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quantum-inspired algorithm for truncated total least squares solution

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS 2024年 451卷

作者： Zuo, Qian Wei, Yimin Xiang, Hua Wuhan Univ Sch Math & Stat Wuhan 430072 Peoples R China Wuhan Univ Hubei Key Lab Computat Sci Wuhan 430072 Peoples R China Peking Univ Sch Comp Sci Beijing 100871 Peoples R China Fudan Univ Sch Math Sci Shanghai 200433 Peoples R China Fudan Univ Shanghai Key Lab Contemporary Appl Math Shanghai 200433 Peoples R China

Compared with the ordinary least squares method, for total least squares (TLS) problem we take into account not only the observation errors, but also the errors in the measurement matrix, which is more realistic in practical applications. Motivated by recent advances in quantum-inspired computing, which have shown promise for solving a variety of optimization problems. For the large-scale discrete ill-posed problem Ax approximate to b, our proposed method leverages quantum-inspired techniques to perform a truncated singular value decomposition (SVD) of the measurement matrix. This allows us to efficiently approximate the TTLS solution, We analyze the accuracy of the quantum-inspired truncated total least squares algorithm both theoretically and numerically. In our theoretical analysis, we compare the approximation accuracy of the proposed quantum-inspired method with TTLS and RTTLS methods. The results of our numerical experiments demonstrate the efficiency of the proposed method in terms of both approximation accuracy and computational efficiency, and show that it can provide accurate solutions for large-scale ill-posed problems.

关键词： Total least squares problems Truncated total least squares Sample model Randomized algorithms quantum-inspired algorithm

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Solving the Flexible Job-shop Scheduling Problem with quantum-inspired algorithm

Solving the Flexible Job-shop Scheduling Problem with Quantu...

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10th World Congress on Intelligent Control and Automation (WCICA)

作者： Wu, Xiuli Univ Sci & Technol Beijing Sch Mech Engn Beijing Peoples R China

ISBN: (纸本)9781467313988

The flexible job shop scheduling problem (FJSP) is typically NP hard. A quantum inspired algorithm is proposed to solve the FJSP. Firstly, the FJSP is formulated. Secondly, the detail of the quantum inspired algorithm is designed, including the quantum chromosome encoding and decoding mechanism, the updating method with the rotation gate matrix. The elitist strategy is integrated to speed up the convergence. The niche technology is combined to avoid trapping into the local optimization. Finally, some benchmark instances are tested to verify the performance of the proposed algorithm. The results shows that the proposed algorithm outperform the compared algorithms.

关键词： Flexible job shop scheduling quantum-inspired algorithm Genetic algorithm

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Optimizing Business Intelligence Classification Rule Mining Using quantum-inspired Genetic algorithm

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IEEE ACCESS 2024年 12卷 137041-137053页

作者： Adnane, Youcef Islem Zerari, Mounira Univ Abdelhamid Mehri Constantine 2 MISC Lab NTIC Fac Constantine 25000 Algeria

This research introduces a novel approach to enhance knowledge discovery through the construction of classification rules for improved event prediction within the domain of business intelligence. One of the applications of the solution can be the improvement of large-scale advertising campaign forecasting. In order to solve the existing problems of data imbalance and high dimensionality in practical applications, we present a new approach of quantum-inspired genetic algorithm (QIGA). Our methodology employs a two-phase strategy: the first phase utilizes QIGA for fast attribute selection while the second phase enhances the manner in which categorical data is represented to enhance rule interpretability. This combined approach is very efficient in producing accurate and usable classification rules without requiring a lot of data pre-processing. Experimental evaluation on benchmark datasets demonstrates the superiority of our proposed method in terms of precision, reliability, and efficiency when compared to traditional approaches. Thus, the proposed algorithm enhances the state-of-art in knowledge discovery by providing a practical and scalable solution to the problem of handling imbalanced data and reducing the effect of high dimensionality, which allows for improving the accuracy of event prediction. Thus, the findings of this research can be applied to various fields other than advertising including fraud detection, customer churn, and medical diagnosis.

关键词： Genetic algorithms Classification algorithms Accuracy Optimization quantum mechanics Business intelligence Probabilistic logic Data mining classification rule data mining genetic algorithm quantum-inspired algorithm

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The Coverage Optimization for Wireless Sensor Networks Based on quantum-inspired Cultural algorithm 1

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Chinese Intelligent Automation Conference (CIAC)

作者： Guo, Yi-nan Liu, Dandan Liu, Yun Chen, Meirong China Univ Min & Technol Coll Informat & Elect Engn Xuzhou 221116 Jiangsu Peoples R China

ISBN: (数字)9783642385247

ISBN: (纸本)9783642385247;9783642385230

In order to properly distribute sensor nodes in wireless sensor networks, a coverage model considering maximum coverage ratio and minimum redundancy is given and the optimization strategy based on quantum-inspired cultural algorithm is proposed. In population space, quantum-inspired evolutionary algorithm is used to increase the observed probability. In belief space, the implicit knowledge embodied in the evolution is extracted from the better individuals chosen from the population. It is used to guide the search direction of evolutionary population and influence the update of quantum individuals. Simulation results indicate that the algorithm is superior to other algorithms in coverage optimization and effectively improve the coverage performance of wireless sensor networks.

关键词： Wireless sensor networks quantum-inspired algorithm Cultural algorithm Coverage optimization

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A Modified quantum-inspired Genetic algorithm for Continuum Structural Topology Optimization

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INTERNATIONAL JOURNAL OF COMPUTATIONAL METHODS 2023年第3期20卷

作者： Wang, Xiaojun Ni, Bowen Wang, Lei Beihang Univ Inst Solid Mech Beijing 100191 Peoples R China

Topology optimization and quantum computing have evolved rapidly over the past three decades. Previous topological optimum design methods suffered from financial burden and mathematical complexity. To overcome these shortcomings, a modified quantum-inspired evolutionary algorithm-based topology optimization method is proposed. This nested approach combines the classic solid isotropic microstructure with the penalization method and the double chains quantum genetic algorithm to establish an integral topology optimization framework. The former is utilized to determine the search direction of design variable updating. Meanwhile, the latter ensures abundant search diversity. The validity and feasibility of the developed methodology are eventually demonstrated by several application examples. The results indicate that the proposed optimization framework is independent of initial values and can lead to optimized structures. In addition, it will be more appropriate and effective if this strategy is deployed on a quantum computer in the future.

关键词： Topology optimization quantum computing quantum-inspired algorithm quantum rotation gate genetic algorithm

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A quantum-inspired Bilevel Optimization algorithm for the First Responder Network Design Problem

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INFORMS JOURNAL ON COMPUTING 2025年第1期37卷 1-196, C2页

作者： Karahalios, Anthony Tayur, Sridhar Tenneti, Ananth Pashapour, Amirreza Salman, F. Sibel Yildiz, Baris Carnegie Mellon Univ Tepper Sch Business Pittsburgh PA 15213 USA Koc Univ Dept Ind Engn TR-34450 Istanbul Turkiye

In the aftermath of a sudden catastrophe, first responders (FRs) strive to reach and rescue immobile victims. Simultaneously, civilians use the same roads to evacuate, access medical facilities and shelters, or reunite with their relatives via private vehicles. The escalated traffic congestion can significantly hinder critical FR operations. A proposal from the Tu rkiye Ministry of Transportation and Infrastructure is to allocate a lane on specific road segments exclusively for FR use, mark them clearly, and precommunicate them publicly. For a successful implementation of this proposal, an FR path should exist from designated entry points to each FR demand point in the network. The reserved FR lanes along these paths will be inaccessible to evacuees, potentially increasing evacuation times. Hence, in this study, we aim to determine a subset of links along which an FR lane should be reserved and analyze the resulting evacuation flow under evacuees' selfish routing behavior. We introduce this problem as the first responder network design problem (FRNDP) and formulate it as a mixed-integer nonlinear program. To efficiently solve FRNDP, we introduce a novel bilevel nested heuristic, the Graver augmented multiseed algorithm (GAMA) within GAMA, called GAGA. We test GAGA on synthetic graph instances of various sizes as well as scenarios related to a potential Istanbul earthquake. Our comparisons with a state-of-the-art exact algorithm for network design problems demonstrate that GAGA offers a promising alternative approach and highlights the need for further exploration of quantum-inspired computing to tackle complex realworld problems.

关键词： disaster preparedness first responder network design problem quantum-inspired algorithm quadratic unconstrained binary optimization (QUBO) Graver augmented multiseed algorithm (GAMA)

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A quantum-inspired Archimedes optimization algorithm for hybrid-load autonomous guided vehicle scheduling problem

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APPLIED INTELLIGENCE 2023年第22期53卷 27725-27778页

作者： Zhou, Binghai Zhao, Lingwei Tongji Univ Inst Ind Engn Sch Mech Engn Caoan Rd 4800Mech Bldg A444 Shanghai 201804 Peoples R China

Facing the two major challenges of just-in-time (JIT) and energy-saving in part-feeding system for mixed-model assembly lines in automotive industry, this paper focuses on optimizing the part-feeding process by investigating the autonomous guided vehicles (AGV) routing and scheduling problem. A hybrid feeding policy, called dual-distribution, is proposed, which considers the utilization of different types of AGVs in various part-feeding policies. The problem is formulated as a mixed-integer programming model with the objectives of simultaneously minimizing the line-side inventory and AGV energy consumption in the part-feeding system. To solve this problem, a Q-learning-based multi-objective quantum-inspired Archimedes optimization algorithm (QMQAOA) is developed with a customized encoding and decoding approach to solve the problem. Besides, the quantum rotation gate initialization mechanism, the Q-learning-based neighborhood search strategy, and the neighboring distance calculation are integrated into the algorithm to improve both solution quality and convergence rate. Finally, numerical experiments are conducted to evaluate the performance of QMQAOA by comparing it with the Gurobi solver and other benchmark algorithms. The results demonstrate the superiority of QMQAOA, with performance superiority rates of 90/90, 77/90, and 90/90 achieved for degree of Pareto optimality (DPO), evenness of solutions (ES), and inverted generational distance (IGD) indicators, respectively. From managerial insights, the application of different types of AGVs in the part-feeding system is shown to enhance efficiency when compared to using a single type of AGV in several instances. These findings provide valuable insights for optimizing the automotive part-feeding system.

关键词： Q-learning quantum-inspired algorithm Archimedes optimization algorithm Hybrid part-feeding policy AGV scheduling

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A Rule-Based Dynamic Decision-Making Stock Trading System Based on quantum-inspired Tabu Search algorithm

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IEEE ACCESS 2014年 2卷 883-896页

作者： Chou, Yao-Hsin Kuo, Shu-Yu Chen, Chi-Yuan Chao, Han-Chieh Natl Chi Nan Univ Dept Comp Sci & Informat Engn Nantou 545 Taiwan Natl Ilan Univ Dept Comp Sci & Informat Engn Yilan 260 Taiwan

Heuristic methods or evolutionary algorithms (such as genetic algorithms and genetic programs) are common approaches applied in financial applications, such as trading systems. Determining the best time to buy or sell stocks in a stock market, and thereby maximizing profit with low risks, is an important issue in financial research. Recent studies have used trading rules based on technique analysis to address this problem. This method can determine trading times by analyzing the value of technical indicators. In other words, we can make trading rules by finding the trading value of technique indicators. An example of a trading rule would be, if one technical indicator's value achieves the setting value, then either buy or sell. A combination of trading rules would become a trading strategy. The process of making trading strategies can be formulated as a combinational optimization problem. In this paper, we propose a novel method for applying a trading system. First, the proposed method uses the quantum-inspired Tabu search algorithm to find the optimal composition and combination of trading strategies. Second, this method uses a sliding window to avoid the major problem of over-fitting. The experiment results of earning money show much better performance than other approaches, and the proposed method outperforms the buy and hold method (which is a benchmark in this field).

关键词： Trading system quantum-inspired algorithm Tabu search decision making

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Faster quantum-inspired algorithms for Solving Linear Systems

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ACM TRANSACTIONS ON quantum COMPUTING 2022年第4期3卷 1–23页

作者： Shao, Changpeng Montanaro, Ashley Univ Bristol Sch Math Bristol BS8 1UG England Phasecraft Ltd Bristol BS1 5DD England

We establish an improved classical algorithm for solving linear systems in a model analogous to the QRAM that is used by quantum linear solvers. Precisely, for the linear systemAx = b, we show that there is a classical algorithm that outputs a data structure for x allowing sampling and querying to the entries, where x is such that ||x - A(+) b|| <= is an element of ||A(+) b ||. This output can be viewed as a classical analogue to the output of quantum linear solvers. The complexity of our algorithm is O-similar to(kappa(6) (F) kappa(2)/C-2), where kappa(F) = ||A || (F) ||A(+) || and kappa = || A || ||A(+) ||. This improves the previous best algorithm [Gilyen, Song and Tang, arXiv:2009.07268] of complexity O(kappa(6) (F) kappa(6/4)). Our algorithm is based on the randomized Kaczmarz method, which is a particular case of stochastic gradient descent. We also find that when A is row sparse, this method already returns an approximate solution x in time O-similar to(kappa(6) (F)), while the best quantum algorithm known returns | x QRAM data structure. As a result, assuming access to QRAM and if A is row sparse, the speedup based on current quantum algorithms is quadratic.

关键词： quantum computing quantum-inspired algorithm Kaczmarz method

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A quantum-inspired Tensor Network algorithm for Constrained Combinatorial Optimization Problems

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FRONTIERS IN PHYSICS 2022年 10卷

作者： Hao, Tianyi Huang, Xuxin Jia, Chunjing Peng, Cheng Stanford Univ Dept Comp Sci Stanford CA USA Stanford Univ Dept Appl Phys Stanford CA USA SLAC Natl Accelerator Lab Stanford Inst Mat & Energy Sci Menlo Pk CA 94025 USA Univ Florida Dept Phys Gainesville FL 32611 USA

Combinatorial optimization is of general interest for both theoretical study and real-world applications. Fast-developing quantum algorithms provide a different perspective on solving combinatorial optimization problems. In this paper, we propose a quantum-inspired tensor-network-based algorithm for general locally constrained combinatorial optimization problems. Our algorithm constructs a Hamiltonian for the problem of interest, effectively mapping it to a quantum problem, then encodes the constraints directly into a tensor network state and solves the optimal solution by evolving the system to the ground state of the Hamiltonian. We demonstrate our algorithm with the open-pit mining problem, which results in a quadratic asymptotic time complexity. Our numerical results show the effectiveness of this construction and potential applications in further studies for general combinatorial optimization problems.

关键词： tensor network algorithm quantum many body models combinatorial optimization problem open-pit mining quantum-inspired algorithm

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