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Regularity-Based Evolutionary Multi-Objective optimization Review

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SSRN

SSRN 2024年

作者： Lu, Yulan Guo, Xueyi Geng, Jinggai Wang, Shuai Wang, Zhengkun Zhou, Aimin Sun, Jianyong Si, Xinhui Sun, Xin Zhang, Hu School of Mathematics and Physics University of Science and Technology Beijing Beijing100083 China School of the Aliyun School of Big Data School of Materials Science & Engineering Changzhou University Jiangsu Changzhou213164 China School of System Design and Intelligent Manufacturing Southern University of Science and Technology Shenzhen518055 China School of Computer Science and Technology East China Normal University Shanghai200062 China School of Mathematics and Statistics Xi’an Jiaotong University Xi’an710049 China CASIC Research Institute of Intelligent Decision Engineering Beijing100074 China

Under mild conditions, the Pareto optimal solutions of a continuous m-dimensional multi-objective optimization problem (MOP) form a piece-wise (m-1)-dimensional manifold structure, which is known as regularity property. As a domain knowledge of MOP, this regularity property has been widely incorporated into the design of multiobjective evolutionary algorithms in the past two decade years. In this paper, we conduct a comprehensive review on the developments of regularity-based evolutionary multi-objective optimization (REMO) approaches, analyzing the current research landscape, summarizing key directions, and anticipating future trends. The aim is to provide some valuable insights for upcoming research endeavors. © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Problem-Driven Scenario Reduction and Scenario Approximation for Robust optimization

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arXiv 2024年

作者： Fairbrother, Jamie Goerigk, Marc Khosravi, Mohammad Department of Management Science Lancaster University United Kingdom Business Decisions and Data Science University of Passau Germany

In robust optimization, we would like to find a solution that is immunized against all scenarios that are modeled in an uncertainty set. Which scenarios to include in such a set is therefore of central importance for the tractability of the robust model and practical usefulness of the resulting solution. We consider problems with a discrete uncertainty set affecting only the objective function. Our aim is reduce the size of the uncertainty set, while staying as true as possible to the original robust problem, measured by an approximation guarantee. Previous reduction approaches ignored the structure of the set of feasible solutions in this process. We show how to achieve better uncertainty sets by taking into account what solutions are possible, providing a theoretical framework and models to this end. In computational experiments, we note that our new framework achieves better uncertainty sets than previous methods or a simple K-means approach. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms

Accelerating Matroid optimization through Fast Imprecise Oracles

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arXiv 2024年

作者： Eberle, Franziska Hommelsheim, Felix Lindermayr, Alexander Liu, Zhenwei Megow, Nicole Schlöter, Jens Institute of Mathematics Technical University of Berlin Germany Faculty of Mathematics and Computer Science University of Bremen Germany Zhejiang University China Centrum Wiskunde & Informatica Netherlands

Querying complex models for precise information (e.g. traffic models, database systems, large ML models) often entails intense computations and results in long response times. Thus, weaker models that give imprecise results quickly can be advantageous, provided inaccuracies can be resolved using few queries to a stronger model. In the fundamental problem of computing a maximum-weight basis of a matroid, a well-known generalization of many combinatorial optimization problems, algorithms have access to a clean oracle to query matroid information. We additionally equip algorithms with a fast but dirty oracle. We design and analyze practical algorithms that only use few clean queries w.r.t. the quality of the dirty oracle, while maintaining robustness against arbitrarily poor dirty oracles, approaching the performance of classic algorithms for the given problem. Notably, we prove that our algorithms are, in many respects, best-possible. Further, we outline extensions to other matroid oracle types, non-free dirty oracles and other matroid problems. © 2024, CC BY.

关键词： optimization algorithms

Research on Online English Teaching Resource Allocation Strategy Based on optimization Algorithm

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Applied Mathematics and Nonlinear Sciences 2024年第1期9卷

作者： Zhang, Buyi School of Foreign Languages Hebei Minzu Normal University Hebei Chengde067000 China

With the arrival of the era of education informatization, online learning has become one of the research hotspots. Aiming at one of the important links, learning resource allocation, this paper designs an online system for distributing English teaching resources. Based on the maximum distance optimization K-means clustering algorithm, a hybrid collaborative filtering personalized recommendation algorithm based on users and items is used to optimize the similarity algorithm, and the online English teaching resources allocation strategy is proposed. A variety of teaching resource recommendation quality experiments are set up and combined with teaching practice applications to explore the model's resource allocation quality and its enhancement effect on English teaching. The model in this paper has higher recommendation accuracy and recommendation quality of English teaching resources, and the comprehensive evaluation index value F is lower than that of the comparison model by 0.18 and 0.07. At the same time, the online English teaching resources allocation strategy has a better effect on improving learning attitudes, with more than 72% of positive evaluations in each dimension of satisfaction. The experiment shows that the online English teaching resource allocation strategy has a positive effect on students' English learning efficiency and motivation. © 2024 Buyi Zhang, published by Sciendo.

关键词： optimization algorithms

OCTOPUS INSPIRED optimization ALGORITHM: MULTI-LEVEL STRUCTURES AND PARALLEL COMPUTING STRATEGIES

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arXiv 2024年

作者： Wang, Xu Xu, Longji Wang, Yiquan Dong, Yuhua Li, Xiang Deng, Jia He, Rui College of Communication Engineering Jilin University Jilin Changchun130000 China College of Mathematics and System Science Xinjiang University Xinjiang Urumqi830046 China Intelligent Software Research Center Institute of Software Chinese Academy of Sciences Beijing100190 China

This paper introduces a novel bionic intelligent optimisation algorithm, Octopus Inspired optimization (OIO) algorithm, which is inspired by the neural structure of octopus, especially its hierarchical and decentralised interaction properties. By simulating the sensory, decision-making, and executive abilities of octopuses, the OIO algorithm adopts a multi-level hierarchical strategy, including tentacles, suckers, individuals and groups, to achieve an effective combination of global and local search. This hierarchical design not only enhances the flexibility and efficiency of the algorithm, but also significantly improves its search efficiency and adaptability. In performance evaluations, including comparisons with existing mainstream intelligent optimisation algorithms, OIO shows faster convergence and higher accuracy, especially when dealing with multimodal functions and high-dimensional optimisation problems. This advantage is even more pronounced as the required minimum accuracy is higher, with the OIO algorithm showing an average speedup of 2.27 times that of conventional particle swarm optimisation (PSO) and 9.63 times that of differential evolution (DE) on multimodal functions. In particular, when dealing with high-dimensional optimisation problems, OIO achieves an average speed of 10.39 times that of DE, demonstrating its superior computational efficiency. In addition, the OIO algorithm also shows a reduction of about 5% in CPU usage efficiency compared to PSO, which is reflected in the efficiency of CPU resource usage also shows its efficiency. These features make the OIO algorithm show great potential in complex optimisation problems, and it is especially suitable for application scenarios that require fast, efficient and robust optimisation methods, such as robot path planning, supply chain management optimisation, and energy system management. © 2024, CC BY-NC-SA.

关键词： optimization algorithms

Distributed optimization Algorithm with Superlinear Convergence Rate

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arXiv 2024年

作者： Xu, Yeming Guo, Ziyuan Lu, Kaihong Zhang, Huanshui The College of Electrical Engineering and Automation Shandong University of Science and Technology Qingdao266590 China The School of Control Science and Engineering Shandong University Shandong Jinan250061 China The School of Electrical and Automation Engineering Shandong University of Science and Technology Qingdao266590 China

This paper considers distributed optimization problems, where each agent cooperatively minimizes the sum of local objective functions through the communication with its neighbors. The widely adopted distributed gradient method in solving this problem suffers from slow convergence rates, which motivates us to incorporate the second-order information of the objective functions. However, the challenge arises from the unique structure of the inverse of the Hessian matrix, which prevents the direct distributed implementation of the second-order method. We overcome this challenge by proposing a novel optimization framework. The key idea is to transform the distributed optimization problem into an optimal control problem. Using Pontryagin’s maximum principle and the associated forward-backward difference equations (FBDEs), we derive a new distributed optimization algorithm that incorporates the second-order information without requiring the computation of the inverse of the Hessian matrix. Furthermore, the superlinear convergence of the proposed algorithm is proved under some mild assumptions. Finally, we also propose a variant of the algorithm to balance the number of iterations and communication. © 2024, CC BY.

关键词： optimization algorithms

Distributed optimization with Finite Bit Adaptive Quantization for Efficient Communication and Precision Enhancement

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arXiv 2024年

作者： Rikos, Apostolos I. Jiang, Wei Charalambous, Themistoklis Johansson, Karl H. Guangzhou China Department of Computer Science and Engineering The Hong Kong University of Science and Technology Clear Water Bay Hong Kong Department of Electrical Engineering and Automation School of Electrical Engineering Aalto University Espoo Finland Department of Electrical and Computer Engineering School of Engineering University of Cyprus Nicosia1678 Cyprus Division of Decision and Control Systems KTH Royal Institute of Technology StockholmSE-100 44 Sweden

In realistic distributed optimization scenarios, individual nodes possess only partial information and communicate over bandwidth constrained channels. For this reason, the development of efficient distributed algorithms is essential. In our paper we addresses the challenge of unconstrained distributed optimization. In our scenario each node’s local function exhibits strong convexity with Lipschitz continuous gradients. The exchange of information between nodes occurs through 3-bit bandwidth-limited channels (i.e., nodes exchange messages represented by a only 3-bits). Our proposed algorithm respects the network’s bandwidth constraints by leveraging zoom-in and zoom-out operations to adjust quantizer parameters dynamically. We show that during our algorithm’s operation nodes are able to converge to the exact optimal solution. Furthermore, we show that our algorithm achieves a linear convergence rate to the optimal solution. We conclude the paper with simulations that highlight our algorithm’s unique characteristics. © 2024, CC BY.

关键词： optimization algorithms

Bayesian optimization of Functions over Node Subsets in Graphs

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arXiv 2024年

作者： Liang, Huidong Wan, Xingchen Dong, Xiaowen Department of Engineering Science University of Oxford United Kingdom

We address the problem of optimizing over functions defined on node subsets in a graph. The optimization of such functions is often a non-trivial task given their combinatorial, black-box and expensive-to-evaluate nature. Although various algorithms have been introduced in the literature, most are either task-specific or computationally inefficient and only utilize information about the graph structure without considering the characteristics of the function. To address these limitations, we utilize Bayesian optimization (BO), a sample-efficient black-box solver, and propose a novel framework for combinatorial optimization on graphs. More specifically, we map each k-node subset in the original graph to a node in a new combinatorial graph and adopt a local modeling approach to efficiently traverse the latter graph by progressively sampling its subgraphs using a recursive algorithm. Extensive experiments under both synthetic and real-world setups demonstrate the effectiveness of the proposed BO framework on various types of graphs and optimization tasks, where its behavior is analyzed in detail with ablation studies. The experiment code can be found at ***/LeonResearch/GraphComBO. © 2024, CC BY-NC-ND.

关键词： optimization algorithms

DECENTRALIZED FINITE-SUM optimization OVER TIME-VARYING NETWORKS

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arXiv 2024年

作者： Metelev, Dmitry Chezhegov, Savelii Rogozin, Alexander Beznosikov, Aleksandr Sholokhov, Alexander Gasnikov, Alexander Kovalev, Dmitry Moscow Institute of Physics and Technology Moscow Russia The National Research University Higher School of Economics Moscow Russia University Innopolis Innopolis Russia Ivannikov Institute for System Programming Russian Academy of Sciences Moscow Russia Yandex Research Moscow Russia

We consider decentralized time-varying stochastic optimization problems where each of the functions held by the nodes has a finite sum structure. Such problems can be efficiently solved using variance reduction techniques. Our aim is to explore the lower complexity bounds (for communication and number of stochastic oracle calls) and find optimal algorithms. The paper studies strongly convex and nonconvex scenarios. To the best of our knowledge, variance reduced schemes and lower bounds for time-varying graphs have not been studied in the literature. For nonconvex objectives, we obtain lower bounds and develop an optimal method GT-PAGE. For strongly convex objectives, we propose the first decentralized time-varying variance-reduction method ADOM+VR and establish lower bound in this scenario, highlighting the open question of matching the algorithms complexity and lower bounds even in static network case. Copyright © 2024, The Authors. All rights reserved.

关键词： optimization algorithms