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A survey of differential privacy algorithms for the $k$-means problem Fan YUAN, Dachuan XU, Dongmei ZHANG Operations Research Transactions    2022, 26 (3): 1-16.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.001 Abstract （7565）   HTML （825）    PDF（pc） （993KB）（1105）       Knowledge map    Save The $k$-means problem is a very important problem in the field of machine learning and combinatorial optimization. It is a classic NP-hard problem, which is widely used in data mining, business production decision-making, image processing, biomedical technology, and more. As people in these fields pay more and more attention to personal privacy protection, which raises a question: In the case that decisions are usually made by artificial intelligence algorithms, how to ensure that as much information as possible is extracted from the data without revealing personal privacy? In the past ten years, experts and scholars have continuously studied and explored the $k$-means problem with privacy protection, and has also obtained many results with theoretical guiding significance and practical application value. In this paper we mainly introduce these differential privacy algorithms of the $k$-means problem for readers. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Optimization model and algorithm for Online to Offline dynamic take-out delivery routing problem centered on business districts Chenghao ZHOU, Boxuan LYU, Hanyu ZHOU, Haiyan LU Operations Research Transactions    2022, 26 (3): 17-30.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.002 Abstract （7576）   HTML （525）    PDF（pc） （1042KB）（932）       Knowledge map    Save In the take-out food industry, improper path planning by couriers often leads to low delivery efficiency. Most of the existing VRP research focuses on the optimization of express delivery and other industries, and there is a lack of optimization algorithm research for the food delivery with real-time characteristics. Aiming at the Online to Offline (O2O) take-out delivery routing optimization problem, this paper takes a comprehensive consideration of its dynamic delivery requirements, cargo differentiation and other characteristics as well as constraints such as time windows and cargo capacities, and establishes an O2O dynamic route optimization model of the take-out delivery personnel, in which the business districts are regarded as a delivery centre, and the number of delivery personnel and the total travel time by the delivery personnel are taken as the minimization targets. Using the method of periodically processing new orders, the resultant dynamic adjustment problem of the delivery personnel's route is converted into a series of static TSP sub-problems and thereby a phased heuristic real-time delivery routing optimization algorithm framework is designed, and a concrete algorithm and a numerical example are given. A set of test cases centered on business districts is generated on the basis of a number of widely used VRP instances, the algorithm is tested through simulation experiment and compared with other algorithms. The results show that the algorithm proposed in this paper can make full use of the delivery personnel near the location of the new orders to conduct the delivery, optimize the corresponding delivery route, and effectively reduce the number of delivery personnel for delivery and the total travel time by the delivery personnel. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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A tensor completion method based on tensor train decomposition and its application in image restoration Wenhui XIE, Chen LING, Chenjian PAN Operations Research Transactions    2022, 26 (3): 31-43.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.003 Abstract （7325）   HTML （65）    PDF（pc） （3899KB）（700）       Knowledge map    Save Low-rank tensor completion is widely used in data recovery, and the tensor completion model based on tensor train (TT) decomposition works well in color image, video and internet data recovery. This paper proposes a tensor completion model based on the third-order tensor TT decomposition. In this model, the sparse regularization and the spatio-temporal regularization are introduced to characterize the sparsity of the kernel tensor and the inherent block similarity of the data, respectively. According to the structural characteristics of the problem, some auxiliary variables are introduced to convert the original model into a separable form equivalently, and the method of combining proximal alternating minimization (PAM) and alternating direction multiplier method (ADMM) is used to solve the model. Numerical experiments show that the introduction of two regular terms is beneficial to improve the stability and practical effect of data recovery, and the proposed method is superior to other methods. When the sampling rate is low or the image is structurally missing, the presented method is more effective. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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The bounded inverse optimal value problem on minimum spanning tree under unit infinity norm Binwu ZHANG, Xiucui GUAN Operations Research Transactions    2022, 26 (3): 44-56.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.004 Abstract （7123）   HTML （45）    PDF（pc） （888KB）（508）       Knowledge map    Save We consider the bounded inverse optimal value problem on minimum spanning tree under unit $l_{\infty}$ norm. Given an edge weighted connected undirected network $G=(V, E, w)$, a spanning tree $T^0$, a lower bound vector $\bm{l}$, an upper bound vector $\bm{u}$ and a value $K$, we aim to obtain a new weight vector $\bm{\bar{w}}$ satisfying the lower and upper bounds such that $T^0$ is a minimum spanning tree under the vector $\bm{\bar{w}}$ with weight $K$. The objective is to minimize the modification cost under unit $l_{\infty}$ norm. We present a mathematical model of the problem. After analyzing optimality conditions of the problem, we develop an $O(|V||E|)$ strongly polynomial time algorithm. Reference | Related Articles | Metrics | Comments（0）

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Operations Research Transactions    2022, 26 (3): 0-0.   Abstract （1998）   HTML （392）    PDF（pc） （1750KB）（468）       Knowledge map    Save Reference | Related Articles | Metrics | Comments（0）

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Modified PRP conjugate gradient method for unconstrained optimization Huiling ZHANG, Naoerzai SAI, Xiaoyun WU Operations Research Transactions    2022, 26 (2): 64-72.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.006 Abstract （2939）   HTML （22）    PDF（pc） （823KB）（372）       Knowledge map    Save Based on the PRP conjugate gradient method, we propose an efficient modified PRP conjugate gradient method for solving large-scaled unconstrained optimization problems by using the structure of the CG_DESCENT conjugate gradient method. The proposed method generates a sufficient descent direction at each iteration, which is independent of any line search. Its global convergence and linear convergence rate are established under standard Wolfe line search. The numerical results show that the proposed methods is effective for the given test problems. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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An SAA approach for a class of second-order cone stochastic inverse quadratic programming problem Bo WANG, Li CHU, Liwei ZHANG, Hongwei ZHANG Operations Research Transactions    2022, 26 (2): 31-44.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.003 Abstract （2738）   HTML （60）    PDF（pc） （829KB）（353）       Knowledge map    Save In this paper, we consider a class of stochastic inverse quadratic second-order cone programming problem. This stochastic model contains complementarity constraints, and is more proper to model some class of real world problems. By employing the techniques of stochastic sampling and smoothing, we construct auxiliary approximate sub-problems to solve the original model. In addition, we proved that if the solutions of the approximate sub-problems converge, then with probability one the limit is the C-stationary point of the original problem. If strict complementarity condition and the second order necessary condition hold, then with probability one the limit is an M-stationary point. A simple numerical test verified the applicability of our approach. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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A stochastic Bregman ADMM with its application in training sparse structure SVMs Jiahao LYU, Honglin LUO, Zehua YANG, Jianwen PENG Operations Research Transactions    2022, 26 (2): 16-30.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.002 Abstract （2705）   HTML （59）    PDF（pc） （895KB）（333）       Knowledge map    Save A new stochastic Bregman multiplier alternating direction method (S-B-ADMM) is proposed for non-convex optimization problems with multiple separable blocks. It is shown that the sequence produced by the S-B-ADMM under the periodic update rule converges asymptotically to a stationary solution of the Lagrangian function of the original problem. Under the random update rule, we prove the almost surely convergence of the sequence produced by the S-B-ADMM. Numerical experiments results illustrate the feasibility of the S-B-ADMM for training sparse structural support vector machines. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Multi-agent deep reinforcement learning-based urban traffic signal management Yun HUA, Xiangfeng WANG, Bo JIN Operations Research Transactions    2023, 27 (2): 49-62.   DOI: 10.15960/j.cnki.issn.1007-6093.2023.02.003 Abstract （1000）   HTML （7）    PDF（pc） （3398KB）（311）       Knowledge map    Save With the rapid improvement of the national economy in recent years, people's travel demand has increased, bringing increasingly severe pressure on the current urban traffic signal system relying on traditional non-intelligent traffic lights. The significant increase in the complexity of the traffic network has led to the development of traffic signal control from a single-point problem to a system engineering problem, and the development of artificial intelligence technology brings more methods to dealing with urban traffic signal control. Swarm intelligence methods, represented by multi-agent reinforcement learning, have been widely used in traffic signal control and optimization, including traffic light control, autonomous driving, and vehicle-road collaboration. Compared to traditional methods, multi-agent reinforcement learning can empower the intelligence of traffic signal systems while implementing large-scale traffic signal system collaboration to improve the efficiency of urban traffic operations. The various components involved in urban transportation must collaborate in the vision of intelligent urban traffic. Multi-agent reinforcement learning is of great research value in urban traffic signal control and optimization. This paper will systematically introduce the basic theory of multi-agent deep reinforcement learning and its use in urban traffic signal optimization, summarize the existing approaches and analyze the drawbacks of each method. In addition, this paper will outline the challenges of multi-agent reinforcement learning methods for urban traffic signal optimization. Then the paper points out possible future research directions to promote the development of multi-agent reinforcement learning methods in urban traffic signal optimization. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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A systematic review of researches and applications of bi-level programming in the context of urban transport He WEI, Haofei LIU, Dandan XU, Xuehua HAN, Liang WANG, Xiaodong ZHANG Operations Research Transactions    2023, 27 (2): 1-26.   DOI: 10.15960/j.cnki.issn.1007-6093.2023.02.001 Abstract （994）   HTML （42）    PDF（pc） （14197KB）（310）       Knowledge map    Save Bi-level programming is a typical NP-Hard problem. It is a nonconvex optimization problem with upper and lower hierarchical structure and contains optimization problems in constraint conditions. This paper systematically reviews the researches and applications of bi-level programming in the context of urban transport, focusing on transportation network design problem and OD estimation/adjustment problem. Firstly, the domestic and international research topics and evolution progress are summarized by bibliometrics. Secondly, it takes pioneering research as the clue to look back upon important researches, the first systematic review paper, the first doctoral dissertation, the first Transportation Research Part-B's issue, and the first review paper in Chinese are introduced. Thirdly, the recent development of network design problems including road, transit and multi-modal, and the static and dynamic OD estimation problems are expounded. Fourthly, some general solutions are concluded, and the trends of solutions are discussed, the relationship between bi-level programming and MPEC is expressed. Finally, it points out three opportunities and challenges in the future should be addressed, including exploring and revealing of smart transportation, the optimization of modeling architecture, and building a computing platform to share and interact. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Sharing bicycle relocating with minimum carbon emission Bing SU, Wyatt CARLSON, Jiabin FAN, Arthur GAO, Yanjun SHAO, Guohui LIN Operations Research Transactions    2022, 26 (3): 75-91.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.006 Abstract （2191）   HTML （47）    PDF（pc） （1155KB）（297）       Knowledge map    Save We formulate the sharing bicycle relocating practice as a novel optimization problem, which can be regarded as a variant of the classic TSP problem while its objective function is no longer the length of the Hamiltonian tour but the carbon emission. A well-adopted carbon emission formula that is the product of the load of the vehicle and the travel distance is employed and we propose two heuristic algorithms Greedy and TSP-based, inside both of which we set the priority to reduce the load of the vehicle for minimizing carbon emission. The feasibility of both algorithms is proven and numerical experiments are conducted to validate their performance empirically. The promise of Greedy over TSP-based algorithm is shown to the sharing bicycle companies for their daily dispatching practice. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Unsolved problems in spectral graph theory Lele LIU, Bo NING Operations Research Transactions    2023, 27 (4): 33-60.   DOI: 10.15960/j.cnki.issn.1007-6093.2023.04.003 Abstract （482）   HTML （18）    PDF（pc） （779KB）（294）       Knowledge map    Save Spectral graph theory is a captivating area of graph theory that employs the eigenvalues and eigenvectors of matrices associated with graphs to study them. In this paper, we present a collection of 20 topics in spectral graph theory, covering a range of open problems and conjectures. Our focus is primarily on the adjacency matrix of graphs, and for each topic, we provide a brief historical overview. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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An adaptive global optimization algorithm for solving quadratically constrained quadratic programming problems Xiaoli HUANG, Yuelin GAO, Bo ZHANG, Xia LIU Operations Research Transactions    2022, 26 (2): 83-100.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.008 Abstract （2733）   HTML （14）    PDF（pc） （871KB）（292）       Knowledge map    Save In order to better solve the quadratically constrained quadratic programming problem(QCQP), an adaptive linearized relaxation technique based on the framework of the branch and bound algorithm is proposed in this paper, which theoretically proved that this new delimitation technique is considerable for solving (QCQP). The branch operation in this paper adopts the conditional dichotomy to facilitate effective division of the rectangle; the reduction technique is used to delete some regions that do not contain the global optimal solution to speed up the convergence of the algorithm. Finally, the numerical results show that the proposed algorithm in this paper is effective and feasible. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Auction in blockchain: Applications and challenges Hongyin CHEN, Yukun CHENG, Xiaotie DENG, Zhanghao YAO Operations Research Transactions    2023, 27 (1): 1-29.   DOI: 10.15960/j.cnki.issn.1007-6093.2023.01.001 Abstract （2462）   HTML （89）    PDF（pc） （1261KB）（291）       Knowledge map    Save Blockchain is an important part of the new generation of information technology. It is a new database software integrated with distributed network, encryption technology, smart contract and other technologies. Over the past decade, blockchain technology has had a wide impact on a global scale. Today's blockchain technology has shifted from its initial focus on the decentralization of cryptocurrency and payment to the decentralization of the market. The emergence of smart contract makes the decentralized finance (De-Fi) based on blockchain technology enter a state of rapid development, and various auction scenarios in the context of blockchain also emerge. From the perspective of mechanism design, this paper is the first to summarize and analyze the auction mechanisms on the blockchain in recent years by taking the transaction fee mechanism, NFT auction and MEV auction as the main objects. In addition, we also highlight the challenges and the open problems of the auction mechanism design, based on the characteristics of blockchain. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Operational research methods for urban traffic flow estimation Hu SHAO, Yue ZHUO, Pengjie LIU, Feng SHAO Operations Research Transactions    2023, 27 (2): 27-48.   DOI: 10.15960/j.cnki.issn.1007-6093.2023.02.002 Abstract （970）   HTML （12）    PDF（pc） （1215KB）（273）       Knowledge map    Save With the development of the social economy and the progress of human production mode, the traffic management system provides a series of subjects for operations research. The operational research methods are widely applied in the field of traffic network modeling, and they also occupy some important positions in the intelligent traffic management system. To solve the problems existing in the traffic system, we can make full use of various branches of operations research, which can effectively ensure the efficiency and orderliness of transportation in real life. In this paper, we first introduce several solution models for solving traffic flow estimation problems and then review the existing research from seven aspects: linear programming, integer programming, dynamic programming, graph theory, statistical, heuristic approach, and machine learning method. Finally, to provide more references for transportation managers and researchers, we discuss the development directions and related problems for traffic flow estimation models and propose the potential problems that need to be further investigated and solved. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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A Shapley solution for bipartite rationing problems and its application to museum pass problems Doudou GONG, Genjiu XU, Dongshuang HOU Operations Research Transactions    2022, 26 (2): 45-54.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.004 Abstract （2681）   HTML （17）    PDF（pc） （816KB）（265）       Knowledge map    Save Bipartite rationing problem was studied to divide a short supply between resource and sink nodes in a bipartite graph. It had been used to deal with numerous issues in the real world, such as, the allocations of aid relief during natural disasters, utilities like electricity and natural gas, and talents of different types to universities, etc. From the view of marginal contribution of coalitions, this paper proposed the Shapley solution of bipartite rationing problems calculated by linear programming, and characterized it by cooperative game and axiomatization. First, we defined the cooperative game of bipartite rationing problems, called the bipartite rationing game, and proved that the Shapley value of the corresponding cooperative game coincides with the solution we propose. Then, we showed that the Shapley solution is the unique feasible allocation satisfying priority-consistency. Finally, we considered the application of the Shapley solution to museum pass problems, and discussed the allocations of the revenue of single tickets and pass tickets of each participating museum. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Equilibrium analysis in the retrial queue with an unreliable server Yu ZHANG, Jinting WANG Operations Research Transactions    2022, 26 (2): 1-15.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.02.001 Abstract （2634）   HTML （141）    PDF（pc） （1036KB）（241）       Knowledge map    Save This paper studies customers' equilibrium joining strategy in an M/M/1 constant retrial queue with an unreliable server, where the server may break down under the busy and idle states. In this system, there is no waiting space in front of the server. If a customer finds the server idle upon arrival, he occupies the server immediately. Otherwise, if the server is found busy, the customer can choose to leave a message so that the server can search for customers in the retrial orbit who have left messages before in order to serve them when it is free. Once the server breaks down, the customer being served will be squeezed out of the system and new customers are not allowed to join again. According to the different information provided for customers, this paper investigates the system characteristics at steady state and customers' equilibrium joining strategies based on a reward-cost function. Further, the server's revenue and social welfare functions are established. Through comparisons, it is found revealing the queue length may not bring a greater revenue for the server or a larger social welfare. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Manufacturer channel rebate strategies with customer experience under new product supply chain Chunming XU, Chenchen WU, Baiyun YUAN Operations Research Transactions    2022, 26 (3): 120-132.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.009 Abstract （2168）   HTML （22）    PDF（pc） （2172KB）（233）       Knowledge map    Save With the advent of experience economy and the competition of new product, it is important for manufacturers to build channel distribution and brand promotion based on the customer experience. In this paper, considering the customer experience factor and the retailer's investment in the experience, offline and online demand models are firstly developed in the new product supply chain, respectively. The manufacturer-led supply chain with the contracts of the wholesale price and the channel rebate are discussed. Furthermore, the characteristics of the equilibrium solution of each decision-maker in the supply chain are analyzed, and the comparisons of the optimality based on the above models are made. Finally, the effects of the manufacturer's rebate point, the retailer's experience investment level, the customer's experience factor, the travel cost and the willingness-to-pay on the optimal performance of supply chain are explored in the numerical examples. Table and Figures | Reference | Related Articles | Metrics | Comments（0）

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Approximation algorithm for mixed batch scheduling on identical machines for jobs with arbitrary sizes Dong WANG, Ganggang LI, Wenchang LUO Operations Research Transactions    2022, 26 (3): 133-142.   DOI: 10.15960/j.cnki.issn.1007-6093.2022.03.010 Abstract （2061）   HTML （18）    PDF（pc） （840KB）（221）       Knowledge map    Save In this paper, we consider the mixed batch scheduling problem in which a set of jobs with arbitrary sizes should be processed on identical batch machines with identical capacities. Each job has its processing time and size. Each machine can process a group of jobs as a batch simultaneously, as long as the total size of the jobs in this batch does not exceed the capacity of the machine. For a given batch, its processing time is equal to the weighted sum of the maximum processing time and the total processing time of jobs in the batch. The objective function is to minimize the makespan. The problem includes the one-dimension bin packing problem as its special case, which is strongly NP-hard. For the studied problem, we provide an approximation algorithm with performance ratio of $\left( {2 +2\alpha+\alpha^{2}} \right)$, where $\alpha$ is a given parameter for weight with $0\leq\alpha\leq 1$. Reference | Related Articles | Metrics | Comments（0）

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Machine learning-driven multi-agent pathfinding: An overview Xiangfeng WANG, Wenhao LI Operations Research Transactions    2023, 27 (4): 106-135.   DOI: 10.15960/j.cnki.issn.1007-6093.2023.04.006 Abstract （208）   HTML （10）    PDF（pc） （3514KB）（209）       Knowledge map    Save The Multi-agent Path Finding (MAPF) problem is a core fundamental issue in multi-agent systems and has been widely applied in practical scenarios such as automated intelligent warehousing, autonomous driving, and swarm robotics. From the perspective of problem attributes, the key difficulty lies in enabling multiple intelligent agents to travel along paths simultaneously while ensuring no collisions occur, making it an NP-hard combinatorial optimization problem. However, the aforementioned realworld applications require algorithms to find high-quality, collision-free paths for a large number of intelligent agents within a short computation time. Shorter paths lead to higher system throughput and lower operating costs, presenting significant challenges for classical MAPF optimization algorithms. As a result, in recent years, numerous studies have begun focusing on using machine learning methods to empower MAPF research, aiming to accelerate solution speed and improve solution quality. This paper presents a comprehensive review in three parts, including the core concepts, optimization objectives, and benchmark tasks of the MAPF problem. It also covers the problem modeling, core ideas, and strengths and weaknesses of traditional MAPF algorithms. Additionally and most importantly, this paper introduces a series of machine learning-empowered MAPF algorithms with varying degrees of machine learning involvement, providing corresponding schematic diagrams and pseudocode. This paper further summarizes the major challenges currently faced by machine learning-driven MAPF algorithms and proposes potential future research directions. This is intended to assist researchers in the field and promote the development of machine learning methods in the classical MAPF domain. Table and Figures | Reference | Related Articles | Metrics | Comments（0）