A simplified group search optimizer algorithm denoted as"SGSO"for large scale global optimization is presented in this paper to obtain a simple algorithm with superior performance on high-dimensional problem...A simplified group search optimizer algorithm denoted as"SGSO"for large scale global optimization is presented in this paper to obtain a simple algorithm with superior performance on high-dimensional problems.The SGSO adopts an improved sharing strategy which shares information of not only the best member but also the other good members,and uses a simpler search method instead of searching by the head angle.Furthermore,the SGSO increases the percentage of scroungers to accelerate convergence speed.Compared with genetic algorithm(GA),particle swarm optimizer(PSO)and group search optimizer(GSO),SGSO is tested on seven benchmark functions with dimensions 30,100,500 and 1 000.It can be concluded that the SGSO has a remarkably superior performance to GA,PSO and GSO for large scale global optimization.展开更多
This paper presents a Butterfly Optimization Algorithm(BOA)with a wind-driven mechanism for avoiding natural enemies known as WDBOA.To further balance the basic BOA algorithm's exploration and exploitation capabil...This paper presents a Butterfly Optimization Algorithm(BOA)with a wind-driven mechanism for avoiding natural enemies known as WDBOA.To further balance the basic BOA algorithm's exploration and exploitation capabilities,the butterfly actions were divided into downwind and upwind states.The algorithm of exploration ability was improved with the wind,while the algorithm of exploitation ability was improved against the wind.Also,a mechanism of avoiding natural enemies based on Lévy flight was introduced for the purpose of enhancing its global searching ability.Aiming at improving the explorative performance at the initial stages and later stages,the fragrance generation method was modified.To evaluate the effectiveness of the suggested algorithm,a comparative study was done with six classical metaheuristic algorithms and three BOA variant optimization techniques on 18 benchmark functions.Further,the performance of the suggested technique in addressing some complicated problems in various dimensions was evaluated using CEC 2017 and CEC 2020.Finally,the WDBOA algorithm is used proportional-integral-derivative(PID)controller parameter optimization.Experimental results demonstrate that the WDBOA based PID controller has better control performance in comparison with other PID controllers tuned by the Genetic Algorithm(GA),Flower Pollination Algorithm(FPA),Cuckoo Search(CS)and BOA.展开更多
This paper presents a two-phase genetic algorithm (TPGA) based on the multi- parent genetic algorithm (MPGA). Through analysis we find MPGA will lead the population' s evol vement to diversity or convergence accor...This paper presents a two-phase genetic algorithm (TPGA) based on the multi- parent genetic algorithm (MPGA). Through analysis we find MPGA will lead the population' s evol vement to diversity or convergence according to the population size and the crossover size, so we make it run in different forms during the global and local optimization phases and then forms TPGA. The experiment results show that TPGA is very efficient for the optimization of low-dimension multi-modal functions, usually we can obtain all the global optimal solutions.展开更多
In this study,we consider the global optimization problem in a hypercube.We use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the curve.Based...In this study,we consider the global optimization problem in a hypercube.We use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the curve.Based on the integral function,we propose an algorithm for solving the global optimization problem.Then,we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm.展开更多
The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. ...The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.展开更多
The stability of the Newton-like algorithm in optimization flow control is considered in this paper. This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theor...The stability of the Newton-like algorithm in optimization flow control is considered in this paper. This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theory,without considering the round trip time of each source. While the stability of this algorithm with considering the round trip time is analyzed as well. The analysis shows that the algorithm with only one bottleneck link accessed by several sources is also globally stable,and all trajectories described by this algorithm ultimately converge to the equilibrium point.展开更多
In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance fu...In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.展开更多
The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence spe...The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence speed and difficulty in jumping out of the local optimum.In order to overcome these shortcomings,a chaotic sparrow search algorithm based on logarithmic spiral strategy and adaptive step strategy(CLSSA)is proposed in this paper.Firstly,in order to balance the exploration and exploitation ability of the algorithm,chaotic mapping is introduced to adjust the main parameters of SSA.Secondly,in order to improve the diversity of the population and enhance the search of the surrounding space,the logarithmic spiral strategy is introduced to improve the sparrow search mechanism.Finally,the adaptive step strategy is introduced to better control the process of algorithm exploitation and exploration.The best chaotic map is determined by different test functions,and the CLSSA with the best chaotic map is applied to solve 23 benchmark functions and 3 classical engineering problems.The simulation results show that the iterative map is the best chaotic map,and CLSSA is efficient and useful for engineering problems,which is better than all comparison algorithms.展开更多
In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each i...In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each iteration point is selected from some randomly generated trial points according to certain criteria.A restarting strategy is adopted to build the restarting version of the algorithm.The performance of the presented algorithm and its restarting version are tested on 13 standard numerical examples.The numerical results suggest that the algorithm and its restarting version are very effective.展开更多
In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region al...In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model展开更多
Harmony search(HS)is a form of stochastic meta-heuristic inspired by the improvisation process of musicians.In this study,a modified HS with a hybrid cuckoo search(CS)operator,HS-CS,is proposed to enhance global searc...Harmony search(HS)is a form of stochastic meta-heuristic inspired by the improvisation process of musicians.In this study,a modified HS with a hybrid cuckoo search(CS)operator,HS-CS,is proposed to enhance global search ability while avoiding falling into local optima.First,the randomness of the HS pitch disturbance adjusting method is analyzed to generate an adaptive inertia weight according to the quality of solutions in the harmony memory and to reconstruct the fine-tuning bandwidth optimization.This is to improve the efficiency and accuracy of HS algorithm optimization.Second,the CS operator is introduced to expand the scope of the solution space and improve the density of the population,which can quickly jump out of the local optimum in the randomly generated harmony and update stage.Finally,a dynamic parameter adjustment mechanism is set to improve the efficiency of optimization.Three theorems are proved to reveal HS-CS as a global convergence meta-heuristic algorithm.In addition,12 benchmark functions are selected for the optimization solution to verify the performance of HS-CS.The analysis shows that HS-CS is significantly better than other algorithms in optimizing high-dimensional problems with strong robustness,high convergence speed,and high convergence accuracy.For further verification,HS-CS is used to optimize the back propagation neural network(BPNN)to extract weighted fuzzy production rules.Simulation results show that the BPNN optimized by HS-CS can obtain higher classification accuracy of weighted fuzzy production rules.Therefore,the proposed HS-CS is proved to be effective.展开更多
Four novel chiral honeycomb structures inspired by the biological arrangement shape are designed.The functional principle is raised to solve the large deformation of bio-inspired structures and the structural constitu...Four novel chiral honeycomb structures inspired by the biological arrangement shape are designed.The functional principle is raised to solve the large deformation of bio-inspired structures and the structural constitutive model is proposed to explain the quasi-static mechanical properties of chiral honeycomb array structures and honeycomb structures.Simulation and experiment results verify the accuracy of theoretical analysis results and the errors are all within 15%.In structural mechanical properties,Equidimensional Chiral Honeycomb Array Structure(ECHS)has excellent mechanical properties.Among ECHS,Small-sized Column Chiral Honeycomb Array Structure(SCHCS)has the best properties.The bearing capacity,specific energy absorption,and specific strength of SCHCS are more than twice as much as the others in this paper.The chiral honeycomb array structure has the best mechanical properties at a certain size.In the structural design,the optimal size model should be obtained first in combination with the optimization algorithm for the protection design.展开更多
基金the Science and Technology Planning Project of Hunan Province(No.2011TP4016-3)the Construct Program of the Key Discipline(Technology of Computer Application)in Xiangnan University
文摘A simplified group search optimizer algorithm denoted as"SGSO"for large scale global optimization is presented in this paper to obtain a simple algorithm with superior performance on high-dimensional problems.The SGSO adopts an improved sharing strategy which shares information of not only the best member but also the other good members,and uses a simpler search method instead of searching by the head angle.Furthermore,the SGSO increases the percentage of scroungers to accelerate convergence speed.Compared with genetic algorithm(GA),particle swarm optimizer(PSO)and group search optimizer(GSO),SGSO is tested on seven benchmark functions with dimensions 30,100,500 and 1 000.It can be concluded that the SGSO has a remarkably superior performance to GA,PSO and GSO for large scale global optimization.
基金This work was supported by National Natural Science Foundation of China under Grant U21A20464,62066005Project of the Guangxi Science and Technology under Grant No.ZL23014016.
文摘This paper presents a Butterfly Optimization Algorithm(BOA)with a wind-driven mechanism for avoiding natural enemies known as WDBOA.To further balance the basic BOA algorithm's exploration and exploitation capabilities,the butterfly actions were divided into downwind and upwind states.The algorithm of exploration ability was improved with the wind,while the algorithm of exploitation ability was improved against the wind.Also,a mechanism of avoiding natural enemies based on Lévy flight was introduced for the purpose of enhancing its global searching ability.Aiming at improving the explorative performance at the initial stages and later stages,the fragrance generation method was modified.To evaluate the effectiveness of the suggested algorithm,a comparative study was done with six classical metaheuristic algorithms and three BOA variant optimization techniques on 18 benchmark functions.Further,the performance of the suggested technique in addressing some complicated problems in various dimensions was evaluated using CEC 2017 and CEC 2020.Finally,the WDBOA algorithm is used proportional-integral-derivative(PID)controller parameter optimization.Experimental results demonstrate that the WDBOA based PID controller has better control performance in comparison with other PID controllers tuned by the Genetic Algorithm(GA),Flower Pollination Algorithm(FPA),Cuckoo Search(CS)and BOA.
基金Supported by the National Natural Science Foundation of China (70071042,60073043,60133010)
文摘This paper presents a two-phase genetic algorithm (TPGA) based on the multi- parent genetic algorithm (MPGA). Through analysis we find MPGA will lead the population' s evol vement to diversity or convergence according to the population size and the crossover size, so we make it run in different forms during the global and local optimization phases and then forms TPGA. The experiment results show that TPGA is very efficient for the optimization of low-dimension multi-modal functions, usually we can obtain all the global optimal solutions.
基金the National Natural Science Foundation of China(No.11771275).
文摘In this study,we consider the global optimization problem in a hypercube.We use a class of series to construct a curve in a hypercube,which can fill the hypercube,and we present an integral function on the curve.Based on the integral function,we propose an algorithm for solving the global optimization problem.Then,we perform a convergence analysis and numerical experiments to demonstrate the effectiveness of the proposed algorithm.
基金supported in part by the National Outstanding Youth Foundation of P.R.China (60525303)the National Natural Science Foundation of P.R.China(60404022,60604004)+2 种基金the Natural Science Foundation of Hebei Province (102160)the special projects in mathematics funded by the Natural Science Foundation of Hebei Province(07M005)the NS of Education Office in Hebei Province (2004123).
文摘The Newton-Like algorithm with price estimation error in optimization flow control in network is analyzed. The estimation error is treated as inexactness of the gradient and the inexact descent direction is analyzed. Based on the optimization theory, a sufficient condition for convergence of this algorithm with bounded price estimation error is obtained. Furthermore, even when this sufficient condition doesn＇t hold, this algorithm can also converge, provided a modified step size, and an attraction region is obtained. Based on Lasalle＇s invariance principle applied to a suitable Lyapunov function, the dynamic system described by this algorithm is proved to be global stability if the error is zero. And the Newton-Like algorithm with bounded price estimation error is also globally stable if the error satisfies the sufficient condition for convergence. All trajectories ultimately converge to the equilibrium point.
基金the National Outstanding Youth Foundation of China (Grant No.60525303)the NNSF of China( Grant No.60404022 and 60604004)+2 种基金the NSF of Hebei Province (Grant No.102160)the Special Projects in Mathematics Funded by Natural Science Foundation of Hebei Prov-ince(Grant No.07M005)the NS of Education Office in Hebei Province (Grant No.2004123).
文摘The stability of the Newton-like algorithm in optimization flow control is considered in this paper. This algorithm is proved to be globally stable under a general network topology by means of Lyapunov stability theory,without considering the round trip time of each source. While the stability of this algorithm with considering the round trip time is analyzed as well. The analysis shows that the algorithm with only one bottleneck link accessed by several sources is also globally stable,and all trajectories described by this algorithm ultimately converge to the equilibrium point.
文摘In this paper, we propose a K-means clustering-based integral level-value estimation algorithm to solve a kind of box-constrained global optimization problem. For this purpose, we introduce the generalized variance function associated with the level-value of the objective function to be minimized. The variance function has a good property when Newton’s method is used to solve a variance equation resulting by setting the variance function to zero. We prove that the largest root of the variance equation is equal to the global minimum value of the corresponding optimization problem. Based on the K-means clustering algorithm, the multiple importance sampling technique is proposed in the implementable algorithm. The main idea of the cross-entropy method is used to update the parameters of sampling density function. The asymptotic convergence of the algorithm is proved, and the validity of the algorithm is verified by numerical experiments.
基金The Science Foundation of Shanxi Province,China(2020JQ-481,2021JM-224)Aero Science Foundation of China(201951096002).
文摘The sparrow search algorithm(SSA)is a newly proposed meta-heuristic optimization algorithm based on the sparrowforaging principle.Similar to other meta-heuristic algorithms,SSA has problems such as slowconvergence speed and difficulty in jumping out of the local optimum.In order to overcome these shortcomings,a chaotic sparrow search algorithm based on logarithmic spiral strategy and adaptive step strategy(CLSSA)is proposed in this paper.Firstly,in order to balance the exploration and exploitation ability of the algorithm,chaotic mapping is introduced to adjust the main parameters of SSA.Secondly,in order to improve the diversity of the population and enhance the search of the surrounding space,the logarithmic spiral strategy is introduced to improve the sparrow search mechanism.Finally,the adaptive step strategy is introduced to better control the process of algorithm exploitation and exploration.The best chaotic map is determined by different test functions,and the CLSSA with the best chaotic map is applied to solve 23 benchmark functions and 3 classical engineering problems.The simulation results show that the iterative map is the best chaotic map,and CLSSA is efficient and useful for engineering problems,which is better than all comparison algorithms.
文摘In this paper,we present a stochastic adaptive algorithm using radial basis function models for global optimization of costly black-box functions.The exploration radii in local searches are generated adaptively.Each iteration point is selected from some randomly generated trial points according to certain criteria.A restarting strategy is adopted to build the restarting version of the algorithm.The performance of the presented algorithm and its restarting version are tested on 13 standard numerical examples.The numerical results suggest that the algorithm and its restarting version are very effective.
文摘In this note, the following unconstrained nonsmooth optimization problem is considered where f(x):R^n→R is only a locally Lipschitzian function. Many papers appear on the convergence properties of the trust region algorithm to solve several different particular nonsmooth problems. Dennis, Li and Tapia proposed a general trust region model by using regular functions. They proved the global convergence of the general trust region model under some mild conditions which are shown to be satisfied by many trust region algorithms including smooth one. Qi and Sun provided another trust region model
基金supported by the National Natural Science Foundation of China (No.62066016)the Natural Science Foundation of Hunan Province,China (No.2020JJ5458)+3 种基金the Research Foundation of Education Bureau of Hunan Province,China (Nos.22B0549 and 22B1046)the Fundamental Research Grant Scheme of Malaysia (No.R.J130000.7809.5F524)the UTMFR Grant (No.Q.J130000.2551.20H71)the Research Management Center (RMC)of Universiti Teknologi Malaysia (UTM)。
文摘Harmony search(HS)is a form of stochastic meta-heuristic inspired by the improvisation process of musicians.In this study,a modified HS with a hybrid cuckoo search(CS)operator,HS-CS,is proposed to enhance global search ability while avoiding falling into local optima.First,the randomness of the HS pitch disturbance adjusting method is analyzed to generate an adaptive inertia weight according to the quality of solutions in the harmony memory and to reconstruct the fine-tuning bandwidth optimization.This is to improve the efficiency and accuracy of HS algorithm optimization.Second,the CS operator is introduced to expand the scope of the solution space and improve the density of the population,which can quickly jump out of the local optimum in the randomly generated harmony and update stage.Finally,a dynamic parameter adjustment mechanism is set to improve the efficiency of optimization.Three theorems are proved to reveal HS-CS as a global convergence meta-heuristic algorithm.In addition,12 benchmark functions are selected for the optimization solution to verify the performance of HS-CS.The analysis shows that HS-CS is significantly better than other algorithms in optimizing high-dimensional problems with strong robustness,high convergence speed,and high convergence accuracy.For further verification,HS-CS is used to optimize the back propagation neural network(BPNN)to extract weighted fuzzy production rules.Simulation results show that the BPNN optimized by HS-CS can obtain higher classification accuracy of weighted fuzzy production rules.Therefore,the proposed HS-CS is proved to be effective.
基金This work is supported by National Key R&D program of of China(No.2022YFB4600500)the National Natural Science Foundation of China(No.51975246)+2 种基金the Science and Technology Development Program of Jilin Province,China(No.20220101192JC)Capital construction fund plan within the budget of Jilin Province(No.2023C041-4)Chongqing Natural Science Foundation(No.CSSTB2022NSCQ-MSX0225).
文摘Four novel chiral honeycomb structures inspired by the biological arrangement shape are designed.The functional principle is raised to solve the large deformation of bio-inspired structures and the structural constitutive model is proposed to explain the quasi-static mechanical properties of chiral honeycomb array structures and honeycomb structures.Simulation and experiment results verify the accuracy of theoretical analysis results and the errors are all within 15%.In structural mechanical properties,Equidimensional Chiral Honeycomb Array Structure(ECHS)has excellent mechanical properties.Among ECHS,Small-sized Column Chiral Honeycomb Array Structure(SCHCS)has the best properties.The bearing capacity,specific energy absorption,and specific strength of SCHCS are more than twice as much as the others in this paper.The chiral honeycomb array structure has the best mechanical properties at a certain size.In the structural design,the optimal size model should be obtained first in combination with the optimization algorithm for the protection design.
