A specialized computer named as the Electronic Probe Computer(EPC)has been developed to address large-scale NP-complete problems.The EPC employs a hybrid serial/parallel computational model,structured around four main...A specialized computer named as the Electronic Probe Computer(EPC)has been developed to address large-scale NP-complete problems.The EPC employs a hybrid serial/parallel computational model,structured around four main subsystems:a converting system,an input/output system,and an operating system.The converting system is a software component that transforms the target problem into the graph coloring problem,while the operating system is designed to solve these graph coloring challenges.Comprised of 60 probe computing cards,this system is referred to as EPC60.In tackling large-scale graph coloring problems with EPC60,1003-colorable graphs were randomly selected,each consisting of 2,000 vertices.The state-of-the-art mathematical optimization solver achieved a success rate of only 6%,while EPC60 excelled with a remarkable 100%success rate.Additionally,EPC60 successfully solved two 3-colorable graphs with 1,500 and 2,000 vertices,which had eluded Gurobi’s attempts for 15 days on a standard workstation.Given the mutual reducibility of NP-complete problems in polynomial time theoretically,the EPC stands out as a universal solver for NP-complete problem.The EPC can be applied to various problems that can be abstracted as combinatorial optimization issues,making it relevant across multiple domains,including supply chain management,financial services,telecommunications,energy systems,manufacturing,and beyond.展开更多
Nondeterministic-polynomial-time(NP)-complete problems are widely involved in various reallife scenarios but are still intractable in being solved efficiently on conventional computers.It is of great practical signifi...Nondeterministic-polynomial-time(NP)-complete problems are widely involved in various reallife scenarios but are still intractable in being solved efficiently on conventional computers.It is of great practical significance to construct versatile computing architectures that solve NP-complete problems with computational advantage.Here,we present a reconfigurable integrated photonic processor to efficiently solve a benchmark NP-complete problem,the subset sum problem.We show that in the case of successive primes,the photonic processor has genuinely surpassed electronic processors launched recently by taking advantage of the high propagation speed and vast parallelism of photons and state-of-the-art integrated photonic technology.Moreover,we are able to program the photonic processor to tackle different problem instances,relying on the tunable integrated modules,variable split junctions,which can be used to build a fully reconfigurable architecture potentially allowing 2^(N) configurations at most.Our experiments confirm the potential of the photonic processor as a versatile and efficient computing platform,suggesting a possible practical route to solving computationally hard problems at a large scale.展开更多
We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for ...We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.展开更多
In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s phe...In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copy- ing how drops form rivers by eroding the ground and de- positing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACt. Several previous experi- ments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACt. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACt in the first exe- cution steps in general, though RFD solutions surpass ACt solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACt. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACt and RFD, to solve two NP-hard problems where ACt and RFD fit in a different manner： the traveling salesman problem （TSP） and the prob- lem of the minimum distances tree in a variable-cost graph （MDV）. We compare the results of each method and we an- alyze the advantages of using the hybrid approach in each case.展开更多
The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the hom...The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the home and local segments.This world-wide network has yet to match the complexity of the human brain,which contains a hundred billion neurons,each with thousands of synaptic connections on average.However,it already exceeds the complexity of brains from primitive organisms,i.e.,the honey bee,which has a brain containing approximately one million neurons.In this study,we present a discussion of the computing potential of optical networks as information carriers.Using a simple fiber network,we provide a proof-of-principle demonstration that this network can be treated as an optical oracle for the Hamiltonian path problem,the famous mathematical complexity problem of finding whether a set of towns can be travelled via a path in which each town is visited only once.Pronouncement of a Hamiltonian path is achieved by monitoring the delay of an optical pulse that interrogates the network,and this delay will be equal to the sum of the travel times needed to visit all of the nodes(towns).We argue that the optical oracle could solve this NP-complete problem hundreds of times faster than brute-force computing.Additionally,we discuss secure communication applications for the optical oracle and propose possible implementation in silicon photonics and plasmonic networks.展开更多
With the development of technology,diffusion model-based solvers have shown significant promise in solving Combinatorial Optimization(CO)problems,particularly in tackling Non-deterministic Polynomial-time hard(NP-hard...With the development of technology,diffusion model-based solvers have shown significant promise in solving Combinatorial Optimization(CO)problems,particularly in tackling Non-deterministic Polynomial-time hard(NP-hard)problems such as the Traveling Salesman Problem(TSP).However,existing diffusion model-based solvers typically employ a fixed,uniform noise schedule(e.g.,linear or cosine annealing)across all training instances,failing to fully account for the unique characteristics of each problem instance.To address this challenge,we present GraphGuided Diffusion Solvers(GGDS),an enhanced method for improving graph-based diffusion models.GGDS leverages Graph Neural Networks(GNNs)to capture graph structural information embedded in node coordinates and adjacency matrices,dynamically adjusting the noise levels in the diffusion model.This study investigates the TSP by examining two distinct time-step noise generation strategies:cosine annealing and a Neural Network(NN)-based approach.We evaluate their performance across different problem scales,particularly after integrating graph structural information.Experimental results indicate that GGDS outperforms previous methods with average performance improvements of 18.7%,6.3%,and 88.7%on TSP-500,TSP-100,and TSP-50,respectively.Specifically,GGDS demonstrates superior performance on TSP-500 and TSP-50,while its performance on TSP-100 is either comparable to or slightly better than that of previous methods,depending on the chosen noise schedule and decoding strategy.展开更多
This study examines the mediating role of positive psychological capital and the moderating role of ethnicity in the relationship between mindfulness and internalizing/externalizing problems among adolescents.The stud...This study examines the mediating role of positive psychological capital and the moderating role of ethnicity in the relationship between mindfulness and internalizing/externalizing problems among adolescents.The study sample comprized Chinese adolescents(N=637 ethnic minority;females=40.97%,meam age=12.68,SD=0.49 years;N=636 Han;females=49.06%,mean age=12.71,SD=0.47 years).The participants completed the Child and Adolescent Mindfulness Measure,the Positive Psycap Questionnaire,and the Youth Self-Report.Results from the moderated mediation analysis showed mindfulness was negatively associated with both internalizing and externalizing problems.Ethnicity moderated the relationship between mindfulness and internalizing problems to be stronger for Han adolescents compared to ethnic minority adolescents.Psychological capital mediated the relationship between mindfulness and internalizing problems in both groups,with a negative direction.Findings support the Conservation of Resources theory and highlight mindfulness as a personal resource fostering adolescent well-being in multicultural contexts.展开更多
In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can student...In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can students truly experience the importance of teamwork and the impact of organizational structure on project complexity?To answer these questions,we introduce the requirement-driven organization structure(R-DOS)approach,which tightly couples software requirements with the actual development process.By extending problem-frames modeling and focusing on requirements,R-DOS allows educators and students to(1)diagnose structural flaws early,(2)prescribe role-level and communication fixes,and(3)observe-in real time-how poor structure can derail a project while good structure accelerates learning and delivery.展开更多
Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy(Q=0.1)aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states.In this system...Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy(Q=0.1)aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states.In this system,three fundamental magnetization configurations are identified:(i)the flower state,(ii)the twisted flower state,and(iii)the vortex state.This problem corresponds to standard problem No.3 proposed by the NIST Micromagnetics Modeling Group,widely adopted as a benchmark for validating computational micromagnetics methods.In this work,we approach the problem using a computational method based on direct dipolar interactions,in contrast to conventional techniques that typically compute the demagnetizing field via finite difference-based fast Fourier transform(FFT)methods,tensor grid approaches,or finite element formulations.Our results are compared with established literature data,focusing on the dimensionless parameterλ=L/l_(ex),where L is the cube edge length and l_(ex)is the exchange length of the material.To analyze equilibrium state transitions,we systematically varied the size L as a function of the simulation cell number N and intercellular spacing a,determining the criticalλvalue associated with configuration changes.Our simulations reveal that the transition between the twisted flower and vortex states occurs atλ≈8.45,consistent with values reported in the literature,validating our code(Grupo de Física da Matéeria Condensada-UFJF),and shows that this standard problem can be resolved using only interaction dipolar of a direct way without the need for sophisticated additional calculations.展开更多
The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a coll...The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft,where launch and recovery tasks are conducted concurrently on the flight deck.The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft.To tackle this challenge,a multiple population self-adaptive differential evolution(MPSADE)algorithm is proposed.This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity,an asynchronous updating scheme,an individual migration operator,and a global crossover mechanism.Additionally,comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm.Ultimately,a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.展开更多
In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zer...In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.展开更多
The airplane refueling problem can be stated as follows.We are given n airplanes which can refuel one another during the flight.Each airplane has a reservoir volume wj(liters)and a consumption rate pj(liters per kilom...The airplane refueling problem can be stated as follows.We are given n airplanes which can refuel one another during the flight.Each airplane has a reservoir volume wj(liters)and a consumption rate pj(liters per kilometer).As soon as one airplane runs out of fuel,it is dropping out of the flight.The problem asks for finding a refueling scheme such that the last plane in the air reach a maximal distance.An equivalent version is the n-vehicle exploration problem.The computational complexity of this non-linear combinatorial optimization problem is open so far.This paper employs the neighborhood exchange method of single-machine scheduling to study the precedence relations of jobs,so as to improve the necessary and sufficiency conditions of optimal solutions,and establish an efficient heuristic algorithm which is a generalization of several existing special algorithms.展开更多
Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recov...Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when ta...Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.展开更多
The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface,with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet ...The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface,with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics,are demonstrated in the current research.Hereby,the 2nd Stokes problem assumes that the surface,with a thin shared layer of the fluid on it,oscillates in a harmonic manner along the x-axis of the rivulet flow,which coincides with the main flow direction streaming down the underlying surface.We obtain the exact extension of the rivulet flow family,clarifying the structure of the pressure field,which fully absorbs the arising perturbation.The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity.Hence,the absolutely non-Newtonian case of the viscoplastic flow solution,which satisfies the motion and continuity equations,is considered(with particular cases of exact solutions for pressure).The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation(ODE),describing the dynamics of the coordinate x(t).The approximated schematic dynamics are presented in graphical plots.展开更多
Physics-informed neural networks(PINNs)have been shown as powerful tools for solving partial differential equations(PDEs)by embedding physical laws into the network training.Despite their remarkable results,complicate...Physics-informed neural networks(PINNs)have been shown as powerful tools for solving partial differential equations(PDEs)by embedding physical laws into the network training.Despite their remarkable results,complicated problems such as irregular boundary conditions(BCs)and discontinuous or high-frequency behaviors remain persistent challenges for PINNs.For these reasons,we propose a novel two-phase framework,where a neural network is first trained to represent shape functions that can capture the irregularity of BCs in the first phase,and then these neural network-based shape functions are used to construct boundary shape functions(BSFs)that exactly satisfy both essential and natural BCs in PINNs in the second phase.This scheme is integrated into both the strong-form and energy PINN approaches,thereby improving the quality of solution prediction in the cases of irregular BCs.In addition,this study examines the benefits and limitations of these approaches in handling discontinuous and high-frequency problems.Overall,our method offers a unified and flexible solution framework that addresses key limitations of existing PINN methods with higher accuracy and stability for general PDE problems in solid mechanics.展开更多
The multi-objective optimization problems,especially in constrained environments such as power distribution planning,demand robust strategies for discovering effective solutions.This work presents the improved variant...The multi-objective optimization problems,especially in constrained environments such as power distribution planning,demand robust strategies for discovering effective solutions.This work presents the improved variant of the Multi-population Cooperative Constrained Multi-Objective Optimization(MCCMO)Algorithm,termed Adaptive Diversity Preservation(ADP).This enhancement is primarily focused on the improvement of constraint handling strategies,local search integration,hybrid selection approaches,and adaptive parameter control.Theimproved variant was experimented on with the RWMOP50 power distribution systemplanning benchmark.As per the findings,the improved variant outperformed the original MCCMO across the eleven performance metrics,particularly in terms of convergence speed,constraint handling efficiency,and solution diversity.The results also establish that MCCMOADP consistently delivers substantial performance gains over the baseline MCCMO,demonstrating its effectiveness across performancemetrics.The new variant also excels atmaintaining the balanced trade-off between exploration and exploitation throughout the search process,making it especially suitable for complex optimization problems in multiconstrained power systems.These enhancements make MCCMO-ADP a valuable and promising candidate for handling problems such as renewable energy scheduling,logistics planning,and power system optimization.Future work will benchmark the MCCMO-ADP against widely recognized algorithms such as NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D and will also extend its validation to large-scale real-world optimization domains to further consolidate its generalizability.展开更多
The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, ...The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution （QKD）, which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors＇ results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure （in case that P, NP） or infrastructures facilitating perfectly confidential communication can be constructed efficiently （in case that P = NP）.展开更多
基金supported by the National Major Research Instrument Development Project(62427811)the Key Program of the National Natural Science Foundation of China(62332006)the General Program of the National Natural Science Foundation of China(62172014).
文摘A specialized computer named as the Electronic Probe Computer(EPC)has been developed to address large-scale NP-complete problems.The EPC employs a hybrid serial/parallel computational model,structured around four main subsystems:a converting system,an input/output system,and an operating system.The converting system is a software component that transforms the target problem into the graph coloring problem,while the operating system is designed to solve these graph coloring challenges.Comprised of 60 probe computing cards,this system is referred to as EPC60.In tackling large-scale graph coloring problems with EPC60,1003-colorable graphs were randomly selected,each consisting of 2,000 vertices.The state-of-the-art mathematical optimization solver achieved a success rate of only 6%,while EPC60 excelled with a remarkable 100%success rate.Additionally,EPC60 successfully solved two 3-colorable graphs with 1,500 and 2,000 vertices,which had eluded Gurobi’s attempts for 15 days on a standard workstation.Given the mutual reducibility of NP-complete problems in polynomial time theoretically,the EPC stands out as a universal solver for NP-complete problem.The EPC can be applied to various problems that can be abstracted as combinatorial optimization issues,making it relevant across multiple domains,including supply chain management,financial services,telecommunications,energy systems,manufacturing,and beyond.
基金supported by the National Key R&D Program of China (Grants Nos. 2019YFA0308703, 2019YFA07063022017YFA0303700)+7 种基金the National Natural Science Foundation of China (NSFC)(Grant Nos. 62235012, 12104299,61734005, 11761141014, 11690033, 11904299, and 12304342)the Innovation Program for Quantum Science and Technology(Grant Nos. 2021ZD0301500 and 2021ZD0300700)the Science and Technology Commission of Shanghai Municipality(STCSM)(Grant Nos. 20JC1416300, 2019SHZDZX01,21ZR1432800, and 22QA1404600)the Shanghai Municipal Education Commission (SMEC)(Grant No. 2017-01-07-00-02-E00049)the China Postdoctoral Science Foundation (Grant Nos. 2022T150415, 2021M692094, and 2020M671091)the Startup Fund for Young Faculty at SJTU (SFYF at SJTU)additional support from a Shanghai Talent Programsupport from the Zhiyuan Innovative Research Center of Shanghai Jiao Tong University
文摘Nondeterministic-polynomial-time(NP)-complete problems are widely involved in various reallife scenarios but are still intractable in being solved efficiently on conventional computers.It is of great practical significance to construct versatile computing architectures that solve NP-complete problems with computational advantage.Here,we present a reconfigurable integrated photonic processor to efficiently solve a benchmark NP-complete problem,the subset sum problem.We show that in the case of successive primes,the photonic processor has genuinely surpassed electronic processors launched recently by taking advantage of the high propagation speed and vast parallelism of photons and state-of-the-art integrated photonic technology.Moreover,we are able to program the photonic processor to tackle different problem instances,relying on the tunable integrated modules,variable split junctions,which can be used to build a fully reconfigurable architecture potentially allowing 2^(N) configurations at most.Our experiments confirm the potential of the photonic processor as a versatile and efficient computing platform,suggesting a possible practical route to solving computationally hard problems at a large scale.
文摘We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.
文摘In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copy- ing how drops form rivers by eroding the ground and de- positing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACt. Several previous experi- ments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACt. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACt in the first exe- cution steps in general, though RFD solutions surpass ACt solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACt. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACt and RFD, to solve two NP-hard problems where ACt and RFD fit in a different manner： the traveling salesman problem （TSP） and the prob- lem of the minimum distances tree in a variable-cost graph （MDV）. We compare the results of each method and we an- alyze the advantages of using the hybrid approach in each case.
基金This work was supported by the Singapore Ministry of Education Academic Research Fund Tier 3(Grant No.MOE2011-T3-1-005)the Singapore Agency for Science,Technology and Research(A*STAR,SERC Project No.1223600007)EPSRC(UK)via the Programme on Nanostructured Photonic Metamaterials.
文摘The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the home and local segments.This world-wide network has yet to match the complexity of the human brain,which contains a hundred billion neurons,each with thousands of synaptic connections on average.However,it already exceeds the complexity of brains from primitive organisms,i.e.,the honey bee,which has a brain containing approximately one million neurons.In this study,we present a discussion of the computing potential of optical networks as information carriers.Using a simple fiber network,we provide a proof-of-principle demonstration that this network can be treated as an optical oracle for the Hamiltonian path problem,the famous mathematical complexity problem of finding whether a set of towns can be travelled via a path in which each town is visited only once.Pronouncement of a Hamiltonian path is achieved by monitoring the delay of an optical pulse that interrogates the network,and this delay will be equal to the sum of the travel times needed to visit all of the nodes(towns).We argue that the optical oracle could solve this NP-complete problem hundreds of times faster than brute-force computing.Additionally,we discuss secure communication applications for the optical oracle and propose possible implementation in silicon photonics and plasmonic networks.
基金supported by the National Science and Technology Council,Taiwan,under grant no.NSTC 114-2221-E-197-005-MY3.
文摘With the development of technology,diffusion model-based solvers have shown significant promise in solving Combinatorial Optimization(CO)problems,particularly in tackling Non-deterministic Polynomial-time hard(NP-hard)problems such as the Traveling Salesman Problem(TSP).However,existing diffusion model-based solvers typically employ a fixed,uniform noise schedule(e.g.,linear or cosine annealing)across all training instances,failing to fully account for the unique characteristics of each problem instance.To address this challenge,we present GraphGuided Diffusion Solvers(GGDS),an enhanced method for improving graph-based diffusion models.GGDS leverages Graph Neural Networks(GNNs)to capture graph structural information embedded in node coordinates and adjacency matrices,dynamically adjusting the noise levels in the diffusion model.This study investigates the TSP by examining two distinct time-step noise generation strategies:cosine annealing and a Neural Network(NN)-based approach.We evaluate their performance across different problem scales,particularly after integrating graph structural information.Experimental results indicate that GGDS outperforms previous methods with average performance improvements of 18.7%,6.3%,and 88.7%on TSP-500,TSP-100,and TSP-50,respectively.Specifically,GGDS demonstrates superior performance on TSP-500 and TSP-50,while its performance on TSP-100 is either comparable to or slightly better than that of previous methods,depending on the chosen noise schedule and decoding strategy.
基金supported by the Guizhou Provincial Science and Technology Projects[Basic Science of Guizhou-[2024]Youth 309,Guizhou Platform Talents[2021]1350-046]Zunyi Science and Technology Cooperation[HZ(2024)311]+3 种基金Funding of the Chinese Academy of Social Sciences(2024SYZH005)Peking University Longitudinal Scientific Research Technical Service Project(G-252)Guizhou Provincial Graduate Student Research Fund Project(2024YJSKYJJ339)Zunyi Medical University Graduate Research Fund Project(ZYK206).
文摘This study examines the mediating role of positive psychological capital and the moderating role of ethnicity in the relationship between mindfulness and internalizing/externalizing problems among adolescents.The study sample comprized Chinese adolescents(N=637 ethnic minority;females=40.97%,meam age=12.68,SD=0.49 years;N=636 Han;females=49.06%,mean age=12.71,SD=0.47 years).The participants completed the Child and Adolescent Mindfulness Measure,the Positive Psycap Questionnaire,and the Youth Self-Report.Results from the moderated mediation analysis showed mindfulness was negatively associated with both internalizing and externalizing problems.Ethnicity moderated the relationship between mindfulness and internalizing problems to be stronger for Han adolescents compared to ethnic minority adolescents.Psychological capital mediated the relationship between mindfulness and internalizing problems in both groups,with a negative direction.Findings support the Conservation of Resources theory and highlight mindfulness as a personal resource fostering adolescent well-being in multicultural contexts.
基金supported by the National Natural Science Foundation of China(No.62362006)Guangxi Science and Technology Project(Key Research&Development)(No.GuiKeAB24010343)+1 种基金Guangxi“Bagui Scholar”Teams for Innovation and Research,Innovation Project of Guangxi Graduate Education(No.YCSW2025193)Guangxi Collaborative Innovation Center of Multi-source Information Integration and Intelligent Processing.
文摘In educational settings,instructors often lead students through hands-on software projects,sometimes engaging two different schools or departments.How can such collaborations be made more efficient,and how can students truly experience the importance of teamwork and the impact of organizational structure on project complexity?To answer these questions,we introduce the requirement-driven organization structure(R-DOS)approach,which tightly couples software requirements with the actual development process.By extending problem-frames modeling and focusing on requirements,R-DOS allows educators and students to(1)diagnose structural flaws early,(2)prescribe role-level and communication fixes,and(3)observe-in real time-how poor structure can derail a project while good structure accelerates learning and delivery.
基金CAPES,CNPq,and FAPEMIG(Brazilian Agencies)for their financial support。
文摘Cubic-shaped magnetic particles subjected to a dimensionless uniaxial anisotropy(Q=0.1)aligned with one of the crystallographic axes provide an ideal system for investigating magnetic equilibrium states.In this system,three fundamental magnetization configurations are identified:(i)the flower state,(ii)the twisted flower state,and(iii)the vortex state.This problem corresponds to standard problem No.3 proposed by the NIST Micromagnetics Modeling Group,widely adopted as a benchmark for validating computational micromagnetics methods.In this work,we approach the problem using a computational method based on direct dipolar interactions,in contrast to conventional techniques that typically compute the demagnetizing field via finite difference-based fast Fourier transform(FFT)methods,tensor grid approaches,or finite element formulations.Our results are compared with established literature data,focusing on the dimensionless parameterλ=L/l_(ex),where L is the cube edge length and l_(ex)is the exchange length of the material.To analyze equilibrium state transitions,we systematically varied the size L as a function of the simulation cell number N and intercellular spacing a,determining the criticalλvalue associated with configuration changes.Our simulations reveal that the transition between the twisted flower and vortex states occurs atλ≈8.45,consistent with values reported in the literature,validating our code(Grupo de Física da Matéeria Condensada-UFJF),and shows that this standard problem can be resolved using only interaction dipolar of a direct way without the need for sophisticated additional calculations.
文摘The proliferation of carrier aircraft and the integration of unmanned aerial vehicles(UAVs)on aircraft carriers present new challenges to the automation of launch and recovery operations.This paper investigates a collaborative scheduling problem inherent to the operational processes of carrier aircraft,where launch and recovery tasks are conducted concurrently on the flight deck.The objective is to minimize the cumulative weighted waiting time in the air for recovering aircraft and the cumulative weighted delay time for launching aircraft.To tackle this challenge,a multiple population self-adaptive differential evolution(MPSADE)algorithm is proposed.This method features a self-adaptive parameter updating mechanism that is contingent upon population diversity,an asynchronous updating scheme,an individual migration operator,and a global crossover mechanism.Additionally,comprehensive experiments are conducted to validate the effectiveness of the proposed model and algorithm.Ultimately,a comparative analysis with existing operation modes confirms the enhanced efficiency of the collaborative operation mode.
基金supported by the National Natural Science Foundation of China(11601525)the Natural Science Foundation of Hunan Province(2024JJ5412),the Changsha Municipal Natural Science Foundation(kq2402193).
文摘In this paper,we study the nonlinear Riemann boundary value problem with square roots that is represented by a Cauchy-type integral with kernel density in variable exponent Lebesgue spaces.We discuss the odd-order zero-points distribution of the solutions and separate the single valued analytic branch of the solutions with square roots,then convert the problem to a Riemann boundary value problem in variable exponent Lebesgue spaces and discuss the singularity of solutions at individual zeros belonging to curve.We consider two types of cases those where the coefficient is Hölder and those where it is piecewise Hölder.Then we solve the Hilbert boundary value problem with square roots in variable exponent Lebesgue spaces.By discussing the distribution of the odd-order zero-points for solutions and the method of symmetric extension,we convert the Hilbert problem to a Riemann boundary value problem.The equivalence of the transformation is discussed.Finally,we get the solvable conditions and the direct expressions of the solutions in variable exponent Lebesgue spaces.
基金Supported by Natural Science Foundation of Henan Province(Grant Nos.232300421218 and 252300421483).
文摘The airplane refueling problem can be stated as follows.We are given n airplanes which can refuel one another during the flight.Each airplane has a reservoir volume wj(liters)and a consumption rate pj(liters per kilometer).As soon as one airplane runs out of fuel,it is dropping out of the flight.The problem asks for finding a refueling scheme such that the last plane in the air reach a maximal distance.An equivalent version is the n-vehicle exploration problem.The computational complexity of this non-linear combinatorial optimization problem is open so far.This paper employs the neighborhood exchange method of single-machine scheduling to study the precedence relations of jobs,so as to improve the necessary and sufficiency conditions of optimal solutions,and establish an efficient heuristic algorithm which is a generalization of several existing special algorithms.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction, sparse signal recovery, and other areas. This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery. We first derive the projection formulas for a vector onto the feasible sets. The centralized circumcentered-reflection method is designed to solve the convex feasibility problem. Some numerical experiments demonstrate the feasibility and effectiveness of the proposed algorithm, showing superior performance compared to conventional alternating projection methods.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金funded by National Natural Science Foundation of China(Nos.12402142,11832013 and 11572134)Natural Science Foundation of Hubei Province(No.2024AFB235)+1 种基金Hubei Provincial Department of Education Science and Technology Research Project(No.Q20221714)the Opening Foundation of Hubei Key Laboratory of Digital Textile Equipment(Nos.DTL2023019 and DTL2022012).
文摘Owing to their global search capabilities and gradient-free operation,metaheuristic algorithms are widely applied to a wide range of optimization problems.However,their computational demands become prohibitive when tackling high-dimensional optimization challenges.To effectively address these challenges,this study introduces cooperative metaheuristics integrating dynamic dimension reduction(DR).Building upon particle swarm optimization(PSO)and differential evolution(DE),the proposed cooperative methods C-PSO and C-DE are developed.In the proposed methods,the modified principal components analysis(PCA)is utilized to reduce the dimension of design variables,thereby decreasing computational costs.The dynamic DR strategy implements periodic execution of modified PCA after a fixed number of iterations,resulting in the important dimensions being dynamically identified.Compared with the static one,the dynamic DR strategy can achieve precise identification of important dimensions,thereby enabling accelerated convergence toward optimal solutions.Furthermore,the influence of cumulative contribution rate thresholds on optimization problems with different dimensions is investigated.Metaheuristic algorithms(PSO,DE)and cooperative metaheuristics(C-PSO,C-DE)are examined by 15 benchmark functions and two engineering design problems(speed reducer and composite pressure vessel).Comparative results demonstrate that the cooperative methods achieve significantly superior performance compared to standard methods in both solution accuracy and computational efficiency.Compared to standard metaheuristic algorithms,cooperative metaheuristics achieve a reduction in computational cost of at least 40%.The cooperative metaheuristics can be effectively used to tackle both high-dimensional unconstrained and constrained optimization problems.
文摘The newly formulated non-Newtonian rivulet flows streaming down an inclined planar surface,with additional periodic perturbations arising from the application of the 2nd Stokes problem to the investigation of rivulet dynamics,are demonstrated in the current research.Hereby,the 2nd Stokes problem assumes that the surface,with a thin shared layer of the fluid on it,oscillates in a harmonic manner along the x-axis of the rivulet flow,which coincides with the main flow direction streaming down the underlying surface.We obtain the exact extension of the rivulet flow family,clarifying the structure of the pressure field,which fully absorbs the arising perturbation.The profile of the velocity field is assumed to be Gaussian-type with a non-zero level of plasticity.Hence,the absolutely non-Newtonian case of the viscoplastic flow solution,which satisfies the motion and continuity equations,is considered(with particular cases of exact solutions for pressure).The perturbed governing equations of motion for rivulet flows then result in the Riccati-type ordinary differential equation(ODE),describing the dynamics of the coordinate x(t).The approximated schematic dynamics are presented in graphical plots.
基金Project supported by the Basic Science Research Program through the National Research Foundation(NRF)of Korea funded by the Ministry of Science and ICT(No.RS-2024-00337001)。
文摘Physics-informed neural networks(PINNs)have been shown as powerful tools for solving partial differential equations(PDEs)by embedding physical laws into the network training.Despite their remarkable results,complicated problems such as irregular boundary conditions(BCs)and discontinuous or high-frequency behaviors remain persistent challenges for PINNs.For these reasons,we propose a novel two-phase framework,where a neural network is first trained to represent shape functions that can capture the irregularity of BCs in the first phase,and then these neural network-based shape functions are used to construct boundary shape functions(BSFs)that exactly satisfy both essential and natural BCs in PINNs in the second phase.This scheme is integrated into both the strong-form and energy PINN approaches,thereby improving the quality of solution prediction in the cases of irregular BCs.In addition,this study examines the benefits and limitations of these approaches in handling discontinuous and high-frequency problems.Overall,our method offers a unified and flexible solution framework that addresses key limitations of existing PINN methods with higher accuracy and stability for general PDE problems in solid mechanics.
文摘The multi-objective optimization problems,especially in constrained environments such as power distribution planning,demand robust strategies for discovering effective solutions.This work presents the improved variant of the Multi-population Cooperative Constrained Multi-Objective Optimization(MCCMO)Algorithm,termed Adaptive Diversity Preservation(ADP).This enhancement is primarily focused on the improvement of constraint handling strategies,local search integration,hybrid selection approaches,and adaptive parameter control.Theimproved variant was experimented on with the RWMOP50 power distribution systemplanning benchmark.As per the findings,the improved variant outperformed the original MCCMO across the eleven performance metrics,particularly in terms of convergence speed,constraint handling efficiency,and solution diversity.The results also establish that MCCMOADP consistently delivers substantial performance gains over the baseline MCCMO,demonstrating its effectiveness across performancemetrics.The new variant also excels atmaintaining the balanced trade-off between exploration and exploitation throughout the search process,making it especially suitable for complex optimization problems in multiconstrained power systems.These enhancements make MCCMO-ADP a valuable and promising candidate for handling problems such as renewable energy scheduling,logistics planning,and power system optimization.Future work will benchmark the MCCMO-ADP against widely recognized algorithms such as NSGA-Ⅱ,NSGA-Ⅲ,and MOEA/D and will also extend its validation to large-scale real-world optimization domains to further consolidate its generalizability.
文摘The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution （QKD）, which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors＇ results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure （in case that P, NP） or infrastructures facilitating perfectly confidential communication can be constructed efficiently （in case that P = NP）.
