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Convergence towards a local minimum by direct search methods with a covering step

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arXiv 2024年

作者： Bouchet, Pierre-Yves Audet, Charles Bourdin, Loïc École Polytechnique de Montréal MontréalQCH3T 1J4 Canada GERAD MontréalQCH3T 1J4 Canada XLIM Research Institute University of Limoges France

This paper introduces a new step to the Direct Search Method (DSM) to strengthen its convergence analysis. By design, this so-called covering step may ensure that, for all refined points of the sequence of incumbent solutions generated by the resulting cDSM (covering DSM), the set of all evaluated trial points is dense in a neighborhood of that refined point. We prove that this additional property guarantees that all refined points are local solutions to the optimization problem. This new result holds true even for a discontinuous objective function, under a mild assumption that we discuss in details. We also provide a practical construction scheme for the covering step that works at low additional cost per iteration. Finally, we show that the covering step may be adapted to classes of algorithms differing from the DSM. © 2024, CC BY.

关键词： optimization algorithms

LINEAR BANDITS ON ELLIPSOIDS: MINIMAX OPTIMAL algorithms

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arXiv 2025年

作者： Zhang, Raymond Hadiji, Hédi Combes, Richard Laboratoire des Signaux et Systèmes Univ. Paris-Saclay CNRS CentraleSupélec France

We consider linear stochastic bandits where the set of actions is an ellipsoid. We provide the first known minimax optimal algorithm for this problem. We first derive a novel information-theoretic lower bound on the regret of any algorithm, which must be at least Ω(min(dσ√T + dθA, θAT)) where d is the dimension, T the time horizon, σ2 the noise variance, A a matrix defining the set of actions and θ the vector of unknown parameters. We then provide an algorithm whose regret matches this bound to a multiplicative universal constant. The algorithm is non-classical in the sense that it is not optimistic, and it is not a sampling algorithm. The main idea is to combine a novel sequential procedure to estimate θ, followed by an explore-and-commit strategy informed by this estimate. The algorithm is highly computationally efficient, and a run requires only time O(dT + d2 log(T/d) + d3) and memory O(d2), in contrast with known optimistic algorithms, which are not implementable in polynomial time. We go beyond minimax optimality and show that our algorithm is locally asymptotically minimax optimal, a much stronger notion of optimality. We further provide numerical experiments to illustrate our theoretical findings. © 2025, CC BY.

关键词： optimization algorithms

Mechanical Properties Estimation Of Ultra Great Workability Concrete By Developing Hybrid algorithms

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淡江理工学刊 2023年第9期26卷 1303-1318页

作者： Lijun Wang Pengcheng Yang

The compressive strength of ultra great workability concrete (UGWC) is a function of the kind, characteristics and quantities of its material components. Empirically gaining this relation sometimes needs the usage of intelligent algorithms to receive a simulative model that fits into experimental data records. In this study, the usefulness of developing hybridized regression analysis on UGWC was analyzed with the aim of reducing the consumed time and experimental efforts. To this aim, a dataset including 170 samples collected from published papers different hybridized support vector regression (SVR) analyses were produced, where the optimal values of determinant attributes of SVR were explored by metaheuristic optimization algorithms named particle swarm optimization (PSO), Cuckoo optimization algorithm (COA), and Bat algorithm (BAT). The performance evaluators demonstrate that all three hybridized SVR models have remarkable potential in compressive strength estimation of UGWC. The first rank belonged to the SVR-COA model, where it could gain the highest value of R^2 and variance account factor (VAF) in both training (R^2=0.9056 and VAF=90.17%) and validating section (R^2=0.9208 and VAF=91.81%), and the lowest value of root mean square error, and mean absolute error in both training and validating sections. Therefore, the hybridized SVR-COA model could receive the proper accuracy in comparison with other models as well as literature.

关键词： Ultra great workability concrete Compressive strength Prediction SVR analysis optimization algorithms

Population-Level Center-Based Sampling for Meta-Heuristic algorithms

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SSRN

SSRN 2024年

作者： Khosrowshahli, Rasa Rahnamayan, Shahryar Ibrahim, Amin Bidgoli, Azam Asilian Makrehchi, Masoud Faculty of Engineering and Applied Sciences Ontario Tech University OshawaON Canada Department of Engineering Brock University St. CatharinesON Canada Faculty of Business and Information Technology Ontario Tech University OshawaON Canada Faculty of Science Wilfrid Laurier University WaterlooON Canada

In recent years, center-based sampling has demonstrated p results for enhancing the efficiency and effectiveness of meta-heuristic algorithms. The strategy of center-based sampling can be utilized at either the operation and/or population levels. Despite the overall efficiency of the center-based sampling in population-based algorithms, utilization at the operation requires customizing the strategy for a specific algorithm, degrading the generalization of the scheme. This study proposes a center-based sampling at the population level, which is operation-independent and correspondingly can be embedded in any population-based optimization algorithm. The proposed center-based sampling uses a collaborative multi-parent approach to generate multiple center-based solutions leading to augmented diversity as well as the exploitation of the solution space. Accordingly, two population-level center-based sampling, namely cluster-driven center-based sampling and ranking-driven center-based sampling are proposed to enhance population-based single- and multi-objective optimization algorithms, respectively. In order to assess the performance of proposed schemes, the proposed strategy is integrated in well-known single- and multi-objective optimization algorithms to solve the CEC-2017 benchmark functions. The experimental outcomes confirm that the algorithm with embedded population-level center-based samplings have a crucial positive impact on the convergence rate of various families of optimization algorithms compared to the parent algorithm. © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

TERIME: An improved RIME algorithm with enhanced exploration and exploitation for robust parameter extraction of photovoltaic models

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arXiv 2024年

作者： Chen, Shi-Shun Jiang, Yu-Tong Chen, Wen-Bin Li, Xiao-Yang School of Reliability and Systems Engineering Beihang University Beijing100191 China

Parameter extraction of photovoltaic (PV) models is crucial for the planning, optimization, and control of PV systems. Although some methods using meta-heuristic algorithms have been proposed to determine these parameters, the robustness of solutions obtained by these methods faces great challenges when the complexity of the PV model increases. The unstable results will affect the reliable operation and maintenance strategies of PV systems. In response to this challenge, an improved RIME algorithm with enhanced exploration and exploitation is proposed for robust and accurate parameter identification for various PV models. Specifically, the differential evolution mutation operator is integrated in the exploration phase to enhance the population diversity. Meanwhile, a new exploitation strategy incorporating randomization and neighborhood strategies simultaneously is developed to maintain the balance of exploitation width and depth. The improved RIME algorithm is applied to estimate the optimal parameters of the single-diode model (SDM), double-diode model (DDM), and triple-diode model (TDM) combined with the Lambert-W function for three PV cell and module types including RTC France, Photo Watt-PWP 201 and S75. According to the statistical analysis in 100 runs, the TEIMRE achieves more accurate and robust parameter estimations than other techniques to various PV models in varying environmental conditions. All of our source codes are publicly available at https://***/dirge1/TERIME. © 2024, CC BY.

关键词： optimization algorithms

SMOP: Stochastic trust region method for multi-objective problems

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arXiv 2025年

作者： Krejić, Nataša Jerinkić, Nataša Krklec Rutešić, Luka Department of Mathematics and Informatics Faculty of Sciences University of Novi Sad Trg Dositeja Obradovića 4 Novi Sad21000 Serbia

The problem considered is a multi-objective optimization problem, in which the goal is to find an optimal value of a vector function representing various criteria. The aim of this work is to develop an algorithm which utilizes the trust region framework with probabilistic model functions, able to cope with noisy problems, using inaccurate functions and gradients. We prove the almost sure convergence of the proposed algorithm to a Pareto critical point if the model functions are good approximations in probabilistic sense. Numerical results demonstrate effectiveness of the probabilistic trust region by comparing it to competitive stochastic multi-objective solvers. The application in supervised machine learning is showcased by training non discriminatory Logistic Regression models on different size data groups. Additionally, we use several test examples with irregularly shaped fronts to exhibit the efficiency of the algorithm. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

HIERARCHICAL MINIMUM VARIANCE PORTFOLIOS: A THEORETICAL AND ALGORITHMIC APPROACH

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arXiv 2025年

作者： Mograby, Gamal Department of Mathematical Sciences University of Cincinnati United States

We introduce a novel approach to portfolio optimization that leverages hierarchical graph structures and the Schur complement method to systematically reduce computational complexity while preserving full covariance information. Inspired by López de Prado’s hierarchical risk parity and Cotton’s Schur complement methods, our framework models the covariance matrix as an adjacency-like structure of a hierarchical graph. We demonstrate that portfolio optimization can be recursively reduced across hierarchical levels, allowing optimal weights to be computed efficiently by inverting only small submatrices regardless of portfolio size. Moreover, we translate our results into a recursive algorithm that constructs optimal portfolio allocations. Our results reveal a transparent and mathematically rigorous connection between classical Markowitz mean-variance optimization, hierarchical clustering, and the Schur complement *** Codes ***, ***, *** © 2025, CC BY-NC-ND.

关键词： optimization algorithms

Subgradient Method for System Identification with Non-Smooth Objectives

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arXiv 2025年

作者： Yalcin, Baturalp Lavaei, Javad University of California Berkeley United States

This paper investigates a subgradient-based algorithm to solve the system identification problem for linear time-invariant systems with non-smooth objectives. This is essential for robust system identification in safety-critical applications. While existing work provides theoretical exact recovery guarantees using optimization solvers, the design of fast learning algorithms with convergence guarantees for practical use remains unexplored. We analyze the subgradient method in this setting where the optimization problems to be solved change over time as new measurements are taken, and we establish linear convergence results for both the best and Polyak step sizes after a burn-in period. Additionally, we characterize the asymptotic convergence of the best average sub-optimality gap under diminishing and constant step sizes. Finally, we compare the time complexity of standard solvers with the subgradient algorithm and support our findings with experimental results. This is the first work to analyze subgradient algorithms for system identification with non-smooth *** Codes 62, 90, 93 © 2025, CC BY-NC-ND.

关键词： optimization algorithms

Partition Constraints for Conjunctive Queries: Bounds and Worst-Case Optimal Joins

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arXiv 2025年

作者： Deeds, Kyle Merkl, Timo Camillo University of Washington SeattleWA United States TU Wien Vienna Austria

In the last decade, various works have used statistics on relations to improve both the theory and practice of conjunctive query execution. Starting with the AGM bound which took advantage of relation sizes, later works incorporated statistics like functional dependencies and degree constraints. Each new statistic prompted work along two lines;bounding the size of conjunctive query outputs and worst-case optimal join algorithms. In this work, we continue in this vein by introducing a new statistic called a partition constraint. This statistic captures latent structure within relations by partitioning them into sub-relations which each have much tighter degree constraints. We show that this approach can both refine existing cardinality bounds and improve existing worst-case optimal join algorithms. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms