Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a m...Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.展开更多
In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reve...In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.展开更多
The knapsack problem is a classical combinatorial optimization problem widely encountered in areas such as logistics,resource allocation,and portfolio optimization.Traditional methods,including dynamic program-ming(DP...The knapsack problem is a classical combinatorial optimization problem widely encountered in areas such as logistics,resource allocation,and portfolio optimization.Traditional methods,including dynamic program-ming(DP)and greedy algorithms,have been effective in solving small problem instances but often struggle with scalability and efficiency as the problem size increases.DP,for instance,has exponential time complexity and can become computationally prohibitive for large problem instances.On the other hand,greedy algorithms offer faster solutions but may not always yield the optimal results,especially when the problem involves complex constraints or large numbers of items.This paper introduces a novel reinforcement learning(RL)approach to solve the knapsack problem by enhancing the state representation within the learning environment.We propose a representation where item weights and volumes are expressed as ratios relative to the knapsack’s capacity,and item values are normalized to represent their percentage of the total value across all items.This novel state modification leads to a 5%improvement in accuracy compared to the state-of-the-art RL-based algorithms,while significantly reducing execution time.Our RL-based method outperforms DP by over 9000 times in terms of speed,making it highly scalable for larger problem instances.Furthermore,we improve the performance of the RL model by incorporating Noisy layers into the neural network architecture.The addition of Noisy layers enhances the exploration capabilities of the agent,resulting in an additional accuracy boost of 0.2%–0.5%.The results demonstrate that our approach not only outperforms existing RL techniques,such as the Transformer model in terms of accuracy,but also provides a substantial improvement than DP in computational efficiency.This combination of enhanced accuracy and speed presents a promising solution for tackling large-scale optimization problems in real-world applications,where both precision and time are critical factors.展开更多
Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static...Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.展开更多
The Vehicle Routing Problem with Time Windows(VRPTW)presents a significant challenge in combinatorial optimization,especially under real-world uncertainties such as variable travel times,service durations,and dynamic ...The Vehicle Routing Problem with Time Windows(VRPTW)presents a significant challenge in combinatorial optimization,especially under real-world uncertainties such as variable travel times,service durations,and dynamic customer demands.These uncertainties make traditional deterministic models inadequate,often leading to suboptimal or infeasible solutions.To address these challenges,this work proposes an adaptive hybrid metaheuristic that integrates Genetic Algorithms(GA)with Local Search(LS),while incorporating stochastic uncertainty modeling through probabilistic travel times.The proposed algorithm dynamically adjusts parameters—such as mutation rate and local search probability—based on real-time search performance.This adaptivity enhances the algorithm’s ability to balance exploration and exploitation during the optimization process.Travel time uncertainties are modeled using Gaussian noise,and solution robustness is evaluated through scenario-based simulations.We test our method on a set of benchmark problems from Solomon’s instance suite,comparing its performance under deterministic and stochastic conditions.Results show that the proposed hybrid approach achieves up to a 9%reduction in expected total travel time and a 40% reduction in time window violations compared to baseline methods,including classical GA and non-adaptive hybrids.Additionally,the algorithm demonstrates strong robustness,with lower solution variance across uncertainty scenarios,and converges faster than competing approaches.These findings highlight the method’s suitability for practical logistics applications such as last-mile delivery and real-time transportation planning,where uncertainty and service-level constraints are critical.The flexibility and effectiveness of the proposed framework make it a promising candidate for deployment in dynamic,uncertainty-aware supply chain environments.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
Objectives:Near misses happen more frequently than actual errors,and highlight system vulnerabilities without causing any harm,thus provide a safe space for organizational learning.Second-order problem solving behavio...Objectives:Near misses happen more frequently than actual errors,and highlight system vulnerabilities without causing any harm,thus provide a safe space for organizational learning.Second-order problem solving behavior offers a new perspective to better understand how nurses promote learning from near misses to improve organizational outcomes.This study aimed to explore frontline nurses’perspectives on using second-order problem solving behavior in learning from near misses to improve patient safety.Methods:A qualitative exploratory study design was employed.This study was conducted in three tertiary hospitals in east China from June to November 2015.Purposive sampling was used to recruit 19 frontline nurses.Semi-structured interviews and a qualitative directed content analysis was undertaken using Crossan’s 4I Framework of Organizational Learning as a coding framework.Results:Second-order problem solving behavior,based on the 4I Framework of Organizational Learning,was referred to as being a leader in exposing near misses,pushing forward the cause analysis within limited capacity,balancing the active and passive role during improvement project,and promoting the continuous improvement with passion while feeling low-powered.Conclusions:4I Framework of Organizational Learning can be an underlying guide to enrich frontline nurses’role in promoting organizations to learn from near misses.In this study,nurses displayed their pivotal role in organizational learning from near misses by using second-order problem solving.However,additional knowledge,skills,and support are needed to maximize the application of second-order problem solving behavior when near misses are recognized.展开更多
Axiomatic design (AD) and theory of inventive problem solving (TRIZ) are widely used in conceptual design. Both of them have limitations, however. We presented an integrated model of these two methods to increase the ...Axiomatic design (AD) and theory of inventive problem solving (TRIZ) are widely used in conceptual design. Both of them have limitations, however. We presented an integrated model of these two methods to increase the efficiency and quality of the problem solving process for conceptual design. AD is used for systematically defining and structuring a problem into a hierarchy. Sometimes, the design matrix is coupled in AD which indicates the functional requirements are coupled. TRIZ separation principles can be used to separate non-independent design parameters, which provide innovative solutions at each hierarchical level. We applied the integrated model to the heating and drying equipment of bitumen reproduction device. The result verifies that the integrated model can work very well in conceptual design.展开更多
BACKGROUND The use of a problem-solving model guided by stimulus-organism-response(SOR)theory for women with postpartum depression after cesarean delivery may inform nursing interventions for women with postpartum dep...BACKGROUND The use of a problem-solving model guided by stimulus-organism-response(SOR)theory for women with postpartum depression after cesarean delivery may inform nursing interventions for women with postpartum depression.AIM To explore the state of mind and coping style of women with depression after cesarean delivery guided by SOR theory.METHODS Eighty postpartum depressed women with cesarean delivery admitted to the hospital between January 2022 and October 2023 were selected and divided into two groups of 40 cases each,according to the random number table method.In the control group,the observation group adopted the problem-solving nursing model under SOR theory.The two groups were consecutively intervened for 12 weeks,and the state of mind,coping styles,and degree of post-partum depression were analyzed at the end of the intervention.RESULTS The Edinburgh Postnatal Depression Scale and Hamilton Depression Scale-24-item scores of the observation group were lower than in the control group after care,and the level of improvement in the state of mind was higher than that of the control group(P<0.05).The level of coping with illness in the observation group after care(26.48±3.35)was higher than that in the control group(21.73±3.20),and the level of avoidance(12.04±2.68)and submission(8.14±1.15)was lower than that in the control group(15.75±2.69 and 9.95±1.20),with significant differences(P<0.05).CONCLUSION Adopting the problem-solving nursing model using SOR theory for postpartum depressed mothers after cesarean delivery reduced maternal depression,improved their state of mind,and coping level with illness.展开更多
There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound o...There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.展开更多
A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems....A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.展开更多
Traveling salesman problem(TSP) is one of the typical NP-hard problems, and it has been used in many engineering applications. However, the previous swarm intelligence(SI) based algorithms for TSP cannot coordinate wi...Traveling salesman problem(TSP) is one of the typical NP-hard problems, and it has been used in many engineering applications. However, the previous swarm intelligence(SI) based algorithms for TSP cannot coordinate with the exploration and exploitation abilities and are easily trapped into local optimum. In order to deal with this situation, a new hybrid optimization algorithm based on wolf pack search and local search(WPS-LS)is proposed for TSP. The new method firstly simulates the predatory process of wolf pack from the broad field to a specific place so that it allows for a search through all possible solution spaces and prevents wolf individuals from getting trapped into local optimum. Then, local search operation is used in the algorithm to improve the speed of solving and the accuracy of solution. The test of benchmarks selected from TSPLIB shows that the results obtained by this algorithm are better and closer to the theoretical optimal values with better robustness than those obtained by other methods.展开更多
In a number of species,males and females have different ecological roles and therefore might be required to solve different problems.Studies on humans have suggested that the 2 sexes often show different efficiencies ...In a number of species,males and females have different ecological roles and therefore might be required to solve different problems.Studies on humans have suggested that the 2 sexes often show different efficiencies in problem solving tasks;similarly,evidence of sex differences has been found in 2 other mammalian species.Here,we assessed whether a teleost fish species,the guppy.Poecilia reticulata,displays sex differences in the ability to solve problems.In Experiment 1,guppies had to learn to dislodge a disc that occluded a feeder from which they had been previously accustomed to feed.In Experiment 2,guppies had to solve a version of the detour task that required them to learn to enter a transparent cylinder from the open sides to reach a food reward previously freely available.We found evidence of sex differences in both problem-solvingi tasks.In Experiment 1,females clearly outperformed males,and in Experiment 2,guppies showed a reversed but smaller sex difference.This study indicates that sex differences may play an important role in fish's problem-solving similar to what has previously been observed in some mammalian species.展开更多
The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inv...The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.展开更多
In this paper a new method based on neural network has been developed for obtaining the solution of the Stokes problem. We transform the mixed Stokes problem into three independent Poisson problems which by solving th...In this paper a new method based on neural network has been developed for obtaining the solution of the Stokes problem. We transform the mixed Stokes problem into three independent Poisson problems which by solving them the solution of the Stokes problem is obtained. The results obtained by this method, has been compared with the existing numerical method and with the exact solution of the problem. It can be observed that the current new approximation has higher accuracy. The number of model parameters required is less than conventional methods. The proposed new method is illustrated by an example.展开更多
The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method （EFGM） for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables...The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method （EFGM） for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.展开更多
This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to ...This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.展开更多
A class of combustion problem with shock layers is considered.A modified perturbation method is presented.Using this simple and valid technique,we construct the boundary and the shock layers solution to the problem,an...A class of combustion problem with shock layers is considered.A modified perturbation method is presented.Using this simple and valid technique,we construct the boundary and the shock layers solution to the problem,and the asymptotic behavior of the solution is discussed.The modifying perturbation method is shown to be a valid method.展开更多
This paper presents an efficient genetic algorithm for solving multiobjective transportation problem, assignment, and transshipment Problems. The proposed approach integrates the merits of both genetic algorithm (GA) ...This paper presents an efficient genetic algorithm for solving multiobjective transportation problem, assignment, and transshipment Problems. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS) scheme. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on clustering algorithm. The use clustering algorithm makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation. To increase GAs’ problem solution power, local search technique is implemented as neighborhood search engine where it intends to explore the less-crowded area in the current archive to possibly obtain more nondominated solutions. The inclusion of local search and clustering algorithm speeds-up the search process and also helps in obtaining a fine-grained value for the objective functions. Finally, we report numerical results in order to establish the actual computational burden of the proposed algorithm and to assess its performances with respect to classical approaches for solving MOTP.展开更多
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
文摘Several results on iterative methods for equilibrium problems have been proposed and studied in the literature.Most of these results are obtained when the associated bifunction of the equilibrium problem is either a monotone or pseudomonotone operator.Results on iterative methods for equilibrium problems without monotonicity conditions on the bifunction are still few in the literature.In this paper,we study equilibrium problems for which the underlined bifunction is not assumed any form of monotonicity.We propose two weakly convergent iterative algorithms and one strongly convergent algorithm.We obtain our convergence results without assuming either monotonicity or pseudomonotonicity condition on the bifunction.Our proposed algorithms are tested numerically to be more efficient and faster than some few available algorithms for equilibrium problems without monotonicity in the literature.
文摘In this paper,the physics informed neural network(PINN)deep learning method is applied to solve two-dimensional nonlocal equations,including the partial reverse space y-nonlocal Mel'nikov equation,the partial reverse space-time nonlocal Mel'nikov equation and the nonlocal twodimensional nonlinear Schr?dinger(NLS)equation.By the PINN method,we successfully derive a data-driven two soliton solution,lump solution and rogue wave solution.Numerical simulation results indicate that the error range between the data-driven solution and the exact solution is relatively small,which verifies the effectiveness of the PINN deep learning method for solving high dimensional nonlocal equations.Moreover,the parameter discovery of the partial reverse space-time nonlocal Mel'nikov equation is analysed in terms of its soliton solution for the first time.
基金supported in part by the Research Start-Up Funds of South-Central Minzu University under Grants YZZ23002,YZY23001,and YZZ18006in part by the Hubei Provincial Natural Science Foundation of China under Grants 2024AFB842 and 2023AFB202+3 种基金in part by the Knowledge Innovation Program of Wuhan Basic Research underGrant 2023010201010151in part by the Spring Sunshine Program of Ministry of Education of the People’s Republic of China under Grant HZKY20220331in part by the Funds for Academic Innovation Teams and Research Platformof South-CentralMinzu University Grant Number:XT224003,PTZ24001in part by the Career Development Fund(CDF)of the Agency for Science,Technology and Research(A*STAR)(Grant Number:C233312007).
文摘The knapsack problem is a classical combinatorial optimization problem widely encountered in areas such as logistics,resource allocation,and portfolio optimization.Traditional methods,including dynamic program-ming(DP)and greedy algorithms,have been effective in solving small problem instances but often struggle with scalability and efficiency as the problem size increases.DP,for instance,has exponential time complexity and can become computationally prohibitive for large problem instances.On the other hand,greedy algorithms offer faster solutions but may not always yield the optimal results,especially when the problem involves complex constraints or large numbers of items.This paper introduces a novel reinforcement learning(RL)approach to solve the knapsack problem by enhancing the state representation within the learning environment.We propose a representation where item weights and volumes are expressed as ratios relative to the knapsack’s capacity,and item values are normalized to represent their percentage of the total value across all items.This novel state modification leads to a 5%improvement in accuracy compared to the state-of-the-art RL-based algorithms,while significantly reducing execution time.Our RL-based method outperforms DP by over 9000 times in terms of speed,making it highly scalable for larger problem instances.Furthermore,we improve the performance of the RL model by incorporating Noisy layers into the neural network architecture.The addition of Noisy layers enhances the exploration capabilities of the agent,resulting in an additional accuracy boost of 0.2%–0.5%.The results demonstrate that our approach not only outperforms existing RL techniques,such as the Transformer model in terms of accuracy,but also provides a substantial improvement than DP in computational efficiency.This combination of enhanced accuracy and speed presents a promising solution for tackling large-scale optimization problems in real-world applications,where both precision and time are critical factors.
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Enforcing initial and boundary conditions(I/BCs)poses challenges in physics-informed neural networks(PINNs).Several PINN studies have gained significant achievements in developing techniques for imposing BCs in static problems;however,the simultaneous enforcement of I/BCs in dynamic problems remains challenging.To overcome this limitation,a novel approach called decoupled physics-informed neural network(d PINN)is proposed in this work.The d PINN operates based on the core idea of converting a partial differential equation(PDE)to a system of ordinary differential equations(ODEs)via the space-time decoupled formulation.To this end,the latent solution is expressed in the form of a linear combination of approximation functions and coefficients,where approximation functions are admissible and coefficients are unknowns of time that must be solved.Subsequently,the system of ODEs is obtained by implementing the weighted-residual form of the original PDE over the spatial domain.A multi-network structure is used to parameterize the set of coefficient functions,and the loss function of d PINN is established based on minimizing the residuals of the gained ODEs.In this scheme,the decoupled formulation leads to the independent handling of I/BCs.Accordingly,the BCs are automatically satisfied based on suitable selections of admissible functions.Meanwhile,the original ICs are replaced by the Galerkin form of the ICs concerning unknown coefficients,and the neural network(NN)outputs are modified to satisfy the gained ICs.Several benchmark problems involving different types of PDEs and I/BCs are used to demonstrate the superior performance of d PINN compared with regular PINN in terms of solution accuracy and computational cost.
文摘The Vehicle Routing Problem with Time Windows(VRPTW)presents a significant challenge in combinatorial optimization,especially under real-world uncertainties such as variable travel times,service durations,and dynamic customer demands.These uncertainties make traditional deterministic models inadequate,often leading to suboptimal or infeasible solutions.To address these challenges,this work proposes an adaptive hybrid metaheuristic that integrates Genetic Algorithms(GA)with Local Search(LS),while incorporating stochastic uncertainty modeling through probabilistic travel times.The proposed algorithm dynamically adjusts parameters—such as mutation rate and local search probability—based on real-time search performance.This adaptivity enhances the algorithm’s ability to balance exploration and exploitation during the optimization process.Travel time uncertainties are modeled using Gaussian noise,and solution robustness is evaluated through scenario-based simulations.We test our method on a set of benchmark problems from Solomon’s instance suite,comparing its performance under deterministic and stochastic conditions.Results show that the proposed hybrid approach achieves up to a 9%reduction in expected total travel time and a 40% reduction in time window violations compared to baseline methods,including classical GA and non-adaptive hybrids.Additionally,the algorithm demonstrates strong robustness,with lower solution variance across uncertainty scenarios,and converges faster than competing approaches.These findings highlight the method’s suitability for practical logistics applications such as last-mile delivery and real-time transportation planning,where uncertainty and service-level constraints are critical.The flexibility and effectiveness of the proposed framework make it a promising candidate for deployment in dynamic,uncertainty-aware supply chain environments.
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.
文摘Objectives:Near misses happen more frequently than actual errors,and highlight system vulnerabilities without causing any harm,thus provide a safe space for organizational learning.Second-order problem solving behavior offers a new perspective to better understand how nurses promote learning from near misses to improve organizational outcomes.This study aimed to explore frontline nurses’perspectives on using second-order problem solving behavior in learning from near misses to improve patient safety.Methods:A qualitative exploratory study design was employed.This study was conducted in three tertiary hospitals in east China from June to November 2015.Purposive sampling was used to recruit 19 frontline nurses.Semi-structured interviews and a qualitative directed content analysis was undertaken using Crossan’s 4I Framework of Organizational Learning as a coding framework.Results:Second-order problem solving behavior,based on the 4I Framework of Organizational Learning,was referred to as being a leader in exposing near misses,pushing forward the cause analysis within limited capacity,balancing the active and passive role during improvement project,and promoting the continuous improvement with passion while feeling low-powered.Conclusions:4I Framework of Organizational Learning can be an underlying guide to enrich frontline nurses’role in promoting organizations to learn from near misses.In this study,nurses displayed their pivotal role in organizational learning from near misses by using second-order problem solving.However,additional knowledge,skills,and support are needed to maximize the application of second-order problem solving behavior when near misses are recognized.
基金Funded by the Natural Science Foundation of China (No. 50575083)
文摘Axiomatic design (AD) and theory of inventive problem solving (TRIZ) are widely used in conceptual design. Both of them have limitations, however. We presented an integrated model of these two methods to increase the efficiency and quality of the problem solving process for conceptual design. AD is used for systematically defining and structuring a problem into a hierarchy. Sometimes, the design matrix is coupled in AD which indicates the functional requirements are coupled. TRIZ separation principles can be used to separate non-independent design parameters, which provide innovative solutions at each hierarchical level. We applied the integrated model to the heating and drying equipment of bitumen reproduction device. The result verifies that the integrated model can work very well in conceptual design.
文摘BACKGROUND The use of a problem-solving model guided by stimulus-organism-response(SOR)theory for women with postpartum depression after cesarean delivery may inform nursing interventions for women with postpartum depression.AIM To explore the state of mind and coping style of women with depression after cesarean delivery guided by SOR theory.METHODS Eighty postpartum depressed women with cesarean delivery admitted to the hospital between January 2022 and October 2023 were selected and divided into two groups of 40 cases each,according to the random number table method.In the control group,the observation group adopted the problem-solving nursing model under SOR theory.The two groups were consecutively intervened for 12 weeks,and the state of mind,coping styles,and degree of post-partum depression were analyzed at the end of the intervention.RESULTS The Edinburgh Postnatal Depression Scale and Hamilton Depression Scale-24-item scores of the observation group were lower than in the control group after care,and the level of improvement in the state of mind was higher than that of the control group(P<0.05).The level of coping with illness in the observation group after care(26.48±3.35)was higher than that in the control group(21.73±3.20),and the level of avoidance(12.04±2.68)and submission(8.14±1.15)was lower than that in the control group(15.75±2.69 and 9.95±1.20),with significant differences(P<0.05).CONCLUSION Adopting the problem-solving nursing model using SOR theory for postpartum depressed mothers after cesarean delivery reduced maternal depression,improved their state of mind,and coping level with illness.
基金sponsored by the Key Knowledge Innovation Program of the Chinese Academy of Sciences (Grant. No. KZCX2-YW-QN203)the National Basic Research Program of China(2007CB411800),the GYHY200906009 of China Meteorological Administration
文摘There are three common types of predictability problems in weather and climate, which each involve different constrained nonlinear optimization problems： the lower bound of maximum predictable time, the upper bound of maximum prediction error, and the lower bound of maximum allowable initial error and parameter error. Highly effcient algorithms have been developed to solve the second optimization problem. And this optimization problem can be used in realistic models for weather and climate to study the upper bound of the maximum prediction error. Although a filtering strategy has been adopted to solve the other two problems, direct solutions are very time-consuming even for a very simple model, which therefore limits the applicability of these two predictability problems in realistic models. In this paper, a new strategy is designed to solve these problems, involving the use of the existing highly effcient algorithms for the second predictability problem in particular. Furthermore, a series of comparisons between the older filtering strategy and the new method are performed. It is demonstrated that the new strategy not only outputs the same results as the old one, but is also more computationally effcient. This would suggest that it is possible to study the predictability problems associated with these two nonlinear optimization problems in realistic forecast models of weather or climate.
基金Projects(50275150,61173052) supported by the National Natural Science Foundation of ChinaProject(14FJ3112) supported by the Planned Science and Technology of Hunan Province,ChinaProject(14B033) supported by Scientific Research Fund Education Department of Hunan Province,China
文摘A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.
基金the National Natural Science Foundation of China(No.61502198)the Science&Technology Development Project of Jilin Province(Nos.20180101334JC and 20190302117GX)the"3th-Five Year" Science and Technology Research Project of Education Department of Jilin Province(No.JJKH20170574KJ)
文摘Traveling salesman problem(TSP) is one of the typical NP-hard problems, and it has been used in many engineering applications. However, the previous swarm intelligence(SI) based algorithms for TSP cannot coordinate with the exploration and exploitation abilities and are easily trapped into local optimum. In order to deal with this situation, a new hybrid optimization algorithm based on wolf pack search and local search(WPS-LS)is proposed for TSP. The new method firstly simulates the predatory process of wolf pack from the broad field to a specific place so that it allows for a search through all possible solution spaces and prevents wolf individuals from getting trapped into local optimum. Then, local search operation is used in the algorithm to improve the speed of solving and the accuracy of solution. The test of benchmarks selected from TSPLIB shows that the results obtained by this algorithm are better and closer to the theoretical optimal values with better robustness than those obtained by other methods.
基金Funding was provided by PRIN 2015 Grant(prot.:2015FFATB7)to A.B.from Ministero dell'Istruzione,Universita e Ricerca(M IUR,Italy)FIR2018 and FAR2018 grants to T.L.X.from University of Ferrara.
文摘In a number of species,males and females have different ecological roles and therefore might be required to solve different problems.Studies on humans have suggested that the 2 sexes often show different efficiencies in problem solving tasks;similarly,evidence of sex differences has been found in 2 other mammalian species.Here,we assessed whether a teleost fish species,the guppy.Poecilia reticulata,displays sex differences in the ability to solve problems.In Experiment 1,guppies had to learn to dislodge a disc that occluded a feeder from which they had been previously accustomed to feed.In Experiment 2,guppies had to solve a version of the detour task that required them to learn to enter a transparent cylinder from the open sides to reach a food reward previously freely available.We found evidence of sex differences in both problem-solvingi tasks.In Experiment 1,females clearly outperformed males,and in Experiment 2,guppies showed a reversed but smaller sex difference.This study indicates that sex differences may play an important role in fish's problem-solving similar to what has previously been observed in some mammalian species.
基金Project supported by the National Natural Science Foundation of China(Grant No.41175025)
文摘The simplified linear model of Grad-Shafranov （GS） reconstruction can be reformulated into an inverse boundary value problem of Laplace＇s equation. Therefore, in this paper we focus on the method of solving the inverse boundary value problem of Laplace＇s equation. In the first place, the variational regularization method is used to deal with the ill- posedness of the Cauchy problem for Laplace＇s equation. Then, the ＇L-Curve＇ principle is suggested to be adopted in choosing the optimal regularization parameter. Finally, a numerical experiment is implemented with a section of Neumann and Dirichlet boundary conditions with observation errors. The results well converge to the exact solution of the problem, which proves the efficiency and robustness of the proposed method. When the order of observation error δ is 10-1, the order of the approximate result error can reach 10-3.
文摘In this paper a new method based on neural network has been developed for obtaining the solution of the Stokes problem. We transform the mixed Stokes problem into three independent Poisson problems which by solving them the solution of the Stokes problem is obtained. The results obtained by this method, has been compared with the existing numerical method and with the exact solution of the problem. It can be observed that the current new approximation has higher accuracy. The number of model parameters required is less than conventional methods. The proposed new method is illustrated by an example.
基金The project supported by the National Natural Science Foundation of China （10421002. 10472019 and 10172024） NKBRSF （2005CB321704） and the Fund of Disciplines Leaders of Young and Middle Age Faculty in Colleges of Liaoning Province. The English text was polished by Yunming Chen.
文摘The paper combines a self-adaptive precise algorithm in the time domain with Meshless Element Free Galerkin Method （EFGM） for solving viscoelastic problems with rotationally periodic symmetry. By expanding variables at a discretized time interval, the variations of variables can be described more precisely, and iteration is not required for non-linear cases. A space-time domain coupled problem with initial and boundary values can be converted into a series of linear recursive boundary value problems, which are solved by a group theory based on EFGM. It has been proved that the coefficient matrix of the global EFG equation for a rotationally periodic system is block-circulant so long as a kind of symmetry-adapted reference coordinate system is adopted, and then a partitioning algorithm for facilitating parallel processing was proposed via a completely orthogonal group transformation. Therefore instead of solving the original system, only a series of independent small sub-problems need to be solved, leading to computational convenience and a higher computing efficiency. Numerical examples are given to illustrate the full advantages of the proposed algorithm.
基金Supported by Natural Science Foundation of Shanghai(14ZR1429200)National Science Foundation of China(11171221)+4 种基金Shanghai Leading Academic Discipline Project(XTKX2012)Innovation Program of Shanghai Municipal Education Commission(14YZ094)Doctoral Program Foundation of Institutions of Higher Educationof China(20123120110004)Doctoral Starting Projection of the University of Shanghai for Science and Technology(ID-10-303-002)Young Teacher Training Projection Program of Shanghai for Science and Technology
文摘This paper deals with a bi-extrapolated subgradient projection algorithm by intro- ducing two extrapolated factors in the iterative step to solve the multiple-sets split feasibility problem. The strategy is intend to improve the convergence. And its convergence is proved un- der some suitable conditions. Numerical results illustrate that the bi-extrapolated subgradient projection algorithm converges more quickly than the existing algorithms.
基金Project supported by the National Natural Science Foundation of China(Grant No.11071205)the Natural Science Foundation of the Education Bureau of Anhui Province,China(Grant No.KJ2011A135)+2 种基金the Natural Science Foundation of Zhejiang Province, China(Grant No.Y6110502)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK2011042)and the Foundation of the Education Department of Fujian Province,China(Grant No.JA10288)
文摘A class of combustion problem with shock layers is considered.A modified perturbation method is presented.Using this simple and valid technique,we construct the boundary and the shock layers solution to the problem,and the asymptotic behavior of the solution is discussed.The modifying perturbation method is shown to be a valid method.
文摘This paper presents an efficient genetic algorithm for solving multiobjective transportation problem, assignment, and transshipment Problems. The proposed approach integrates the merits of both genetic algorithm (GA) and local search (LS) scheme. The algorithm maintains a finite-sized archive of non-dominated solutions which gets iteratively updated in the presence of new solutions based on clustering algorithm. The use clustering algorithm makes the algorithms practical by allowing a decision maker to control the resolution of the Pareto set approximation. To increase GAs’ problem solution power, local search technique is implemented as neighborhood search engine where it intends to explore the less-crowded area in the current archive to possibly obtain more nondominated solutions. The inclusion of local search and clustering algorithm speeds-up the search process and also helps in obtaining a fine-grained value for the objective functions. Finally, we report numerical results in order to establish the actual computational burden of the proposed algorithm and to assess its performances with respect to classical approaches for solving MOTP.
