The application of multi-material topology optimization affords greater design flexibility compared to traditional single-material methods.However,density-based topology optimization methods encounter three unique cha...The application of multi-material topology optimization affords greater design flexibility compared to traditional single-material methods.However,density-based topology optimization methods encounter three unique challenges when inertial loads become dominant:non-monotonous behavior of the objective function,possible unconstrained characterization of the optimal solution,and parasitic effects.Herein,an improved Guide-Weight approach is introduced,which effectively addresses the structural topology optimization problem when subjected to inertial loads.Smooth and fast convergence of the compliance is achieved by the approach,while also maintaining the effectiveness of the volume constraints.The rational approximation of material properties model and smooth design are utilized to guarantee clear boundaries of the final structure,facilitating its seamless integration into manufacturing processes.The framework provided by the alternating active-phase algorithm is employed to decompose the multi-material topological problem under inertial loading into a set of sub-problems.The optimization of multi-material under inertial loads is accomplished through the effective resolution of these sub-problems using the improved Guide-Weight method.The effectiveness of the proposed approach is demonstrated through numerical examples involving two-phase and multi-phase materials.展开更多
The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a prog...The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a progressive quantum algorithm(PQA)to reduce qubit requirements for QAOA+in solving the maximum independent set(MIS)problem.PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution.Specifically,PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies.After each expansion,PQA solves the MIS problem on the newly generated subgraph using QAOA+.In each run,PQA repeats the expansion and solving process until a predefined stopping condition is reached.Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57%(2.17%)of the qubits and 17.59%(6.43%)of the runtime compared with directly solving the original problem with QAOA+on Erd?s-Rényi(3-regular)graphs,highlighting the efficiency and scalability of PQA.展开更多
In this study,we present a novel approach to multi-threshold image segmentation using an adaptive method that combines the Ebola Optimization Search Algorithm(EOSA)with the Aquila Optimizer,termed the Integrated Enhan...In this study,we present a novel approach to multi-threshold image segmentation using an adaptive method that combines the Ebola Optimization Search Algorithm(EOSA)with the Aquila Optimizer,termed the Integrated Enhanced Ebola Optimization Search Algorithm(IEOSA).Our approach leverages this integration to produce high-quality segmented images.The IEOSA method introduces two distinct optimization mechanisms to identify optimal solutions.By blending the randomness of the Aquila Optimizer with the capabilities of EOSA,we enhance the exploration potential of the algorithm.Additionally,we incorporate a self-transition learning system within the IEOSA to further boost its performance.To tackle multi-level threshold image segmentation,we apply Kapur’s entropy between-class variance within the IEOSA framework.Our findings show that the IEOSA-based techniques outperform other comparable methods,offering faster convergence and more stable segmentation results.Through comparative analysis using standard test images,we demonstrate that IEOSA achieves higher solution accuracy than other methods.Ultimately,the proposed IEOSA methodologies effectively address multi-level threshold image segmentation challenges,accurately segmenting even the minor errors that are often overlooked in high-resolution images.展开更多
In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of dista...In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.展开更多
In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algor...In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.展开更多
When deploying Reconfigurable Intelligent Surface(RIS)to improve System Sum-Rate(SSR),the timeliness and accuracy of SSR optimization methods are difficult to achieve simultaneously through a single algorithm.Some alg...When deploying Reconfigurable Intelligent Surface(RIS)to improve System Sum-Rate(SSR),the timeliness and accuracy of SSR optimization methods are difficult to achieve simultaneously through a single algorithm.Some algorithms focus on timeliness,while some focus on accuracy.In this paper,in order to take into account the timeliness and accuracy of the system comprehensively,we construct SSR analysis model of RIS-assisted multiuser downlink communication system and propose several new optimization methods.The goal is to maximize SSR by using the proposed algorithms to jointly optimize power allocation and reflection coefficients.To solve this comprehensive problem,two sets of Alternating Optimization(AO)-based timeliness algorithms and one set of Monotonic Optimization(MO)-based accuracy algorithms are proposed separately to jointly optimize system performance.First,the Water-Filling(WF)-based and penalty-based low complexity algorithms are developed to optimize power allocation and reflection coefficients respectively.To improve the reality of the calculation,penalty-based algorithm cleverly considers residual noise that is difficult to calculate.Then,for further improve the timeliness,a new Successive Convex Approximation(SCA)-based low complexity algorithm is designed to further optimize reflection coefficients and its convergence is proved.Third,in order to verify the effectiveness of the proposed timeliness algorithms,we further propose MO-based accuracy algorithms,in which,the Polyblock Outer Approximation(POA)algorithm,the Semidefinite Relaxation(SDR)method,and the bisection search algorithm are combined in a novel way.Numerical results confirm the timeliness of AO-based algorithms and the accuracy of MO-based algorithms.They supervise and complement each other.展开更多
The growing interest in addressing minimax optimization problem has been fueled by recent applications in machine learning.Although extensively studied in the convex–concave regime,where a global solution can be effi...The growing interest in addressing minimax optimization problem has been fueled by recent applications in machine learning.Although extensively studied in the convex–concave regime,where a global solution can be efficiently computed,this paper delves into the minimax problem within the nonconvex–concave setup.We propose an alternating gradient projection algorithm with momentum(M-AGP),belonging to single-loop algorithms that not only are easier to implement but also require only the computation of gradient projection updates.We demonstrate that the proposed algorithm identifies an-stationary point of the nonconvex–strongly concave minimax problem in O(ε-2)iterations,representing the best-known rate in the literature.Finally,we utilize two test problems,namely robust nonlinear regression and an image classification problem,to showcase the efficacy of the proposed algorithm.展开更多
In this paper,we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints,which have attracted wide attention in machine learning,signa...In this paper,we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints,which have attracted wide attention in machine learning,signal processing and many other fields in recent years.The iteration complexity of the proposed algorithm is proved to be O(ε-3)to reach anε-stationary point.To our knowledge,this is the first algorithm with iteration complexity guarantee for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints.展开更多
Traditional heuristic algorithms often fall into local optima and converge slowly when test case prioritization is addressed in regression testing,making them inadequate for complex real-world scenarios.The Aquila opt...Traditional heuristic algorithms often fall into local optima and converge slowly when test case prioritization is addressed in regression testing,making them inadequate for complex real-world scenarios.The Aquila optimizer,a novel metaheuristic algorithm,demonstrates strong global exploration capability but still faces limitations,including insufficient exploitation capability and slow convergence.To overcome these challenges,a multi-strategy improved chaotic Cauchy inverse cumulative distribution Aquila optimizer for test case prioritization is proposed.First,a logistic–sine–cosine composite chaotic mapping is introduced during the initialization phase of the Aquila optimizer to increase population diversity.Second,the mutated random walk strategy is used to improve global exploration,further enhancing the global search ability of the Aquila optimizer.Moreover,during the narrowed exploration and narrowed exploitation phases,the Cauchy inverse cumulative distribution flight replaces the Lévy flight strategy to reallocate individual positions,strengthening individuals’optimization capability and preventing the algorithm from becoming trapped in local optima.Finally,in the later iteration stage,the specular reflection learning strategy is used to perturb the optimal individual positions and improve the Aquila optimizer’s convergence accuracy and comprehensive optimization performance.Five Java projects were selected from the Defects4J benchmark datasets to conduct comparative experiments with the Aquila optimizer and seven other metaheuristic algorithms.The results demonstrate the effectiveness and superiority of the improved algorithm in test case prioritization.It achieves average improvements of approximately 4.96%in the average percentage of fault detection,3.82%in the average percentage of block coverage,and 5.64%in the average percentage of decision coverage,enabling faster coverage of code blocks and branches.The results provide an efficient priority sorting solution for complex regression testing scenarios.展开更多
针对混合比特语义通信网络(Heterogeneous bit and semantic communication network,HBSCN)存在的能量供应受限和传输性能不足问题,本文构建了无线供电混合比特语义通信网络(Wireless powered HBSCN,WP-HBSCN),并提出了可移动天线(Movab...针对混合比特语义通信网络(Heterogeneous bit and semantic communication network,HBSCN)存在的能量供应受限和传输性能不足问题,本文构建了无线供电混合比特语义通信网络(Wireless powered HBSCN,WP-HBSCN),并提出了可移动天线(Movable antennas,MAs)赋能的高效传输方案。在该方案中,混合接入点(Hybrid access point,HAP)首先向所有用户发送射频信号以实现远程能量供应,然后比特用户和语义用户分别利用收集的能量以时分多址方式向HAP传输比特信息和语义信息。通过在HAP中部署MAs并调整其位置来构建良好的信道条件,实现下行能量传输效率和上行信息传输效率的提升。在保证语义用户的服务质量(Quality of service,QoS)约束的前提下,定义了总比特信息量最大化问题。为了处理该问题的非凸性,设计了基于连续凸近似(Successive convex approximation,SCA)方法和粒子群优化(Particle swarm optimization,PSO)算法的交替优化算法。仿真结果表明,相较于参考方案,所提出的方案最多可以将系统的总比特信息量提升100%。展开更多
针对窃听者的被动特性导致的信道状态信息(channel state information,CSI)不完美问题,引入外部友好干扰节点降级窃听信道质量,提出了一种可同时传输和反射智能超表面(simultaneously transmitting and reflecting reconfigurable intel...针对窃听者的被动特性导致的信道状态信息(channel state information,CSI)不完美问题,引入外部友好干扰节点降级窃听信道质量,提出了一种可同时传输和反射智能超表面(simultaneously transmitting and reflecting reconfigurable intelligent surface,STAR-RIS)联合协作干扰辅助的双侧单用户多窃听下行通信系统的鲁棒物理层安全优化方法.以系统最坏情况下最大化系统的和保密速率(sum secrecy rate,SSR)为优化目标,联合优化基站/干扰节点发射波束成形向量和STAR-RIS传输/反射系数矩阵.由于原始优化问题为多个变量相互耦合的非凸优化问题,提出一种联合交替优化(alternative optimization,AO)、半正定松弛(semidefinite relaxation,SDR)和S-procedure的高效迭代算法,求解得到原问题的次优解.仿真结果表明,与基准方案相比,所提的鲁棒方案能显著提升系统的保密性能.展开更多
Douglas-Rachford splitting(DRS)and the alternating direction method of multipliers(ADMM)are two fundamental first-order methods for structured convex optimization.Although derived from different viewpoints,ADMM can be...Douglas-Rachford splitting(DRS)and the alternating direction method of multipliers(ADMM)are two fundamental first-order methods for structured convex optimization.Although derived from different viewpoints,ADMM can be interpreted as the application of DRS to the dual problem.Based on this structural equivalence,this paper studies how algorithmic improvement strategies can be transferred between the two methods.We classify transferable strategies into three categories:exact operator-level transfer,parameterdriven transfer,and heuristic transfer.Representative examples including relaxation,metric scaling,adaptive parameter updates,and residual balancing are discussed to illustrate the different levels of transferability.This perspective provides a systematic way to understand the relationship between DRS and ADMM and clarifies how algorithmic ideas developed for one method may inform the design of variants of the other,offering a unified framework that both explains existing variants and guides the design of new ones.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.52172356)the Hunan Provincial Natural Science Foundation of China(Grant No.2022JJ10012).
摘要The application of multi-material topology optimization affords greater design flexibility compared to traditional single-material methods.However,density-based topology optimization methods encounter three unique challenges when inertial loads become dominant:non-monotonous behavior of the objective function,possible unconstrained characterization of the optimal solution,and parasitic effects.Herein,an improved Guide-Weight approach is introduced,which effectively addresses the structural topology optimization problem when subjected to inertial loads.Smooth and fast convergence of the compliance is achieved by the approach,while also maintaining the effectiveness of the volume constraints.The rational approximation of material properties model and smooth design are utilized to guarantee clear boundaries of the final structure,facilitating its seamless integration into manufacturing processes.The framework provided by the alternating active-phase algorithm is employed to decompose the multi-material topological problem under inertial loading into a set of sub-problems.The optimization of multi-material under inertial loads is accomplished through the effective resolution of these sub-problems using the improved Guide-Weight method.The effectiveness of the proposed approach is demonstrated through numerical examples involving two-phase and multi-phase materials.
基金supported by the National Natural Science Foundation of China(Grant Nos.62371069,62372048,and 62272056)BUPT Excellent Ph.D.Students Foundation(Grant No.CX2023123)。
摘要The quantum alternating operator ansatz algorithm(QAOA+)is widely used for constrained combinatorial optimization problems(CCOPs)due to its ability to construct feasible solution spaces.In this paper,we propose a progressive quantum algorithm(PQA)to reduce qubit requirements for QAOA+in solving the maximum independent set(MIS)problem.PQA iteratively constructs a subgraph likely to include the MIS solution of the original graph and solves the problem on it to approximate the global solution.Specifically,PQA starts with a small-scale subgraph and progressively expands its graph size utilizing heuristic expansion strategies.After each expansion,PQA solves the MIS problem on the newly generated subgraph using QAOA+.In each run,PQA repeats the expansion and solving process until a predefined stopping condition is reached.Simulation results show that PQA achieves an approximation ratio of 0.95 using only 5.57%(2.17%)of the qubits and 17.59%(6.43%)of the runtime compared with directly solving the original problem with QAOA+on Erd?s-Rényi(3-regular)graphs,highlighting the efficiency and scalability of PQA.
基金King Saud University,Saudi Arabia for funding this work through Ongoing Research Funding Program,(ORF-2026-704)supported by the National Natural Science Foundation of China under Grant 62471493+1 种基金partially supported by the Natural Science Foundation of Shandong Province under Grant ZR2023LZH017,ZR2024MF066partially supported by the National Vocational Education Teacher Teaching Innovation Team Characteristic Project under Grant CXTD003.
摘要In this study,we present a novel approach to multi-threshold image segmentation using an adaptive method that combines the Ebola Optimization Search Algorithm(EOSA)with the Aquila Optimizer,termed the Integrated Enhanced Ebola Optimization Search Algorithm(IEOSA).Our approach leverages this integration to produce high-quality segmented images.The IEOSA method introduces two distinct optimization mechanisms to identify optimal solutions.By blending the randomness of the Aquila Optimizer with the capabilities of EOSA,we enhance the exploration potential of the algorithm.Additionally,we incorporate a self-transition learning system within the IEOSA to further boost its performance.To tackle multi-level threshold image segmentation,we apply Kapur’s entropy between-class variance within the IEOSA framework.Our findings show that the IEOSA-based techniques outperform other comparable methods,offering faster convergence and more stable segmentation results.Through comparative analysis using standard test images,we demonstrate that IEOSA achieves higher solution accuracy than other methods.Ultimately,the proposed IEOSA methodologies effectively address multi-level threshold image segmentation challenges,accurately segmenting even the minor errors that are often overlooked in high-resolution images.
摘要In this paper,we consider the NP-hard problem of finding the minimum dominant resolving set of graphs.A vertex set B of a connected graph G resolves G if every vertex of G is uniquely identified by its vector of distances to the vertices in B.A resolving set is dominating if every vertex of G that does not belong to B is a neighbor to some vertices in B.The dominant metric dimension of G is the cardinality number of the minimum dominant resolving set.The dominant metric dimension is computed by a binary version of the Archimedes optimization algorithm(BAOA).The objects of BAOA are binary encoded and used to represent which one of the vertices of the graph belongs to the dominant resolving set.The feasibility is enforced by repairing objects such that an additional vertex generated from vertices of G is added to B and this repairing process is iterated until B becomes the dominant resolving set.This is the first attempt to determine the dominant metric dimension problem heuristically.The proposed BAOA is compared to binary whale optimization(BWOA)and binary particle optimization(BPSO)algorithms.Computational results confirm the superiority of the BAOA for computing the dominant metric dimension.
摘要In this paper, a distributed algorithm is proposed to solve a kind of multi-objective optimization problem based on the alternating direction method of multipliers. Compared with the centralized algorithms, this algorithm does not need a central node. Therefore, it has the characteristics of low communication burden and high privacy. In addition, numerical experiments are provided to validate the effectiveness of the proposed algorithm.
基金supported in part by Natural Science Foundation of China(92367102)in part by National Science and Technology Major Project(2024ZD1300400).
摘要When deploying Reconfigurable Intelligent Surface(RIS)to improve System Sum-Rate(SSR),the timeliness and accuracy of SSR optimization methods are difficult to achieve simultaneously through a single algorithm.Some algorithms focus on timeliness,while some focus on accuracy.In this paper,in order to take into account the timeliness and accuracy of the system comprehensively,we construct SSR analysis model of RIS-assisted multiuser downlink communication system and propose several new optimization methods.The goal is to maximize SSR by using the proposed algorithms to jointly optimize power allocation and reflection coefficients.To solve this comprehensive problem,two sets of Alternating Optimization(AO)-based timeliness algorithms and one set of Monotonic Optimization(MO)-based accuracy algorithms are proposed separately to jointly optimize system performance.First,the Water-Filling(WF)-based and penalty-based low complexity algorithms are developed to optimize power allocation and reflection coefficients respectively.To improve the reality of the calculation,penalty-based algorithm cleverly considers residual noise that is difficult to calculate.Then,for further improve the timeliness,a new Successive Convex Approximation(SCA)-based low complexity algorithm is designed to further optimize reflection coefficients and its convergence is proved.Third,in order to verify the effectiveness of the proposed timeliness algorithms,we further propose MO-based accuracy algorithms,in which,the Polyblock Outer Approximation(POA)algorithm,the Semidefinite Relaxation(SDR)method,and the bisection search algorithm are combined in a novel way.Numerical results confirm the timeliness of AO-based algorithms and the accuracy of MO-based algorithms.They supervise and complement each other.
基金supported by the National Key R&D Program of China(No.2023YFA1011303)the National Natural Science Foundation of China(Nos.11971083 and 11991024)+1 种基金the Team Project of Innovation Leading Talent in Chongqing(No.CQYC20210309536)the Contract System Project of Chongqing Talent Plan(No.cstc2022ycjh-bgzxm0147).
摘要The growing interest in addressing minimax optimization problem has been fueled by recent applications in machine learning.Although extensively studied in the convex–concave regime,where a global solution can be efficiently computed,this paper delves into the minimax problem within the nonconvex–concave setup.We propose an alternating gradient projection algorithm with momentum(M-AGP),belonging to single-loop algorithms that not only are easier to implement but also require only the computation of gradient projection updates.We demonstrate that the proposed algorithm identifies an-stationary point of the nonconvex–strongly concave minimax problem in O(ε-2)iterations,representing the best-known rate in the literature.Finally,we utilize two test problems,namely robust nonlinear regression and an image classification problem,to showcase the efficacy of the proposed algorithm.
基金supported by the National Natural Science Foundation of China(No.12071279).
摘要In this paper,we propose an alternating proximal gradient algorithm for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints,which have attracted wide attention in machine learning,signal processing and many other fields in recent years.The iteration complexity of the proposed algorithm is proved to be O(ε-3)to reach anε-stationary point.To our knowledge,this is the first algorithm with iteration complexity guarantee for solving nonsmooth nonconvex-linear minimax problems with coupled linear constraints.
基金funded by Natural Science Foundation of Fujian Province,grant numbers 2023J01975,2026J0011041,and 2026J0011042Educational research projects of young and middle-aged teachers in Fujian Province,grant number JAT220362Industry-University-Research Project of Longyan Nonferrous Metals Research Institute,grant number PT202502.
摘要Traditional heuristic algorithms often fall into local optima and converge slowly when test case prioritization is addressed in regression testing,making them inadequate for complex real-world scenarios.The Aquila optimizer,a novel metaheuristic algorithm,demonstrates strong global exploration capability but still faces limitations,including insufficient exploitation capability and slow convergence.To overcome these challenges,a multi-strategy improved chaotic Cauchy inverse cumulative distribution Aquila optimizer for test case prioritization is proposed.First,a logistic–sine–cosine composite chaotic mapping is introduced during the initialization phase of the Aquila optimizer to increase population diversity.Second,the mutated random walk strategy is used to improve global exploration,further enhancing the global search ability of the Aquila optimizer.Moreover,during the narrowed exploration and narrowed exploitation phases,the Cauchy inverse cumulative distribution flight replaces the Lévy flight strategy to reallocate individual positions,strengthening individuals’optimization capability and preventing the algorithm from becoming trapped in local optima.Finally,in the later iteration stage,the specular reflection learning strategy is used to perturb the optimal individual positions and improve the Aquila optimizer’s convergence accuracy and comprehensive optimization performance.Five Java projects were selected from the Defects4J benchmark datasets to conduct comparative experiments with the Aquila optimizer and seven other metaheuristic algorithms.The results demonstrate the effectiveness and superiority of the improved algorithm in test case prioritization.It achieves average improvements of approximately 4.96%in the average percentage of fault detection,3.82%in the average percentage of block coverage,and 5.64%in the average percentage of decision coverage,enabling faster coverage of code blocks and branches.The results provide an efficient priority sorting solution for complex regression testing scenarios.
摘要针对混合比特语义通信网络(Heterogeneous bit and semantic communication network,HBSCN)存在的能量供应受限和传输性能不足问题,本文构建了无线供电混合比特语义通信网络(Wireless powered HBSCN,WP-HBSCN),并提出了可移动天线(Movable antennas,MAs)赋能的高效传输方案。在该方案中,混合接入点(Hybrid access point,HAP)首先向所有用户发送射频信号以实现远程能量供应,然后比特用户和语义用户分别利用收集的能量以时分多址方式向HAP传输比特信息和语义信息。通过在HAP中部署MAs并调整其位置来构建良好的信道条件,实现下行能量传输效率和上行信息传输效率的提升。在保证语义用户的服务质量(Quality of service,QoS)约束的前提下,定义了总比特信息量最大化问题。为了处理该问题的非凸性,设计了基于连续凸近似(Successive convex approximation,SCA)方法和粒子群优化(Particle swarm optimization,PSO)算法的交替优化算法。仿真结果表明,相较于参考方案,所提出的方案最多可以将系统的总比特信息量提升100%。
摘要Douglas-Rachford splitting(DRS)and the alternating direction method of multipliers(ADMM)are two fundamental first-order methods for structured convex optimization.Although derived from different viewpoints,ADMM can be interpreted as the application of DRS to the dual problem.Based on this structural equivalence,this paper studies how algorithmic improvement strategies can be transferred between the two methods.We classify transferable strategies into three categories:exact operator-level transfer,parameterdriven transfer,and heuristic transfer.Representative examples including relaxation,metric scaling,adaptive parameter updates,and residual balancing are discussed to illustrate the different levels of transferability.This perspective provides a systematic way to understand the relationship between DRS and ADMM and clarifies how algorithmic ideas developed for one method may inform the design of variants of the other,offering a unified framework that both explains existing variants and guides the design of new ones.