

作者： Manieri, Lucrezia Falsone, Alessandro Prandini, Maria Politecn Milan Dipartimento Elettron Informaz & Bioingn I-20133 Milan Italy

We address economic dispatch of power generators with prohibited operating zones. The problem can be formulated as an optimization program with a quadratic cost, non-convex local operating constraints, and a scalar quadratic coupling constraint accounting for load demand and power losses. A duality-based resolution approach integrating a bisection iterative scheme is proposed to reduce computational complexity while guaranteeing finite time feasibility of the primal iterates and a cost improvement throughout iterations. Extensive simulations show that the approach outperforms state-of-the-art competitors and consistently computes feasible primal solutions with a close-to-zero optimality gap at a low computational cost.

关键词： Energy systems large-scale systems optimization algorithms

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Prediction of evaporation from dam reservoirs under climate change using soft computing techniques

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ENVIRONMENTAL SCIENCE AND POLLUTION RESEARCH 2023年第10期30卷 27912-27935页

作者： Kayhomayoon, Zahra Naghizadeh, Fariba Malekpoor, Mohammadreza Azar, Naser Arya Ball, James Milan, Sami Ghordoyee Payame Noor Univ Dept Geol Tehran Iran Univ Guilan Coll Agr Sci Dept Water Engn Rasht Iran Islamic Azad Univ Dept Civil Engn Azarshahr Branch Azarshahr Iran Univ Tabriz Fac Agr Dept Water Engn Tabriz Iran Univ Technol Sydney Sch Civil & Environm Engn Sydney NSW Australia Univ Tehran Dept Irrigat & Drainage Engn Aburaihan Campus Tehran Iran

This study aimed to predict evaporation from dam reservoirs using artificial intelligence considering climate change. Mahabad Dam, near Lake Urmia, in northwestern Iran, is used to investigate the proposed approach. There are three parts to the study presented herein. In the first part, two machine learning models, namely group method of data handling (GMDH) and least squares support vector regression (LS-SVR), were used to model the inflow to the dam reservoir. Temperature, precipitation, and inflow during the previous month from 1990 to 2017 were used as input data. In the second part, the evaporation from the dam reservoir was modeled using the adaptive neuro-fuzzy inference system (ANFIS) and optimized ANFIS using Harris hawks optimization (HHO) and the arithmetic optimization algorithm (AOA) optimization algorithms. The input parameters in this part were temperature, precipitation, inflow to the dam reservoir, along with evaporation from the dam reservoir in the previous month. In the third part, precipitation and temperature were predicted using the fifth report of IPCC based on RCP2.6, RCP4.5, and RCP8.5 scenarios for the period 2020-2040. Out of 28 models presented in the fifth report, EC-ERATH and FIO-ESM had the greatest similarity with observational data of temperature and precipitation, respectively. The results of scatter plots and Taylor's diagram showed the higher performance of LS-SVR (root mean square error (RMSE), mean absolute percentage error (MAPE), and Nash-Sutcliffe efficiency (NSE) of 8.65, 4.69, and 0.96) compared to GMDH (RMSE, MAPE, and NSE of 11.65, 7.81, and 0.93) in modeling the inflow. Moreover, both hybrid modes (AOA-ANFIS and HHO-ANFIS) improved the performance of ANFIS in modeling the evaporation from the dam reservoir. The RMSE, MAPE, and NSE values for ANFIS were 0.56, 0.52, and 0.89, respectively, while these values for the AOA-ANFIS (RMSE, MAPE, and NSE of 0.31, 0.24, and 0.93) and HHO-ANFIS (RMSE, MAPE, and NSE of 0.20, 0.30, a

关键词： Climate change Machine learning optimization algorithms Reservoir evaporation Time-series data

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