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A New Optimization Idea: Parallel Search-Based Golden Jackal Algorithm

IEEE ACCESS 2023年 11卷 102115-102131页

作者： Wang, Bin Jin, Qibing Zhao, Ruilian Zhang, Yang Beijing Univ Chem Technol Coll Informat Sci & Technol Beijing 100029 Peoples R China Beijing Univ Chem Technol Coll Mech & Elect Engn Beijing 100029 Peoples R China

As the variety and scope of optimization problems continue to expand, the applicability of a single algorithm may not be universal. To address this challenge, this paper introduces an enhanced iteration of the Golden Jackal Optimization (GJO) algorithm, termed the Parallel Search-based Golden Jackal Optimization (PGJO) algorithm. This algorithm integrates the concept of parallel search into the initialization, updating, and selection mechanisms. It includes a chaotic mapping preselection during the initialization phase, employs a cloning-like strategy for population updates, and incorporates an advanced simulated annealing approach during the selection phase. Through a comprehensive comparison of PGJO with various intelligent optimization algorithms across diverse benchmark functions and real-world scenarios, we affirm its effectiveness in terms of enhanced convergence accuracy and reduced required iterations.

关键词： Optimization Statistics Sociology Behavioral sciences Search problems Particle swarm optimization approximation algorithms Globalization Golden jackal optimization parallel search global search initialization mechanism

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Maximization of nonsubmodular functions under multiple constraints with applications

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AUTOMATICA 2023年第1期155卷

作者： Ye, Lintao Liu, Zhi-Wei Chi, Ming Gupta, Vijay Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China Minist Educ Key Lab Image Proc & Intelligent Control Wuhan 430074 Peoples R China Hubei Key Lab Brain Inspired Intelligent Syst Wuhan 430074 Peoples R China Purdue Univ Elmore Family Sch Elect & Comp Engn W Lafayette IN 47907 USA

We consider the problem of maximizing a monotone nondecreasing set function under multiple constraints, where the constraints are also characterized by monotone nondecreasing set functions. We propose two greedy algorithms to solve the problem with provable approximation guarantees. The first algorithm exploits the structure of a special class of the general problem instance to obtain a better time complexity. The second algorithm is suitable for the general problem. We characterize the approximation guarantees of the two algorithms, leveraging the notions of submodularity ratio and curvature introduced for set functions. We then discuss particular applications of the general problem formulation to problems that have been considered in the literature. We validate our theoretical results using numerical examples.& COPY;2023 Elsevier Ltd. All rights reserved.

关键词： Combinatorial optimization approximation algorithms Greedy algorithms Submodularity

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Accelerated Distributed Approximate Newton Method

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第11期34卷 8642-8653页

作者： Ye, Haishan He, Chaoyang Chang, Xiangyu Xi An Jiao Tong Univ Ctr Intelligent Decis Making & Machine Learning Sch Management Xian 710049 Peoples R China Univ Southern Calif Dept Comp Sci Los Angeles CA 90007 USA

Distributed second-order optimization, as an effective strategy for training large-scale machine learning systems, has been widely investigated due to its low communication complexity. However, the existing distributed second-order optimization algorithms, including distributed approximate Newton (DANE), accelerated inexact DANE (AIDE), and statistically preconditioned accelerated gradient (SPAG), are all required to precisely solve an expensive subproblem up to the target precision. Therefore, this causes these algorithms to suffer from high computation costs and this hinders their development. In this article, we design a novel distributed second-order algorithm called the accelerated distributed approximate Newton (ADAN) method to overcome the high computation costs of the existing ones. Compared with DANE, AIDE, and SPAG, which are constructed based on the relative smooth theory, ADAN's theoretical foundation is built upon the inexact Newton theory. The different theoretical foundations lead to handle the expensive subproblem efficiently, and steps required to solve the subproblem are independent of the target precision. At the same time, ADAN resorts to the acceleration and can effectively exploit the objective function's curvature information, making ADAN to achieve a low communication complexity. Thus, ADAN can achieve both the communication and computation efficiencies, while DANE, AIDE, and SPAG can achieve only the communication efficiency. Our empirical study also validates the advantages of ADAN over extant distributed second-order algorithms.

关键词： Complexity theory approximation algorithms Convergence Servers Optimization Linear programming Machine learning algorithms Acceleration approximate Newton distributed algorithm

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Improvement of Reinforcement Learning With Supermodularity

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第9期34卷 5298-5309页

作者： Meng, Ying Shi, Fengyuan Tang, Lixin Sun, Defeng Northeastern Univ Natl Frontiers Sci Ctr Ind Intelligence & Syst Opt Minist Educ Shenyang Peoples R China Northeastern Univ Key Lab Data Analyt & Optimizat Smart Ind Shenyang Peoples R China Northeastern Univ Key Lab Data Analyt & Optimizat Smart Ind Minist Educ Shenyang 110819 Peoples R China Northeastern Univ Liaoning Engn Lab Data Analyt & Optimizat Smart In Shenyang 110819 Peoples R China Northeastern Univ Natl Frontiers Sci Ctr Ind Intelligence & Syst Opt Shenyang 110819 Peoples R China Northeastern Univ Key Lab Data Analyt & Optimizat Smart Ind Minist Educ Shenyang 110819 Peoples R China Northeastern Univ Liaoning Key Lab Mfg Syst & Logist Optimizat Shenyang 110819 Peoples R China

Reinforcement learning (RL) is a promising approach to tackling learning and decision-making problems in a dynamic environment. Most studies on RL focus on the improvement of state evaluation or action evaluation. In this article, we investigate how to reduce action space by using supermodularity. We consider the decision tasks in the multistage decision process as a collection of parameterized optimization problems, where state parameters dynamically vary along with the time or stage. The optimal solutions of these parameterized optimization problems correspond to the optimal actions in RL. For a given Markov decision process (MDP) with supermodularity, the monotonicity of the optimal action set and the optimal selection with respect to state parameters can be obtained by using the monotone comparative statics. Accordingly, we propose a monotonicity cut to remove unpromising actions from the action space. Taking bin packing problem (BPP) as an example, we show how the supermodularity and monotonicity cut work in RL. Finally, we evaluate the monotonicity cut on the benchmark datasets reported in the literature and compare the proposed RL with some popular baseline algorithms. The results show that the monotonicity cut can effectively improve the performance of RL.

关键词： Optimization Dynamic programming Industries Heuristic algorithms Data analysis approximation algorithms Sufficient conditions Dynamic parameter monotone comparative statics optimization reinforcement learning (RL) supermodularity

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Novel Resolution of Unit Commitment Problems Through Quantum Surrogate Lagrangian Relaxation

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IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第3期38卷 2460-2471页

作者： Feng, Fei Zhang, Peng Bragin, Mikhail A. Zhou, Yifan SUNY Stony Brook Dept Elect & Comp Engn Stony Brook NY 11794 USA

Unit commitment (UC) problems faced by Independent System Operators on a daily basis are becoming increasingly complex due to the recent push for renewables and the consideration of sub-hourly UC to accommodate the increasing variability in the net load. A disruptive solution methodology to address the growing complexity is therefore required. Quantum computing offers a promise to overcome the combinatorial complexity through the use of the so-called "qubits." To make the best use of near-term quantum computers to solve UC problems with a much larger number of binary variables than the number of qubits available, this paper devises a novel solution methodology based on a synergistic combination of quantum computing and Surrogate Lagrangian Relaxation (SLR) to solve UC problems. Our new contributions include: 1) A Quantum-SLR (QSLR) algorithm incorporating quantum approximate optimization algorithm (QAOA) into the SLR method, which overcomes the fundamental difficulties of previous LR-based quantum methods such as zigzagging of multipliers and the need to know or estimate the optimal dual value for convergence;2) A Distributed QSLR framework (D-QSLR) capable of coordinating local quantum/classical computing resources with those within neighborhoods and, in the meantime, protecting data privacy;3) A Quantized UC model to obtain accurate commitment unit subproblems decision by using a quantum machine;and 4) A time-unit-decomposed quantum UC approach to overcoming the quantum resources' limitations. Promising quantum test results validate the effectiveness of QSLR and the scalability of the UC-oriented D-QSLR algorithm, which demonstrate QSLR's enormous potential in UC optimization.

关键词： Quantum computing Optimization Qubit Complexity theory Quantum entanglement Computers approximation algorithms Distributed quantum optimization quantum approximate optimization algorithm quantum computing surrogate lagrangian relaxation unit commitment

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Robust Communication Complexity of Matching: EDCS Achieves 5/6 approximation 50

Robust Communication Complexity of Matching: EDCS Achieves 5...

引用

50th International Colloquium on Automata, Languages, and Programming, ICALP 2023

作者： Azarmehr, Amir Behnezhad, Soheil Northeastern University BostonMA United States

ISBN: (纸本)9783959772785

We study the robust communication complexity of maximum matching. Edges of an arbitrary n-vertex graph G are randomly partitioned between Alice and Bob independently and uniformly. Alice has to send a single message to Bob such that Bob can find an (approximate) maximum matching of the whole graph G. We specifically study the best approximation ratio achievable via protocols where Alice communicates only Oe(n) bits to Bob. There has been a growing interest on the robust communication model due to its connections to the random-order streaming model. An algorithm of Assadi and Behnezhad [ICALP’21] implies a (2/3 + Ε0 ∼ .667)-approximation for a small constant 0 −18, which remains the best-known approximation for general graphs. For bipartite graphs, Assadi and Behnezhad [Random’21] improved the approximation to .716 albeit with a computationally inefficient (i.e., exponential time) protocol. In this paper, we study a natural and efficient protocol implied by a random-order streaming algorithm of Bernstein [ICALP’20] which is based on edge-degree constrained subgraphs (EDCS) [Bernstein and Stein;ICALP’15]. The result of Bernstein immediately implies that this protocol achieves an (almost) (2/3 ∼ .666)-approximation in the robust communication model. We present a new analysis, proving that it achieves a much better (almost) (5/6 ∼ .833)-approximation. This significantly improves previous approximations both for general and bipartite graphs. We also prove that our analysis of Bernstein’s protocol is tight. © Amir Azarmehr and Soheil Behnezhad.

关键词： approximation algorithms

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Operation Optimization Adapting to Active Distribution Networks Under Three-Phase Unbalanced Conditions: Parametric Linear Relaxation Programming

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IEEE SYSTEMS JOURNAL 2023年第3期17卷 4324-4335页

作者： Wang, Jie Wang, Weiqing Yuan, Zhi Xinjiang Univ Dept Elect Engn Urumqi 830049 Xinjiang Peoples R China

Asymmetric phase distributed generation, which is widely used in distribution systems, aggravates the severity of the intrinsic three-phase unbalanced condition of distribution systems. To overcome these problems, operation optimization formulas of the three-phase unbalanced active distribution network (ADN) are established considering soft open point (SOP) and belong to a nonconvex quadratic programming (NQP) problem. However, in conventional methods, either approximations that are not valid for an unbalanced distribution system are used or convex relaxation methods are applied to primitive nonlinear optimization models. However, these methods do not guarantee a feasible optimization solution. Therefore, determining the solution to the NQP problem is challenging. In this article, we propose a parametric linear relaxation algorithm to obtain the optimal feasible solution by solving the operation optimization problem of the three-phase unbalanced ADN with the SOP. The parametric linear relaxation technique is constructed based on the properties of quadratic functions and the mean value theorem, and the NQP is converted to a series of parametric linear relaxation programming problems. The results revealed that the proposed algorithm can achieve the optimal and feasible solution and considerably reduce the computation time compared with an equivalent NLP optimization model for the same distribution system.

关键词： Mathematical models Optimization Distribution networks Voltage Programming Biological system modeling approximation algorithms Active distribution network (ADN) distributed generator (DG) parametric linear relaxation programming (PLRP) soft open point (SOP) unbalanced operation

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An Annealing Mechanism for Adversarial Training Acceleration

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IEEE TRANSACTIONS ON NEURAL NETWORKS AND LEARNING SYSTEMS 2023年第2期34卷 882-893页

作者： Ye, Nanyang Li, Qianxiao Zhou, Xiao-Yun Zhu, Zhanxing Shanghai Jiao Tong Univ Shanghai 200240 Peoples R China Natl Univ Singapore Dept Math Singapore 119077 Singapore PAII Inc Rockville MD 20817 USA Beijing Inst Big Data Res Beijing 100871 Peoples R China

Despite the empirical success in various domains, it has been revealed that deep neural networks are vulnerable to maliciously perturbed input data that can dramatically degrade their performance. These are known as adversarial attacks. To counter adversarial attacks, adversarial training formulated as a form of robust optimization has been demonstrated to be effective. However, conducting adversarial training brings much computational overhead compared with standard training. In order to reduce the computational cost, we propose an annealing mechanism, annealing mechanism for adversarial training acceleration (Amata), to reduce the overhead associated with adversarial training. The proposed Amata is provably convergent, well-motivated from the lens of optimal control theory, and can be combined with existing acceleration methods to further enhance performance. It is demonstrated that, on standard datasets, Amata can achieve similar or better robustness with around 1/3-1/2 the computational time compared with traditional methods. In addition, Amata can be incorporated into other adversarial training acceleration algorithms (e.g., YOPO, Free, Fast, and ATTA), which leads to a further reduction in computational time on large-scale problems.

关键词： Training Annealing Optimization Optimal control Neural networks Perturbation methods approximation algorithms Acceleration adversarial training deep neural networks (DNNs)

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AC Transmission Network Expansion Planning Using the Line-Wise Model for Representing Meshed Transmission Networks

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IEEE TRANSACTIONS ON POWER SYSTEMS 2023年第3期38卷 2204-2223页

作者： Aldik, Abdel Rahman Venkatesh, Bala Ryerson Univ Dept Elect Comp & Biomed Engn Toronto ON M5B 1G3 Canada Ryerson Univ Ctr Urban Energy Toronto ON M5B 1G3 Canada

In this paper, a Line-Wise (LW) formulation of the AC Transmission Network Expansion Planning (AC-TNEP) problem for meshed transmission networks is proposed. The proposed formulation is then relaxed using a novel Quadratic Convex (QC) relaxation that can handle the mixed-integer nature of the problem and be solved efficiently using commercial solvers. The exact and relaxed formulations have been integrated into an algorithm for solving the AC-TNEP problem that has been introduced as an enhancement of an existing algorithm in the literature for obtaining feasible solutions of the AC-TNEP problem upon the use of convex relaxations to solve it. The AC-TNEP problem is solved for different scenarios that involve test cases ranging from 6 to 118 buses. The obtained solutions for the 6-bus to 46-bus test cases are shown to be globally optimal or reinforced to identical or better than the available solutions in the literature. Moreover, as distinguished from solutions in the literature, the proposed algorithm does not utilize approximations and heuristic constraints that are used to ease solving the AC-TNEP problem and were found to potentially lead to locally optimal solutions. Furthermore, the proposed algorithm is used to solve the AC-TNEP problem for the 87-bus and 118-bus test cases to establish its ability to solve for larger test cases. Extensions of the proposed algorithm to account for Reactive Power Planning (RPP) and dynamic planning are studied to further demonstrate its merits.

关键词： Reactive power Power systems Voltage Planning approximation algorithms Costs Mathematical models Convex relaxation power system planning power system optimization

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Limitations of Deep Learning for Inverse Problems on Digital Hardware

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IEEE TRANSACTIONS ON INFORMATION THEORY 2023年第12期69卷 7887-7908页

作者： Boche, Holger Fono, Adalbert Kutyniok, Gitta Tech Univ Munich Inst Theoret Informat Technol D-80333 Munich Germany Ruhr Univ Bochum BMBF Res Hub 6G Life Excellence Cluster Cyber Secu D-44801 Bochum Germany Munich Ctr Quantum Sci & Technol MCQST D-80799 Munich Germany Munich Quantum Valley MQV D-80807 Munich Germany Ludwig Maximilians Univ Munchen Dept Math D-80539 Munich Germany Ludwig Maximilians Univ Munchen Dept Math D-80539 Munich Germany Munich Ctr Machine Learning MCML D-80538 Munich Germany

Deep neural networks have seen tremendous success over the last years. Since the training is performed on digital hardware, in this paper, we analyze what actually can be computed on current hardware platforms modeled as Turing machines, which would lead to inherent restrictions of deep learning. For this, we focus on the class of inverse problems, which, in particular, encompasses any task to reconstruct data from measurements. We prove that finite-dimensional inverse problems are not Banach-Mazur computable for small relaxation parameters. Even more, our results introduce a lower bound on the accuracy that can be obtained algorithmically.

关键词： Neural networks Computational modeling Hardware Inverse problems Deep learning approximation algorithms Task analysis Computing theory deep learning signal processing turing machine

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