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A Theoretical Analysis of Analogy-Based Evolutionary Transfer optimization

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arXiv 2025年

作者： Xue, Xiaoming Feng, Liang Feng, Yinglan Liu, Rui Zhang, Kai Tan, Kay Chen Department of Data Science and Artificial Intelligence The Hong Kong Polytechnic University Hong Kong College of Computer Science Chongqing University China School of Civil Engineering Qingdao University of Technology China

Evolutionary transfer optimization (ETO) has been gaining popularity in research over the years due to its outstanding knowledge transfer ability to address various challenges in optimization. However, a pressing issue in this field is that the invention of new ETO algorithms has far outpaced the development of fundamental theories needed to clearly understand the key factors contributing to the success of these algorithms for effective generalization. In response to this challenge, this study aims to establish theoretical foundations for analogy-based ETO, specifically to support various algorithms that frequently reference a key concept known as similarity. First, we introduce analogical reasoning and link its subprocesses to three key issues in ETO. Then, we develop theories for analogy-based knowledge transfer, rooted in the principles that underlie the subprocesses. Afterwards, we present two theorems related to the performance gain of analogy-based knowledge transfer, namely unconditionally nonnegative performance gain and conditionally positive performance gain, to theoretically demonstrate the effectiveness of various analogy-based ETO methods. Last but not least, we offer a novel insight into analogy-based ETO that interprets its conditional superiority over traditional evolutionary optimization through the lens of the no free lunch theorem for optimization. 1156v1 [***] 27 Mar Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Distributed Forgetting-factor Regret-based Online optimization over Undirected Connected Networks

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arXiv 2025年

作者： Mo, Lipo Li, Jianjun Zuo, Min Wang, Lei Institute of Systems Science Beijing Wuzi University Beijing101126 China School of Mathematics and Statistics Beijing Technology and Business University Beijing100048 China School of Automation Science and Electrical Engineering Beihang University Beijing100191 China

The evaluation of final-iteration tracking performance is a formidable obstacle in distributed online optimization algorithms. To address this issue, this paper proposes a novel evaluation metric named distributed forgetting-factor regret (DFFR). It incorporates a weight into the loss function at each iteration, which progressively reduces the weights of historical loss functions while enabling dynamic weights allocation across optimization horizon. Furthermore, we develop two distributed online optimization algorithms based on DFFR over undirected connected networks: the Distributed Online Gradient-free Algorithm for bandit-feedback problems and the Distributed Online Projection-free Algorithm for high-dimensional problems. Through theoretical analysis, we derive the upper bounds of DFFR for both algorithms and further prove that under mild conditions, DFFR either converges to zero or maintains a tight upper bound as iterations approach infinity. Experimental simulation demonstrates the effectiveness of the algorithms and the superior performance of DFFR. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Robust optimization Approach for Solving Uncertain Multiobjective optimization Problems Using the Projected Gradient Method

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arXiv 2025年

作者： Kumar, Shubham Mahato, Nihar Kumar Ghosh, Debdas PDPM IIITDM Jabalpur Madhya Pradesh Jabalpur482005 India India

Numerous real-world applications of uncertain multiobjective optimization problems (UMOPs) can be found in science, engineering, business, and management. To handle the solution of uncertain optimization problems, robust optimization is a relatively new field. An extended version of the projected gradient method (PGM) for deterministic smooth multiobjective optimization problem (MOP) is presented in the current study as a PGM for UMOP. An objective-wise worst-case cost (OWWC) type robust counterpart is considered, and the PGM is used to solve a UMOP by using OWWC. A projected gradient descent algorithm is created using theoretical findings. It is demonstrated that the projected gradient descent algorithm’s generated sequence converges to the robust counterpart’s weak Pareto optimal solution, which will be the robust weak Pareto optimal solution for UMOP. Under a few reasonable presumptions, the projected gradient descent algorithm’s full convergent behavior is also justified. Finally, numerical tests are presented to validate the proposed method. © 2025, CC BY-NC-ND.

关键词： optimization algorithms

optimization of sliding mode control with PID surface for robot manipulator by Evolutionary algorithms

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OPEN COMPUTER SCIENCE 2020年第1期10卷 396-407页

作者： Loucif, Fatiha Kechida, Sihem Univ 8 Mai 1945 Lab Automat & Informat Guelma Guelma Algeria

In this paper, a sliding mode controller (SMC) with PID surface is designed for the trajectory tracking control of a robot manipulator using different optimization algorithms such as, Antlion optimization Algorithm (ALO) Sine Cosine Algorithm (SCA) Grey Wolf Optimizer (GWO) and Whale Optimizer Algorithm (WOA). The aim of this work is to introduce a novel SMC-PID-ALO to control nonlinear systems, especially the position of two of the joints of a 2DOF robot manipulator. The basic idea is to determinate four optimal parameters (K-p, K-i, K-d and lamda) ensuring the best performance of a robot manipulator system, minimizing the integral time absolute error criterion (ITAE) and the integral time square error criterion (ISTE). The robot manipulator is modeled in Simulink and the control is implemented using the MATLAB environment. The obtained simulation results prove the robustness of ALO in comparison with other algorithms.

关键词： Sliding mode control optimization algorithms Robot manipulator

Malicious Node Detection in Industrial Internet of Things Using Swarm-Based optimization Algorithm: A Cyber Security Perspective 6th

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Malicious Node Detection in Industrial Internet of Things Us...

6th International Conference on Computational Intelligence in Communications and Business Analytics, CICBA 2024

作者： Addimulam, Sushanth Chandra Sr. Infrastructure and Security Engineer Applied Computer Techniques 28345 Beck Road STE 308 WixomMI48393 United States

ISBN: (纸本)9783031813351

The IIoT saw rapid evolution throughout the early years of the twenty-first century. The complexity of certain services in the industrial arena, poses challenges for our understanding. The task of identifying the most suitable malicious nodes is complex due to the need to consider several quality of service (QoS) factors, such as information transmission and network. There exist a multitude of limited evolutionary optimization algorithms that have been developed to tackle these issues. The present work introduces an expanded conceptualization of Bat optimization algorithm incorporates a rapid adaption approach and an optimization-oriented design. The proposed approach is evaluated in the architecture of IIoT services and in applications based on IIoT. The results are subsequently compared utilizing cutting-edge algorithms. The findings indicate that the suggested methodology yields superior outcomes in relation to the cyber security of QoS, fitness cost, and identification of IIoT nodes inside the IIoT service network. © The Author(s), under exclusive license to Springer Nature Switzerland AG 2025.

关键词： optimization algorithms

Fast Expectation Value Calculation Speedup of Quantum Approximate optimization Algorithm: HoLCUs QAOA

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arXiv 2025年

作者： Ali, Alejandro Mata Instituto Tecnológico de Castilla y León Burgos Spain

In this paper, we present a new method for calculating expectation values of operators that can be expressed as a linear combination of unitary (LCU) operators. This method allows to perform this calculation in a single quantum circuit measuring a single qubit, which speeds up the computation process. This method is general for any quantum algorithm and is of particular interest in the acceleration of variational quantum algorithms, both in real devices and in simulations. We analyze its application to the parameter optimization process of the Quantum Approximate optimization Algorithm (QAOA) and the case of having degenerate values in the matrix of the Ising problem. Finally, we apply it to several Quadratic Unconstrained Binary optimization (QUBO) problems to analyze the speedup of the method in circuit *** Codes 81P68, 68Q12, 90C27 © 2025, CC BY.

关键词： optimization algorithms

A TUTORIAL ON KRIGING-BASED STOCHASTIC SIMULATION optimization

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arXiv 2025年

作者： Amini, Sasan Van Nieuwenhuyse, Inneke Hasselt University Agoralaan Diepenbeek3590 Belgium

This tutorial focuses on kriging-based simulation optimization, emphasizing the importance of data efficiency in optimization problems involving expensive simulation models. It discusses how kriging models contribute to developing algorithms that minimize the number of required simulations, particularly in the presence of noisy evaluations. The tutorial compares the performance of kriging-based algorithms against traditional polynomial-based optimization methods using an illustrative example. Additionally, it discusses key extensions of kriging-based algorithms, including multi-objective and constrained optimization, providing insights into their application in complex, real-world settings. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Gradient-free stochastic optimization for additive models

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arXiv 2025年

作者： Akhavan, Arya Tsybakov, Alexandre B. University of Oxford United Kingdom CREST ENSAE IP Paris France

We address the problem of zero-order optimization from noisy observations for an objective function satisfying the Polyak-Lojasiewicz or the strong convexity condition. Additionally, we assume that the objective function has an additive structure and satisfies a higher-order smoothness property, characterized by the Hölder family of functions. The additive model for Hölder classes of functions is well-studied in the literature on nonparametric function estimation, where it is shown that such a model benefits from a substantial improvement of the estimation accuracy compared to the Hölder model without additive structure. We study this established framework in the context of gradient-free optimization. We propose a randomized gradient estimator that, when plugged into a gradient descent algorithm, allows one to achieve minimax optimal optimization error of the order dT−(β−1)/β, where d is the dimension of the problem, T is the number of queries and β ≥ 2 is the Hölder degree of smoothness. We conclude that, in contrast to nonparametric estimation problems, no substantial gain of accuracy can be achieved when using additive models in gradient-free optimization. © 2025, CC BY.

关键词： optimization algorithms

ASGO: Adaptive Structured Gradient optimization

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arXiv 2025年

作者： An, Kang Liu, Yuxing Pan, Rui Ma, Shiqian Goldfarb, Donald Zhang, Tong Rice University United States University of Illinois Urbana-Champaign United States Columbia University United States

Training deep neural networks (DNNs) is a structured optimization problem, because the parameters are naturally represented by matrices and tensors rather than simple vectors. Under this structural representation, it has been widely observed that gradients are low-rank and Hessians are approximately block-wise diagonal. These structured properties are crucial for designing efficient optimization algorithms but may not be utilized by current popular optimizers like Adam. In this paper, we present a novel optimization algorithm ASGO that capitalizes on these properties by employing a preconditioner that is adaptively updated using structured gradients. By fine-grained theoretical analysis, ASGO is proven to achieve superior convergence rates compared to existing structured gradient methods. Based on the convergence theory, we further demonstrate that ASGO can benefit from the low-rank and block-wise diagonal properties. We also discuss practical modifications of ASGO and empirically verify the effectiveness of the algorithm on language model tasks. © 2025, CC BY.

关键词： optimization algorithms