In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained du...In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of functions evaluations have been reduced obviously through our algorithms.展开更多
For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass t...For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.展开更多
A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its referenc...A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its reference objectives were the best particle and the centroid of all particles except the best particle.The convergence theorems of linear time-varying discrete system proved that simplex-PSO is of consistent asymptotic convergence.In order to reduce the probability of trapping into a local optimal value,an extremum mutation was introduced into simplex-PSO and simplex-PSO-t(simplex-PSO with turbulence) was devised.Several experiments were carried out to verify the validity of simplex-PSO and simplex-PSO-t,and the experimental results confirmed the conclusions:(1) simplex-PSO-t can optimize high-dimension functions with 200-dimensionality;(2) compared PSO with chaos PSO(CPSO),the best optimum index increases by a factor of 1×102-1×104.展开更多
A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equ...A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.展开更多
Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliabilit...Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE.The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs,and reliable error information cannot be available.This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element.It is a derivative-free technique that can deal with various orbit types.Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable,stable,and effective than those from the batch least squares method.As an application example,the optimal TLE and its uncertainty are used for predicting the fallen area,keeping the actual fallen site in the prediction areas.展开更多
A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control syst...A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control system for a turbine engine was developed. A performance index based on the integral of absolute error （IAE） was given as an objective function of optimization. In order to avoid the sensitivity that resulted from the initial values of the simplex search method, the traditional Ziegler-Nichols method was used to tune PID parameters to obtain the initial values at first, then the simplex search method was applied to optimize PID parameters for the turbine engine. Simulation results indicate that the simplex search method is a reasonable and effective method for PID controller parameters tuning and optimization.展开更多
This work presents an application of the Simplex Method for solving an optimal planning problem for cancer treatment by radiotherapy. Linear Programming can aid the optimal planning for radiation therapy, where the co...This work presents an application of the Simplex Method for solving an optimal planning problem for cancer treatment by radiotherapy. Linear Programming can aid the optimal planning for radiation therapy, where the concern is to apply a high enough radiation in the tumor while saving significantly healthy regions or critical organs.展开更多
In this paper, a new hybrid algorithm based on exploration power of a new improvement self-adaptive strategy for controlling parameters in DE （differential evolution） algorithm and exploitation capability of Nelder-...In this paper, a new hybrid algorithm based on exploration power of a new improvement self-adaptive strategy for controlling parameters in DE （differential evolution） algorithm and exploitation capability of Nelder-Mead simplex method is presented （HISADE-NMS）. The DE has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters as number of particles （NP）, scaling factor （F） and crossover control （CR）, which are kept fixed throughout the entire evolutionary process. However, these control parameters are very sensitive to the setting of the control parameters based on their experiments. The value of control parameters depends on the characteristics of each objective function, therefore, we have to tune their value in each problem that mean it will take too long time to perform. In the new manner, we present a new version of the DE algorithm for obtaining self-adaptive control parameter settings. Some modifications are imposed on DE to improve its capability and efficiency while being hybridized with Nelder-Mead simplex method. To valid the robustness of new hybrid algorithm, we apply it to solve some examples of structural optimization constraints.展开更多
The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and con...The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and convergence speed.To address these concerns,this paper develops a Simplex Improved Grey Wolf Optimizer(SMIGWO)algorithm.The randomly generating initial populations are replaced with the iterative chaotic sequences.The search process is optimized using the convergence factor optimization algorithm based on the inverse incompleteГfunction.The simplex method is utilized to address issues related to poorly positioned grey wolves.Experimental results demonstrate that,compared to the conventional GWO algorithm-based AE localization algorithm,the proposed algorithm achieves a higher solution accuracy and showcases a shorter search time.Additionally,the algorithm demonstrates fewer convergence steps,indicating superior convergence efficiency.These findings highlight that the proposed SMIGWO algorithm offers enhanced solution accuracy,stability,and optimization performance.The benefits of the SMIGWO algorithm extend universally across various materials,such as aluminum,granite,and sandstone,showcasing consistent effectiveness irrespective of material type.Consequently,this algorithm emerges as a highly effective tool for identifying acoustic emission signals and improving the precision of rock acoustic emission localization.展开更多
Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model ...Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.展开更多
The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. 13enetic algorithm （GA） has been proved to be a teasibte method when the gradient ...The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. 13enetic algorithm （GA） has been proved to be a teasibte method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously, but its convergence is very slow in the later period of evolution and it is easily trapped in the local optimum. In this study, a hybrid improved genetic algorithm （HIGA） for solving dynamic optimization problems is proposed to overcome these defects. Simplex method （SM） is used to perform the local search in the neighborhood of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved. The hybrid algorithm presents some improvements, such as protecting the best individual, accepting immigrations, as well as employing adaptive crossover and Ganssian mutation operators. The efficiency of the proposed algorithm is demonstrated by solving several dynamic optimization problems. At last, HIGA is applied to the optimal production of secreted protein in a fed batch reactor and the optimal feed-rate found by HIGA is effective and relatively stable.展开更多
An improved multidirectional velocity model was proposed for more accurately locating micro-seismic events in rock engineering. It was assumed that the stress wave propagation velocities from a micro-seismic source to...An improved multidirectional velocity model was proposed for more accurately locating micro-seismic events in rock engineering. It was assumed that the stress wave propagation velocities from a micro-seismic source to three nearest monitoring sensors in a sensor's array arrangement were the same. Since the defined objective function does not require pre-measurement of the stress wave propagation velocity in the field, errors from the velocity measurement can be avoided in comparison to three traditional velocity models. By analyzing 24 different cases, the proposed multidirectional velocity model iterated by the Simplex method is found to be the best option no matter the source is within the region of the sensor's array or not. The proposed model and the adopted iterative algorithm are verified by field data and it is concluded that it can significantly reduce the error of the estimated source location.展开更多
Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network mode...Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.展开更多
This work presents an optimal design method of antenna aperture illumination for microwave power transmission with an annular collection area.The objective is to maximize the ratio of the power radiated on the annular...This work presents an optimal design method of antenna aperture illumination for microwave power transmission with an annular collection area.The objective is to maximize the ratio of the power radiated on the annular collection area to the total transmitted power.By formulating the aperture amplitude distribution through a summation of a special set of series,the optimal design problem can be reduced to finding the maximum ratio of two real quadratic forms.Based on the theory of matrices,the solution to the formulated optimization problem is to determine the largest characteristic value and its associated characteristic vector.To meet security requirements,the peak radiation levels outside the receiving area are considered to be extra constraints.A hybrid grey wolf optimizer and Nelder–Mead simplex method is developed to deal with this constrained optimization problem.In order to demonstrate the effectiveness of the proposed method,numerical experiments on continuous apertures are conducted;then,discrete arrays of isotropic elements are employed to validate the correctness of the optimized results.Finally,patch arrays are adopted to further verify the validity of the proposed method.展开更多
In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, t...In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.展开更多
During the conventional continuous casting process of high-aluminum steels(w([Al])>0.5 wt.%),some components of slag,such as SiO_(2),B_(2)O_(3),and TiO_(2),could be reduced by aluminum in molten steel.Therefore,the...During the conventional continuous casting process of high-aluminum steels(w([Al])>0.5 wt.%),some components of slag,such as SiO_(2),B_(2)O_(3),and TiO_(2),could be reduced by aluminum in molten steel.Therefore,the CaO-BaO-Al_(2)O_(3)-CaF2-Li2O non-reactive mold fluxes were designed using the simplex grid method and molecular dynamics to mitigate the slag-metal interface reaction and stabilize the performance of mold fluxes.The results show that the components of nonreactive quinary system are 20-40 wt.% CaO,14-34 wt.% BaO,14-34 wt.% Al_(2)O_(3),4-12 wt.% F,and 4-8 wt.% Li_(2)O.Molecular dynamics simulation results show that[AlO_(4)]-tetrahedron acts as network formers and melt network structure is mainly chain and lamellar in the low-viscosity area.The cross sections of w(F)=8 wt.%,w(Li_(2)O)=8 wt.%and w(F)=12 wt.%,w(Li2O)=8 wt.% are important reference sections for the design of mold flux,with the compositions of 22-40 wt.%CaO,14-34 wt.% BaO,20-34 wt.%Al_(2)O_(3) and 23-40 wt.%CaO,14-34 wt.%BaO,20-28 wt.% Al_(2)O_(3),respectively.展开更多
The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the pro...The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.展开更多
This paper reviews alternative market equilibrium models for policy analysis. The origin of spatial equilibrium models and their application to wood and wood-processing industries are described. Three mathematical pro...This paper reviews alternative market equilibrium models for policy analysis. The origin of spatial equilibrium models and their application to wood and wood-processing industries are described. Three mathematical programming models commonly applied to solve spatial problems - namely linear programming, non-linear programming and mixed complementary programming - are reviewed in terms of forms of objective functions and constraint equalities and inequalities. These programming are illustrated with numerical examples. Linear programming is only applied in transportation problems to solve quantities trans, ported between regions when quantities supplied and demanded in each region are already known. It is argued that linear programming can be applied in broader context to transportation problems where supply and demand quantities are unknown and are linear. In this context, linear programming is seen as a more convenient method for modelers because it has a simpler objective function and does not require as strict conditions, for instance the equal numbers of variables and equations required in mixed complementary programming. Finally, some critical insights are provided on the interpretation of optimal solutions generated by solving spatial equilibrium models.展开更多
Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic opt...Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic optimization algorithm with fast convergence speed has the ability of prominent optimization and the defect of collapsing in the local best.To avoid BES collapse at local optima,inspired by the fact that the volume of the sphere is the largest when the surface area is certain,an improved bald eagle search optimization algorithm(INMBES)integrating the random shrinkage mechanism of the sphere is proposed.Firstly,the INMBES embeds spherical coordinates to design a more accurate parameter update method to modify the coverage and dispersion of the population.Secondly,the population splits into elite and non-elite groups and the Bernoulli chaos is applied to elite group to tap around potential solutions of the INMBES.The non-elite group is redistributed again and the Nelder-Mead simplex strategy is applied to each group to accelerate the evolution of the worst individual and the convergence process of the INMBES.The results of Friedman and Wilcoxon rank sum tests of CEC2017 in 10,30,50,and 100 dimensions numerical optimization confirm that the INMBES has superior performance in convergence accuracy and avoiding falling into local optimization compared with other potential improved algorithms but inferior to the champion algorithm and ranking third.The three engineering constraint optimization problems and 26 real world problems and the problem of extracting the best feature subset by encapsulated feature selection method verify that the INMBES’s performance ranks first and has achieved satisfactory accuracy in solving practical problems.展开更多
基金partially supported by the Doctoral Foundation of Hebei University(Grant No.Y2006084)the National Natural Science Foundation of China(Grant No.10231060)
文摘In this paper,we investigate the quadratic approximation methods.After studying the basic idea of simplex methods,we construct several new search directions by combining the local information progressively obtained during the iterates of the algorithm to form new subspaces.And the quadratic model is solved in the new subspaces.The motivation is to use the information disclosed by the former steps to construct more promising directions.For most tested problems,the number of functions evaluations have been reduced obviously through our algorithms.
基金Project(2011467001)supported by the Ministry of Environment Protection of ChinaProject(2010DFB94130)supported by the Ministry of Science and Technology of China
文摘For physical ozone absorption without reaction,two parametric estimation methods,i.e.the common linear least square fitting and non-linear Simplex search methods,were applied,respectively,to determine the ozone mass transfer coefficient during absorption and both methods give almost the same mass transfer coefficient.While for chemical absorption with ozone decomposition reaction,the common linear least square fitting method is not applicable for the evaluation of ozone mass transfer coefficient due to the difficulty of model linearization for describing ozone concentration dissolved in water.The nonlinear Simplex method obtains the mass transfer coefficient by minimizing the sum of the differences between the simulated and experimental ozone concentration during the whole absorption process,without the limitation of linear relationship between the dissolved ozone concentration and absorption time during the initial stage of absorption.Comparison of the ozone concentration profiles between the simulation and experimental data demonstrates that Simplex method may determine ozone mass transfer coefficient during absorption in an accurate and high efficiency way with wide applicability.
基金Project(50275150) supported by the National Natural Science Foundation of ChinaProject(20070533131) supported by Research Fund for the Doctoral Program of Higher Education of China
文摘A simplex particle swarm optimization(simplex-PSO) derived from the Nelder-Mead simplex method was proposed to optimize the high dimensionality functions.In simplex-PSO,the velocity term was abandoned and its reference objectives were the best particle and the centroid of all particles except the best particle.The convergence theorems of linear time-varying discrete system proved that simplex-PSO is of consistent asymptotic convergence.In order to reduce the probability of trapping into a local optimal value,an extremum mutation was introduced into simplex-PSO and simplex-PSO-t(simplex-PSO with turbulence) was devised.Several experiments were carried out to verify the validity of simplex-PSO and simplex-PSO-t,and the experimental results confirmed the conclusions:(1) simplex-PSO-t can optimize high-dimension functions with 200-dimensionality;(2) compared PSO with chaos PSO(CPSO),the best optimum index increases by a factor of 1×102-1×104.
基金supported by the National Natural Science Foundation of China(70771080)the Special Fund for Basic Scientific Research of Central Colleges+2 种基金China University of Geosciences(Wuhan) (CUG090113)the Research Foundation for Outstanding Young TeachersChina University of Geosciences(Wuhan)(CUGQNW0801)
文摘A global convergent algorithm is proposed to solve bilevel linear fractional-linear programming, which is a special class of bilevel programming. In our algorithm, replacing the lower level problem by its dual gap equaling to zero, the bilevel linear fractional-linear programming is transformed into a traditional sin- gle level programming problem, which can be transformed into a series of linear fractional programming problem. Thus, the modi- fied convex simplex method is used to solve the infinite linear fractional programming to obtain the global convergent solution of the original bilevel linear fractional-linear programming. Finally, an example demonstrates the feasibility of the proposed algorithm.
基金supported by Chongqing Municipal Natural Science Foundation of General Program(CSTB2022NSCQMSX1093)the Science and Technology Research Program of Chongqing Municipal Education Commission(Grant No.KJQN202200701)China Postdoctoral Science Foundation(2021M703487).
文摘Two-Line Element(TLE)datasets are the only orbital data source of Earth-orbiting space objects for many civil users for their research and applications.The datasets have uneven qualities that may affect the reliability of the propagated positions of space objects using a single TLE.The least squares approach to use multiple TLEs also suffers from the poor quality of some TLEs,and reliable error information cannot be available.This paper proposes a simplex algorithm to estimate an optimal TLE from multiple TLEs and obtain the uncertainty of each element.It is a derivative-free technique that can deal with various orbit types.Experiments have demonstrated that using the TLE estimated from the simplex method is more reliable,stable,and effective than those from the batch least squares method.As an application example,the optimal TLE and its uncertainty are used for predicting the fallen area,keeping the actual fallen site in the prediction areas.
文摘A PID parameters tuning and optimization method for a turbine engine based on the simplex search method was proposed. Taking time delay of combustion and actuator into account, a simulation model of a PID control system for a turbine engine was developed. A performance index based on the integral of absolute error （IAE） was given as an objective function of optimization. In order to avoid the sensitivity that resulted from the initial values of the simplex search method, the traditional Ziegler-Nichols method was used to tune PID parameters to obtain the initial values at first, then the simplex search method was applied to optimize PID parameters for the turbine engine. Simulation results indicate that the simplex search method is a reasonable and effective method for PID controller parameters tuning and optimization.
文摘This work presents an application of the Simplex Method for solving an optimal planning problem for cancer treatment by radiotherapy. Linear Programming can aid the optimal planning for radiation therapy, where the concern is to apply a high enough radiation in the tumor while saving significantly healthy regions or critical organs.
文摘In this paper, a new hybrid algorithm based on exploration power of a new improvement self-adaptive strategy for controlling parameters in DE （differential evolution） algorithm and exploitation capability of Nelder-Mead simplex method is presented （HISADE-NMS）. The DE has been used in many practical cases and has demonstrated good convergence properties. It has only a few control parameters as number of particles （NP）, scaling factor （F） and crossover control （CR）, which are kept fixed throughout the entire evolutionary process. However, these control parameters are very sensitive to the setting of the control parameters based on their experiments. The value of control parameters depends on the characteristics of each objective function, therefore, we have to tune their value in each problem that mean it will take too long time to perform. In the new manner, we present a new version of the DE algorithm for obtaining self-adaptive control parameter settings. Some modifications are imposed on DE to improve its capability and efficiency while being hybridized with Nelder-Mead simplex method. To valid the robustness of new hybrid algorithm, we apply it to solve some examples of structural optimization constraints.
基金support from the National Science Foundation of China(52304137,5192780752274124,52325403)Tiandi Science and Technology Co.,Ltd.(2022-2-TDMS012 and SKLIS202417)Sichuan University(SKHL2215).
文摘The Grey Wolf Optimization(GWO)algorithm is acknowledged as an effective method for rock acoustic emission localization.However,the conventional GWO algorithm encounters challenges related to solution accuracy and convergence speed.To address these concerns,this paper develops a Simplex Improved Grey Wolf Optimizer(SMIGWO)algorithm.The randomly generating initial populations are replaced with the iterative chaotic sequences.The search process is optimized using the convergence factor optimization algorithm based on the inverse incompleteГfunction.The simplex method is utilized to address issues related to poorly positioned grey wolves.Experimental results demonstrate that,compared to the conventional GWO algorithm-based AE localization algorithm,the proposed algorithm achieves a higher solution accuracy and showcases a shorter search time.Additionally,the algorithm demonstrates fewer convergence steps,indicating superior convergence efficiency.These findings highlight that the proposed SMIGWO algorithm offers enhanced solution accuracy,stability,and optimization performance.The benefits of the SMIGWO algorithm extend universally across various materials,such as aluminum,granite,and sandstone,showcasing consistent effectiveness irrespective of material type.Consequently,this algorithm emerges as a highly effective tool for identifying acoustic emission signals and improving the precision of rock acoustic emission localization.
基金part of the Program of"Study on the mechanism of complex heat and mass transfer during batch transport process in products pipelines"funded under the National Natural Science Foundation of China(grant number 51474228)
文摘Oil product pipelines have features such as transporting multiple materials, ever-changing operating conditions, and synchronism between the oil input plan and the oil offloading plan. In this paper, an optimal model was established for a single-source multi-distribution oil pro- duct pipeline, and scheduling plans were made based on supply. In the model, time node constraints, oil offloading plan constraints, and migration of batch constraints were taken into consideration. The minimum deviation between the demanded oil volumes and the actual offloading volumes was chosen as the objective function, and a linear programming model was established on the basis of known time nodes＇ sequence. The ant colony optimization algo- rithm and simplex method were used to solve the model. The model was applied to a real pipeline and it performed well.
基金Supported by Major State Basic Research Development Program of China （2012CB720500）, National Natural Science Foundation of China （Key Program： Ul162202）, National Science Fund for Outstanding Young Scholars （61222303）, National Natural Science Foundation of China （21276078, 21206037） and the Fundamental Research Funds for the Central Universities.
文摘The solutions of dynamic optimization problems are usually very difficult due to their highly nonlinear and multidimensional nature. 13enetic algorithm （GA） has been proved to be a teasibte method when the gradient is difficult to calculate. Its advantage is that the control profiles at all time stages are optimized simultaneously, but its convergence is very slow in the later period of evolution and it is easily trapped in the local optimum. In this study, a hybrid improved genetic algorithm （HIGA） for solving dynamic optimization problems is proposed to overcome these defects. Simplex method （SM） is used to perform the local search in the neighborhood of the optimal solution. By using SM, the ideal searching direction of global optimal solution could be found as soon as possible and the convergence speed of the algorithm is improved. The hybrid algorithm presents some improvements, such as protecting the best individual, accepting immigrations, as well as employing adaptive crossover and Ganssian mutation operators. The efficiency of the proposed algorithm is demonstrated by solving several dynamic optimization problems. At last, HIGA is applied to the optimal production of secreted protein in a fed batch reactor and the optimal feed-rate found by HIGA is effective and relatively stable.
基金Project(IRT0950)supported by the Cheung Kong Scholars and the Development Plan of Innovative Team,ChinaProject supported by China Scholarship Council
文摘An improved multidirectional velocity model was proposed for more accurately locating micro-seismic events in rock engineering. It was assumed that the stress wave propagation velocities from a micro-seismic source to three nearest monitoring sensors in a sensor's array arrangement were the same. Since the defined objective function does not require pre-measurement of the stress wave propagation velocity in the field, errors from the velocity measurement can be avoided in comparison to three traditional velocity models. By analyzing 24 different cases, the proposed multidirectional velocity model iterated by the Simplex method is found to be the best option no matter the source is within the region of the sensor's array or not. The proposed model and the adopted iterative algorithm are verified by field data and it is concluded that it can significantly reduce the error of the estimated source location.
基金Project(51321065)supported by the Innovative Research Groups of the National Natural Science Foundation of ChinaProject(2013CB035904)supported by the National Basic Research Program of China(973 Program)Project(51439005)supported by the National Natural Science Foundation of China
文摘Accurate 3-D fracture network model for rock mass in dam foundation is of vital importance for stability,grouting and seepage analysis of dam foundation.With the aim of reducing deviation between fracture network model and measured data,a 3-D fracture network dynamic modeling method based on error analysis was proposed.Firstly,errors of four fracture volume density estimation methods(proposed by ODA,KULATILAKE,MAULDON,and SONG)and that of four fracture size estimation methods(proposed by EINSTEIN,SONG and TONON)were respectively compared,and the optimal methods were determined.Additionally,error index representing the deviation between fracture network model and measured data was established with integrated use of fractal dimension and relative absolute error(RAE).On this basis,the downhill simplex method was used to build the dynamic modeling method,which takes the minimum of error index as objective function and dynamically adjusts the fracture density and size parameters to correct the error index.Finally,the 3-D fracture network model could be obtained which meets the requirements.The proposed method was applied for 3-D fractures simulation in Miao Wei hydropower project in China for feasibility verification and the error index reduced from 2.618 to 0.337.
基金supported in part by the National Key Research and Development Program of China(2021YFB3900300)in part by the National Natural Science Foundation of China(62201416)+2 种基金in part by the Fundamental Research Funds for the Central Universities(QTZX23070)in part by the Qin Chuang Yuan High-Level Innovative and Entrepreneurial Talents Project(QCYRCXM-2022-314)in part by Singapore Ministry of Education Academic Research Fund Tier 1。
文摘This work presents an optimal design method of antenna aperture illumination for microwave power transmission with an annular collection area.The objective is to maximize the ratio of the power radiated on the annular collection area to the total transmitted power.By formulating the aperture amplitude distribution through a summation of a special set of series,the optimal design problem can be reduced to finding the maximum ratio of two real quadratic forms.Based on the theory of matrices,the solution to the formulated optimization problem is to determine the largest characteristic value and its associated characteristic vector.To meet security requirements,the peak radiation levels outside the receiving area are considered to be extra constraints.A hybrid grey wolf optimizer and Nelder–Mead simplex method is developed to deal with this constrained optimization problem.In order to demonstrate the effectiveness of the proposed method,numerical experiments on continuous apertures are conducted;then,discrete arrays of isotropic elements are employed to validate the correctness of the optimized results.Finally,patch arrays are adopted to further verify the validity of the proposed method.
基金Supported by the Research Foundation of Jinan University(04SKZD01).
文摘In this paper, the nonlinear programming problem with quasimonotonic （ both quasiconvex and quasiconcave ）objective function and linear constraints is considered. With the decomposition theorem of polyhedral sets, the structure of optimal solution set for the programming problem is depicted. Based on a simplified version of the convex simplex method, the uniqueness condition of optimal solution and the computational procedures to determine all optimal solutions are given, if the uniqueness condition is not satisfied. An illustrative example is also presented.
基金the fund support from the National Natural Science Foundation of China(Project Nos.U20A20270 and U1660204).
文摘During the conventional continuous casting process of high-aluminum steels(w([Al])>0.5 wt.%),some components of slag,such as SiO_(2),B_(2)O_(3),and TiO_(2),could be reduced by aluminum in molten steel.Therefore,the CaO-BaO-Al_(2)O_(3)-CaF2-Li2O non-reactive mold fluxes were designed using the simplex grid method and molecular dynamics to mitigate the slag-metal interface reaction and stabilize the performance of mold fluxes.The results show that the components of nonreactive quinary system are 20-40 wt.% CaO,14-34 wt.% BaO,14-34 wt.% Al_(2)O_(3),4-12 wt.% F,and 4-8 wt.% Li_(2)O.Molecular dynamics simulation results show that[AlO_(4)]-tetrahedron acts as network formers and melt network structure is mainly chain and lamellar in the low-viscosity area.The cross sections of w(F)=8 wt.%,w(Li_(2)O)=8 wt.%and w(F)=12 wt.%,w(Li2O)=8 wt.% are important reference sections for the design of mold flux,with the compositions of 22-40 wt.%CaO,14-34 wt.% BaO,20-34 wt.%Al_(2)O_(3) and 23-40 wt.%CaO,14-34 wt.%BaO,20-28 wt.% Al_(2)O_(3),respectively.
文摘The optimization problem is considered in which the objective function is pseudolinear（both pseudoconvex and pseudoconcave） and the constraints are linear. The general expression for the optimal solutions to the problem is derived with the representation theorem of polyhedral sets, and the uniqueness condition of the optimal solution and the computational procedures to determine all optimal solutions （if the uniqueness condition is not satisfied ） are provided. Finally, an illustrative example is also given.
文摘This paper reviews alternative market equilibrium models for policy analysis. The origin of spatial equilibrium models and their application to wood and wood-processing industries are described. Three mathematical programming models commonly applied to solve spatial problems - namely linear programming, non-linear programming and mixed complementary programming - are reviewed in terms of forms of objective functions and constraint equalities and inequalities. These programming are illustrated with numerical examples. Linear programming is only applied in transportation problems to solve quantities trans, ported between regions when quantities supplied and demanded in each region are already known. It is argued that linear programming can be applied in broader context to transportation problems where supply and demand quantities are unknown and are linear. In this context, linear programming is seen as a more convenient method for modelers because it has a simpler objective function and does not require as strict conditions, for instance the equal numbers of variables and equations required in mixed complementary programming. Finally, some critical insights are provided on the interpretation of optimal solutions generated by solving spatial equilibrium models.
基金supported by the National Natural Science Foundation of China No.61976176.
文摘Over the last two decades,stochastic optimization algorithms have proved to be a very promising approach to solving a variety of complex optimization problems.Bald eagle search optimization(BES)as a new stochastic optimization algorithm with fast convergence speed has the ability of prominent optimization and the defect of collapsing in the local best.To avoid BES collapse at local optima,inspired by the fact that the volume of the sphere is the largest when the surface area is certain,an improved bald eagle search optimization algorithm(INMBES)integrating the random shrinkage mechanism of the sphere is proposed.Firstly,the INMBES embeds spherical coordinates to design a more accurate parameter update method to modify the coverage and dispersion of the population.Secondly,the population splits into elite and non-elite groups and the Bernoulli chaos is applied to elite group to tap around potential solutions of the INMBES.The non-elite group is redistributed again and the Nelder-Mead simplex strategy is applied to each group to accelerate the evolution of the worst individual and the convergence process of the INMBES.The results of Friedman and Wilcoxon rank sum tests of CEC2017 in 10,30,50,and 100 dimensions numerical optimization confirm that the INMBES has superior performance in convergence accuracy and avoiding falling into local optimization compared with other potential improved algorithms but inferior to the champion algorithm and ranking third.The three engineering constraint optimization problems and 26 real world problems and the problem of extracting the best feature subset by encapsulated feature selection method verify that the INMBES’s performance ranks first and has achieved satisfactory accuracy in solving practical problems.
