The on-line problem of scheduling on a batch processing machine with nonidentical job sizes to minimize makespan is considered. The batch processing machine can process a number of jobs simultaneously as long as the t...The on-line problem of scheduling on a batch processing machine with nonidentical job sizes to minimize makespan is considered. The batch processing machine can process a number of jobs simultaneously as long as the total size of these jobs being processed does not exceed the machine capacity. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. The paper deals with two variants： the case only with two distinct arrival times and the general case. For the first case, an on-line algorithm with competitive ratio 119/44 is given. For the latter one, a simple algorithm with competitive ratio 3 is given. For both variants the better ratios can be obtained if the problem satisfies proportional assumption.展开更多
In this paper, a semi on-line version on m ide ntical machines M 1, M 2, …,M m(m≥3) was considered, where th e processing time of the largest job is known in advance. Our goal is to maximiz e the minimum machine ...In this paper, a semi on-line version on m ide ntical machines M 1, M 2, …,M m(m≥3) was considered, where th e processing time of the largest job is known in advance. Our goal is to maximiz e the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m-1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2m-1)p max where p max is the largest job' s processing time, then the worst-case ratio is 2-1/m.展开更多
Differential evolution （DE） is a global optimizer for continuous design variables. To enhance DE, it is necessary to handle discrete design variables. In this paper, a discrete differential evolution （DDE） algorit...Differential evolution （DE） is a global optimizer for continuous design variables. To enhance DE, it is necessary to handle discrete design variables. In this paper, a discrete differential evolution （DDE） algorithm is proposed to handle discrete design variables The proposed DDE is based on the DE/l/rand/bin method. In the proposed DDE, the mutation ratio is regarded as the exchange probability, and thus, no modifications of DE/l/rand/bin are required. In addition, in order to maintain diversity through the search process, we initialize all search points. By introducing the initialization of all search points, global or quasi-optimum solution can be found. We validate the proposed DDE by applying it to several benchmark problems.展开更多
Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Br...Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.展开更多
A variational formulation of the synthesis problem for plane radiating systems according to the prescribed power directivity pattern (DP) is considered. The function representing the mean-square deviation of the presc...A variational formulation of the synthesis problem for plane radiating systems according to the prescribed power directivity pattern (DP) is considered. The function representing the mean-square deviation of the prescribed and synthesized power DPs and containing the additional term with squared norm of the current or field in the antenna aperture is considered as the criterion of optimization. Freedom to choose the phase DP is used to improve the proximity of the prescribed and synthesized DPs. In such formulation, the classes of non-linear problems, for which the non-uniqueness of solutions, their branching and bifurcation are characteristic, arise. The properties of solutions depend on the electric size of radiating system and prescribed power DP. From a practical point of view, the existence of different solutions creating the same or similar DPs, gives the opportunity to choose the solution that has a simpler implementation. The synthesis problems for plane radiating systems and plane arrays are considered.展开更多
Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear te...Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.展开更多
A mathematical model to describe the enzyme reaction, mass transfer and heat effects in the calorimetric system is discussed. The model is based on non-stationary diffusion Equation containing a nonlinear term related...A mathematical model to describe the enzyme reaction, mass transfer and heat effects in the calorimetric system is discussed. The model is based on non-stationary diffusion Equation containing a nonlinear term related to immobilize liver esterase by flow calorimetry. This paper presents the complex numerical methods (Adomian decomposition method, Homotopy analysis and perturbation method) to solve the non-linear differential Equations that depict the diffusion coupled with a non-linear reaction terms. Approximate analytical expressions for substrate concentration have been derived for all values of parameters α, β and γE. These analytical results are compared with the available numerical results and are found to be in good agreement.展开更多
Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triax...Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.展开更多
In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx...In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.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
A rapid and simple liquid chromatography method with on-line solid phase extraction was developed and validated for the quantitative determination of cyclophosphamide in rat plasma.The plasma sample was first extracte...A rapid and simple liquid chromatography method with on-line solid phase extraction was developed and validated for the quantitative determination of cyclophosphamide in rat plasma.The plasma sample was first extracted on an Acclaim？ Polar Advantage II C18 guard column（PA II C18,10 mm×4.6 mm,5 μm）,which was also the on-line Extraction Cartridge SPE column,by washing with 100% H2O for 1 min.The extracted sample was then eluted onto a PA II C18 column（150 mm×4.6 mm,5 μm） and separated by isocratic elution with acetonitrile-water（40：60,v/v）.The mobile phase was run at a flow rate of 1.0 mL/min,and the UV detector was set at 195 nm.Retention time of cyclophosphamide was 4.3 min and the total run-time was 6 min.The linear range of the standard curve was from 1.0 to 200 μg/mL（r2 = 0.9999）,and the limits of quantification and detection were 1.0 μg/mL（RSD10%,n = 5） and 0.3 μg/mL（RSD13%,n = 5）,respectively.Both intra-and inter-day variations were less than 5.6%.The developed method can be used for the therapeutic drug monitoring of cyclophosphamide in the clinic.展开更多
The principle and the constitution of an intelligent system for on-line and real-time montitoring tool cutting state were discussed and a synthetic sensors schedule combined a new type fluid acoustic emission sens...The principle and the constitution of an intelligent system for on-line and real-time montitoring tool cutting state were discussed and a synthetic sensors schedule combined a new type fluid acoustic emission sensor (AE) with motor current sensor was presented. The parallel communication between control system of machine tools, the monitoring intelligent system,and several decision-making systems for identifying tool cutting state was established It can auto - matically select the sensor way ,monitoring mode and identifying method in machining process- ing so as to build a successful and effective intelligent system for on -line and real-time moni- toring cutting tool states in FMS.展开更多
This paper introduces the development and industrial application of an on-line corrosion monitoring device for condenser tubes. Corrosion sensors are made up of representative condenser tubes chosen by eddy current te...This paper introduces the development and industrial application of an on-line corrosion monitoring device for condenser tubes. Corrosion sensors are made up of representative condenser tubes chosen by eddy current test, which enable the monitoring result to be consistent with the corrosion of actual condenser tubes. Localized corrosion rate of condenser tubes can be measured indirectly by a galvanic couple made up of tube segments with and without pits. Using this technology, corrosion problems can be found in time and accurately, and anticorrosive measures be made more economic and effective. Applications in two power plants showed the corrosion measurements are fast and accurate.展开更多
The effects of on-line solution, off-line solution and aging heat treatment on the microstructure and hardness of the die-cast AZ91D alloys were investigated. Brinell hardness of die-cast AZ91D alloy increases through...The effects of on-line solution, off-line solution and aging heat treatment on the microstructure and hardness of the die-cast AZ91D alloys were investigated. Brinell hardness of die-cast AZ91D alloy increases through on-line solution and off-line aging treatment but decreases after off-line solution treatment. By X-ray diffractometry, optical microscopy, differential thermal analysis, scanning electron microscopy and X-ray energy dispersive spectroscopy, it is found that the microstructures of the die-cast AZ91D magnesium alloy before and after on-line solution and off-line aging are similar, consisting of α-Mg and β-Al12Mg17. The precipitation of Al element is prevented by on-line solution so that the effect of solid solution strengthening is enhanced. The β-Al12Mg17 phases precipitate from supersaturated Mg solid solution after off-line aging treatment, and lead to microstructure refinement of AZ91D alloy, so the effect of precipitation hardening is enhanced. The β-Al12Mg17 phases dissolve in the substructure after off-line solution treatment, which leads to that the grain boundary strengthening phase is reduced significantly and the hardness of die cast AZ91D is reduced.展开更多
文摘The on-line problem of scheduling on a batch processing machine with nonidentical job sizes to minimize makespan is considered. The batch processing machine can process a number of jobs simultaneously as long as the total size of these jobs being processed does not exceed the machine capacity. The processing time of a batch is given by the longest processing time of any job in the batch. Each job becomes available at its arrival time, which is unknown in advance, and its processing time becomes known upon its arrival. The paper deals with two variants： the case only with two distinct arrival times and the general case. For the first case, an on-line algorithm with competitive ratio 119/44 is given. For the latter one, a simple algorithm with competitive ratio 3 is given. For both variants the better ratios can be obtained if the problem satisfies proportional assumption.
文摘In this paper, a semi on-line version on m ide ntical machines M 1, M 2, …,M m(m≥3) was considered, where th e processing time of the largest job is known in advance. Our goal is to maximiz e the minimum machine load, an NPLS algorithm was presented and its worst-case ratio was proved to be equal to m-1 which is the best possible value. It is concluded that if the total processing time of jobs is also known to be greater than (2m-1)p max where p max is the largest job' s processing time, then the worst-case ratio is 2-1/m.
文摘Differential evolution （DE） is a global optimizer for continuous design variables. To enhance DE, it is necessary to handle discrete design variables. In this paper, a discrete differential evolution （DDE） algorithm is proposed to handle discrete design variables The proposed DDE is based on the DE/l/rand/bin method. In the proposed DDE, the mutation ratio is regarded as the exchange probability, and thus, no modifications of DE/l/rand/bin are required. In addition, in order to maintain diversity through the search process, we initialize all search points. By introducing the initialization of all search points, global or quasi-optimum solution can be found. We validate the proposed DDE by applying it to several benchmark problems.
文摘Several problems arising in science and engineering are modeled by differential equations that involve conditions that are specified at more than one point. The non-linear two-point boundary value problem (TPBVP) (Bratu’s equation, Troesch’s problems) occurs engineering and science, including the modeling of chemical reactions diffusion processes and heat transfer. An analytical expression pertaining to the concentration of substrate is obtained using Homotopy perturbation method for all values of parameters. These approximate analytical results were found to be in good agreement with the simulation results.
文摘A variational formulation of the synthesis problem for plane radiating systems according to the prescribed power directivity pattern (DP) is considered. The function representing the mean-square deviation of the prescribed and synthesized power DPs and containing the additional term with squared norm of the current or field in the antenna aperture is considered as the criterion of optimization. Freedom to choose the phase DP is used to improve the proximity of the prescribed and synthesized DPs. In such formulation, the classes of non-linear problems, for which the non-uniqueness of solutions, their branching and bifurcation are characteristic, arise. The properties of solutions depend on the electric size of radiating system and prescribed power DP. From a practical point of view, the existence of different solutions creating the same or similar DPs, gives the opportunity to choose the solution that has a simpler implementation. The synthesis problems for plane radiating systems and plane arrays are considered.
文摘Restrictions of classical mechanics which take place because of holonomic constraints hypothesis used for obtaining canonical Lagrange equation are analyzed. As it was shown that this hypothesis excludes non-linear terms in the expression for forces which are responsible for energy exchange between different degrees of freedom of a many-body system. An oscillator passing a potential barrier is considered as an example which demonstrated this fact. It was found that the oscillator can pass the barrier even if kinetic energy of its mass center is below the potential barrier’s height due to non-linear terms. This effect is lost because of holonomic constraints hypothesis. We also explained how one can derive a system’s motion equation without the use of holonomic constraints hypothesis. This equation can be used to describe non-linear irreversible processes within the frames of Newton’s laws.
文摘A mathematical model to describe the enzyme reaction, mass transfer and heat effects in the calorimetric system is discussed. The model is based on non-stationary diffusion Equation containing a nonlinear term related to immobilize liver esterase by flow calorimetry. This paper presents the complex numerical methods (Adomian decomposition method, Homotopy analysis and perturbation method) to solve the non-linear differential Equations that depict the diffusion coupled with a non-linear reaction terms. Approximate analytical expressions for substrate concentration have been derived for all values of parameters α, β and γE. These analytical results are compared with the available numerical results and are found to be in good agreement.
文摘Effect of perturbations in Coriolis and centrifugal forces on the non-linear stability of the libration point L4 in the restricted three body problem is studied when both the primaries are axis symmetric bodies (triaxial rigid bodies) and the bigger primary is a source of radiation. Moser’s conditions are utilized in this study by employing the iterative scheme of Henrard for transforming the Hamiltonian to the Birkhoff’s normal form with the help of double D’Alembert’s series. It is found that L4 is stable for all mass ratios in the range of linear stability except for the three mass ratios μc1, μc2 and μc3, which depend upon the perturbations ε1 and ε1 in the Coriolis and centrifugal forces respectively and the parameters A1,A2,A3 and A4 which depend upon the semi-axes a1,b1,c1;a2,b2,c2 of the triaxial rigid bodies and p, the radiation parameter.
基金Supported by the National Natural Science Foundation of China（10671182）
文摘In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
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.
基金National Natural Science Foundation of China(Grant No.81072612)the Natural Science Foundation of Beijing(Grant No.7102107)+1 种基金the Open Foundation of State Key Laboratory of Natural and Biomimetic Drugs(Grant No.K20110109)Specialized Research Fund for the Doctoral Program of Higher Education(Grant No.20110001110021)
文摘A rapid and simple liquid chromatography method with on-line solid phase extraction was developed and validated for the quantitative determination of cyclophosphamide in rat plasma.The plasma sample was first extracted on an Acclaim？ Polar Advantage II C18 guard column（PA II C18,10 mm×4.6 mm,5 μm）,which was also the on-line Extraction Cartridge SPE column,by washing with 100% H2O for 1 min.The extracted sample was then eluted onto a PA II C18 column（150 mm×4.6 mm,5 μm） and separated by isocratic elution with acetonitrile-water（40：60,v/v）.The mobile phase was run at a flow rate of 1.0 mL/min,and the UV detector was set at 195 nm.Retention time of cyclophosphamide was 4.3 min and the total run-time was 6 min.The linear range of the standard curve was from 1.0 to 200 μg/mL（r2 = 0.9999）,and the limits of quantification and detection were 1.0 μg/mL（RSD10%,n = 5） and 0.3 μg/mL（RSD13%,n = 5）,respectively.Both intra-and inter-day variations were less than 5.6%.The developed method can be used for the therapeutic drug monitoring of cyclophosphamide in the clinic.
文摘The principle and the constitution of an intelligent system for on-line and real-time montitoring tool cutting state were discussed and a synthetic sensors schedule combined a new type fluid acoustic emission sensor (AE) with motor current sensor was presented. The parallel communication between control system of machine tools, the monitoring intelligent system,and several decision-making systems for identifying tool cutting state was established It can auto - matically select the sensor way ,monitoring mode and identifying method in machining process- ing so as to build a successful and effective intelligent system for on -line and real-time moni- toring cutting tool states in FMS.
文摘This paper introduces the development and industrial application of an on-line corrosion monitoring device for condenser tubes. Corrosion sensors are made up of representative condenser tubes chosen by eddy current test, which enable the monitoring result to be consistent with the corrosion of actual condenser tubes. Localized corrosion rate of condenser tubes can be measured indirectly by a galvanic couple made up of tube segments with and without pits. Using this technology, corrosion problems can be found in time and accurately, and anticorrosive measures be made more economic and effective. Applications in two power plants showed the corrosion measurements are fast and accurate.
基金Projects (2011BAE22B01, 2011BAE22B06) supported by the National Key Technologies R&D Program During the 12th Five-Year Plan Period of ChinaProject (2010NC018) supported by the Innovation Fund of Inner Mongolia University of Science and Technology, China
文摘The effects of on-line solution, off-line solution and aging heat treatment on the microstructure and hardness of the die-cast AZ91D alloys were investigated. Brinell hardness of die-cast AZ91D alloy increases through on-line solution and off-line aging treatment but decreases after off-line solution treatment. By X-ray diffractometry, optical microscopy, differential thermal analysis, scanning electron microscopy and X-ray energy dispersive spectroscopy, it is found that the microstructures of the die-cast AZ91D magnesium alloy before and after on-line solution and off-line aging are similar, consisting of α-Mg and β-Al12Mg17. The precipitation of Al element is prevented by on-line solution so that the effect of solid solution strengthening is enhanced. The β-Al12Mg17 phases precipitate from supersaturated Mg solid solution after off-line aging treatment, and lead to microstructure refinement of AZ91D alloy, so the effect of precipitation hardening is enhanced. The β-Al12Mg17 phases dissolve in the substructure after off-line solution treatment, which leads to that the grain boundary strengthening phase is reduced significantly and the hardness of die cast AZ91D is reduced.
