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Bidirectional Dijkstra's Algorithm is Instance-Optimal 8

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Bidirectional Dijkstra's Algorithm is Instance-Optimal

8th SIAM Symposium on Simplicity of algorithms, SOSA 2025

作者： Haeupler, Bernhard Hladík, Richard Rozhoň, Václav Tarjan, Robert E. Tětek, Jakub INSAIT Sofia University "St. Kliment Ohridski" & ETH Zurich Princeton University United States

ISBN: (纸本)9781611978315

While Dijkstra's algorithm has near-optimal time complexity for the problem of finding the shortest st-path, in practice, other algorithms are often superior on huge graphs. A prominent such example is the bidirectional search, which executes Dijkstra's algorithm from both endpoints in parallel and stops when these executions meet. In this paper, we give a strong theoretical justification for the use of such bidirectional search algorithms. We prove that for weighted multigraphs, both directed and undirected, a careful implementation of bidirectional search is instance-optimal with respect to the number of edges it explores. That is, we prove that no correct algorithm can outperform our implementation of bidirectional search on any single instance by more than a constant factor. For unweighted graphs, we show that bidirectional search is instace-optimal up to a factor of O(∆) where ∆ is the maximum degree of the graph. We also show that this is the best possible. Copyright © 2025 by SIAM.

关键词： optimization algorithms

Controlled optimization with a Prescribed Finite-Time Convergence Using a Time Varying Feedback Gradient Flow

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arXiv 2025年

作者： Abdel Aal, Osama F. Özbek, Necdet Sinan Viola, Jairo Chen, YangQuan Dept. of Mechanical Engineering University of California Merced 5200 N. Lake Rd MercedCA95343 United States Adana Alparslan Türkeş Science and Technology University Faculty of Engineering Department of Electrical Electronics Engineering Adana Turkey

From the perspective of control theory, the gradient descent optimization methods can be regarded as a dynamic system where various control techniques can be designed to enhance the performance of the optimization method. In this paper, we propose a prescribed finite-time convergent gradient flow that uses time-varying gain nonlinear feedback that can drive the states smoothly towards the minimum. This idea is different from the traditional finite-time convergence algorithms that relies on fractional-power or signed gradient as a nonlinear feedback, that is proved to have finite/fixed time convergence satisfying strongly convex or the Polyak-Lojasiewicz (PL) inequality, where due to its nature, the proposed approach was shown to achieve this property for both strongly convex function, and for those satisfies Polyak-Lojasiewic inequality. Our method is proved to converge in a prescribed finite time via Lyapunov theory. Numerical experiments were presented to illustrate our results. © 2025, CC BY.

关键词： optimization algorithms

Marginal Price optimization

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arXiv 2025年

作者： Loesch, Stefan Richardson, Mark

We introduce a new framework for optimal routing and arbitrage in AMM driven markets. This framework improves on the original best-practice convex optimization by restricting the search to the boundary of the optimal space. We can parameterize this boundary using a set of prices, and a potentially very high dimensional optimization problem (2 optimization variables per curve) gets reduced to to a much lower dimensional root finding problem (1 optimization variable per token, irregardless of number of the curves). Our reformulation is similar to the dual problem of a reformulation of the original convex problem. We show our reformulation of the problem is equivalent to the original formulation except in the case of infinitely concentrated liquidity, where we provide a suitable approximation. Our formulation performs far better than the original one in terms of speed – we obtain an improvement of up to 200x against Clarabel, the new CVXPY default solver – and robustness, especially on levered curves. Copyright © 2025, The Authors. All rights reserved.

关键词： optimization algorithms

Reward-aware Preference optimization: A Unified Mathematical Framework for Model Alignment

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arXiv 2025年

作者： Sun, Shengyang Zhang, Yian Bukharin, Alexander Mosallanezhad, David Zeng, Jiaqi Singhal, Soumye Shen, Gerald Renduchintala, Adithya Konuk, Tugrul Dong, Yi Wang, Zhilin Chichkov, Dmitry Delalleau, Olivier Kuchaiev, Oleksii NVIDIA United States

The rapid development of large language model (LLM) alignment algorithms has resulted in a complex and fragmented landscape, with limited clarity on the effectiveness of different methods and their inter-connections. This paper introduces Reward-Aware Preference optimization (RPO), a mathematical framework that unifies popular preference optimization techniques in LLM alignment, including DPO, IPO, SimPO, and REINFORCE (LOO), among others. RPO provides a structured approach to disentangle and systematically study the impact of various design choices—such as the optimization objective, the number of responses per prompt, and the use of implicit versus explicit reward models—on LLM preference optimization. We additionally propose a new experimental setup that enables the clean and direct ablation of such design choices. Through an extensive series of ablation studies within the RPO framework, we gain insights into the critical factors shaping model alignment, offering practical guidance on the most effective strategies for improving LLM alignment. © 2025, CC BY.

关键词： optimization algorithms

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

Systematic Design of Decentralized algorithms for Consensus optimization

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IEEE CONTROL SYSTEMS LETTERS 2019年第4期3卷 966-971页

作者： Han, Shuo Univ Illinois Dept Elect & Comp Engn Chicago IL 60607 USA

We propose a separation principle that enables a systematic way of designing decentralized algorithms used in consensus optimization. Specifically, we show that a decentralized optimization algorithm can be constructed by combining a non-decentralized base optimization algorithm and decentralized consensus tracking. The separation principle provides modularity in both the design and analysis of algorithms under an automated convergence analysis framework using integral quadratic constraints (IQCs). We show that consensus tracking can be incorporated into the IQC-based analysis. The workflow is illustrated through the design and analysis of a decentralized algorithm based on the alternating direction method of multipliers.

关键词： optimization algorithms robust control

Advancements in Bat algorithm 4th

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Advancements in Bat algorithm

4th International Conference on Computational Methods in Science and Technology, ICCMST 2024

作者： Kaur, Arvinder Kumar, Yugal Sidhu, Jagpreet Department of Information Technology Chandigarh Engineering College-CGC Landran Punjab Mohali India Computer Engineering/STME NMIMS Chandigarh Campus India

ISBN: (纸本)9781032911571

The modern times have led to the adoption of distinctive meta-heuristic procedures for solving distinct class of optimization-problems. The meta-heuristics procedures have benefit above conventional algorithms because of strong capabilities of exploration and exploitation. In a similar vein, a Bat algorithm was created based on the echolocation habits of bats to address optimisation difficulties. Several advancements have been made in bat algorithm since then to achieve the state-of art results. The purpose of the study is to investigate bat algorithm for the various advancements done. Henceforth, the study presents the miniature analysis on advancements in bat algorithm. The bat algorithm applications in different areas are also investigated. © 2025 the Author(s).

关键词： optimization algorithms

A Graph Clustering Algorithm Based on Gravitational Vector 16th

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A Graph Clustering Algorithm Based on Gravitational Vector

16th International Conference on Genetic and Evolutionary Computing, ICGEC 2024

作者： Li, Jitao Yao, Yao Xu, Chugui Tian, Xue Department of Information Science and Technology Taishan University Tai’an271000 China

ISBN: (纸本)9789819615346

The traditional clustering algorithms mostly use simple one-dimensional distance measurement and overall optimization strategy for classification, one-dimensional measurement method can identify similarity matrix, but cannot keep the spatial location relationship between samples, because of the loss of data information between the sample which cause the clustering accuracy problem, this paper puts forward a graph clustering algorithm based on gravitational vector. This method combines the principle of gravity principle, uses the multi-dimensional vector instead of the traditional one-dimensional distance measurement method, and excavates the connection between the samples by establishing the local balance relationship, and finally achieves the purpose of improving the local information extraction and data distribution perception ability of the algorithm. Using the present algorithm in artificial datasets and UCI datasets can show that the present algorithm can cope well with multi-type, unbalanced, high complexity data and get good clustering results. © The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd. 2025.

关键词： optimization algorithms

Maximizing Throughput and Minimizing Latency: Evolutionary algorithms for Optimizing Wireless Cellular Networks 3

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Maximizing Throughput and Minimizing Latency: Evolutionary A...

3rd International Conference on Intelligent Data Communication Technologies and Internet of Things, IDCIoT 2025

作者： Pechetti, Jyoshitha Yadav, Sneha Tarunya, G. Rajagopal, Shinu M. Department of Computer Science and Engineering Amrita School of Computing Amrita Vishwa Vidyapeetham Bengaluru India

ISBN: (纸本)9798331527549

In the rapidly evolving world of wireless cellular network, optimizing key parameters like data throughput and latency is of critical importance for ensuring high quality communication services. The proposed presents a novel approach to multi-objective optimization to enhance overall network performance using Genetic algorithms (GA), Pareto, and Particle Swarm optimization (PSO). By employing optimization algorithms, a balance is sought in terms of trade-off of other parameters while maximizing data throughput and minimizing latency. Simulation layers indicate the comparative study further solidifies the efficacy of the value of evolutionary algorithms in optimizing wireless networks to satisfy the growing needs of high speed and less latency services in today’s communication landscape. © 2025 IEEE.

关键词： optimization algorithms