The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions proble...The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.展开更多
This paper is a continuation of our previous work [Front. Math. China, 2016, 11（6）： 1379-1418] where an efficient algorithm for computing the maximal eigenpalr was introduced first for tridiagonal matrices and then...This paper is a continuation of our previous work [Front. Math. China, 2016, 11（6）： 1379-1418] where an efficient algorithm for computing the maximal eigenpalr was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements. This paper introduces mainly two global algorithms for computing the maximal eigenpair in a rather general setup, including even a class of real （with some negative off-diagonal elements） or complex matrices.展开更多
This paper is a continuation of our previous paper[Front.Math.China,2017,12(5):10231043]where global algorithms for computing the maximal cigcnpair were introduced in a rather general setup.The efficiency of the globa...This paper is a continuation of our previous paper[Front.Math.China,2017,12(5):10231043]where global algorithms for computing the maximal cigcnpair were introduced in a rather general setup.The efficiency of the global algorithms is improved in this paper in terms of a good use of power iteration and two quasi-symmetric techniques.Finally,the new algorithms are applied to Hua’s economic optimization model.展开更多
The Firefly Algorithm(FA)is a highly efficient population-based optimization technique developed by mimicking the flashing behavior of fireflies when mating.This article proposes a method based on Differential Evoluti...The Firefly Algorithm(FA)is a highly efficient population-based optimization technique developed by mimicking the flashing behavior of fireflies when mating.This article proposes a method based on Differential Evolution(DE)/current-to-best/1 for enhancing the FA's movement process.The proposed modification increases the global search ability and the convergence rates while maintaining a balance between exploration and exploitation by deploying the global best solution.However,employing the best solution can lead to premature algorithm convergence,but this study handles this issue using a loop adjacent to the algorithm's main loop.Additionally,the suggested algorithm’s sensitivity to the alpha parameter is reduced compared to the original FA.The GbFA surpasses both the original and five-version of enhanced FAs in finding the optimal solution to 30 CEC2014 real parameter benchmark problems with all selected alpha values.Additionally,the CEC 2017 benchmark functions and the eight engineering optimization challenges are also utilized to evaluate GbFA’s efficacy and robustness on real-world problems against several enhanced algorithms.In all cases,GbFA provides the optimal result compared to other methods.Note that the source code of the GbFA algorithm is publicly available at https://www.optim-app.com/projects/gbfa.展开更多
In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we ...In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.展开更多
This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current mi...This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and contraction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.展开更多
Rankine source method,optimization technology,parametric modeling technology,and improved multiobjective optimization algorithm were combined to investigate the multiobjective optimization design of hull form.A multio...Rankine source method,optimization technology,parametric modeling technology,and improved multiobjective optimization algorithm were combined to investigate the multiobjective optimization design of hull form.A multiobjective and multilevel optimization design framework was constructed for the comprehensive navigation performance of ships.CAESES software was utilized as the optimization platform,and nondominated sorting genetic algorithm II(NSGA-II)was used to conduct multiobjective optimization research on the resistance and sea-keeping performance of the ITTC Ship A-2 fishing vessel.Optimization objectives of this study are heave/pitch response amplitude and wave-making resistance.Taking the displacement and the length between perpendiculars as constraints,we optimized the profile of the hull.Analytic hierarchy process(AHP)and technique for order preference by similarity to ideal solution(TOPSIS)were used to sort and select Pareto solutions and determine weight coefficient of each navigation performance objective in the general objective.Finally,the hydrodynamic performance before and after the parametric deformation of the hull was compared.The results show that both the wave-making resistance and heave/pitch amplitude of the optimized hull form are reduced,and the satisfactory optimal hull form is obtained.The results of this study have a certain reference value for the initial stage of multiobjective optimization design of hull form.展开更多
A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorith...A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorithm which includes two phases is that chaotic behavior is exploited to conduct a rough search of the problem space in order to find the promising individuals in Phase I. Adjustment strategy of steplength and intensive searches in Phase II are employed. The population sequences generated by the algorithm asymptotically converge to global optimal solutions with probability one. The proposed algorithm is applied to several typical test problems. Numerical results illustrate that this algorithm can more efficiently solve complex global optimization problems than evolutionary programming and evolution strategies in most cases.展开更多
A new dynamical evolutionary algorithm (DEA) based on the theory of statistical mechanics is presented. This algorithm is very different from the traditional evolutionary algorithm and the two novel features are the u...A new dynamical evolutionary algorithm (DEA) based on the theory of statistical mechanics is presented. This algorithm is very different from the traditional evolutionary algorithm and the two novel features are the unique of selecting strategy and the determination of individuals that are selected to crossover and mutate. We use DEA to solve a lot of global optimization problems that are nonlinear, multimodal and multidimensional and obtain satisfactory results.展开更多
Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstructio...Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstruction and evolution of the sampling distributions over the space of candidate solutions. Iterativeconstruction of the sampling distributions is based on the idea of the global random search of generationalmethods. Under this frame, propontional selection is characterized as a gobal search operator, and recombination is characerized as the search process that exploits similarities. It is shown-that by properly constraining the search breadth of recombination operators, weak convergence of evolutionary algorithms to aglobal optimum can be ensured.展开更多
A new genetic algorithm (GA) is developed. It features three new operations: restoration, reconstruction and recording the better, so as to produce a limited monotonic sequence of fitness value, to realize a globally ...A new genetic algorithm (GA) is developed. It features three new operations: restoration, reconstruction and recording the better, so as to produce a limited monotonic sequence of fitness value, to realize a globally optimal choosing, and to converge to a globally optimal solution through a perfectly stochastic process. Practical examples are given to illustrate the superiority of this new GA.展开更多
A novel heuristic search algorithm called seeker op- timization algorithm （SOA） is proposed for the real-parameter optimization. The proposed SOA is based on simulating the act of human searching. In the SOA, search...A novel heuristic search algorithm called seeker op- timization algorithm （SOA） is proposed for the real-parameter optimization. The proposed SOA is based on simulating the act of human searching. In the SOA, search direction is based on empir- ical gradients by evaluating the response to the position changes, while step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the SOA is evaluated by using a challenging set of typically complex functions in compari- son to differential evolution （DE） and three modified particle swarm optimization （PSO） algorithms. The simulation results show that the performance of the SOA is superior or comparable to that of the other algorithms.展开更多
This paper discusses the algorithms for achieving global states and self-stabilizationfor communication protocols. It first describes a primary algorithm including its suitability forachieving global states and limita...This paper discusses the algorithms for achieving global states and self-stabilizationfor communication protocols. It first describes a primary algorithm including its suitability forachieving global states and limitation of self-stabilization for communication protocols, and thenpresents an improved algorithm that can be suitable to achieve global states and can be also usedto self-stabilizing communication protocols. Filially, it gives the proof of correctness and analysis ofcomplexity of the improved algorithm, and verifies its availability and efficiency by illustrating anexample protocol.展开更多
Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selecti...Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.展开更多
An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective f...An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.展开更多
This paper is dedicated to virtual world exploration techniques, which have to help a human being to understand a 3D scene. A new method to compute a global view of a scene is presented in the paper. The global view o...This paper is dedicated to virtual world exploration techniques, which have to help a human being to understand a 3D scene. A new method to compute a global view of a scene is presented in the paper. The global view of a scene is determined by a “good” set off points of view. This method is based on a genetic algorithm. The “good” set of points of view is used to compute a camera path around the scene.展开更多
A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm i...A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.展开更多
Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability ...Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory展开更多
基金the National Natural Science Foundation of China(No.19971002)
文摘The authors consider optimization methods for box constrained variational inequalities. First, the authors study the KKT-conditions problem based on the original problem. A merit function for the KKT-conditions problem is proposed, and some desirable properties of the merit function are obtained. Through the merit function, the original problem is reformulated as minimization with simple constraints. Then, the authors show that any stationary point of the optimization problem is a solution of the original problem. Finally, a descent algorithm is presented for the optimization problem, and global convergence is shown.
文摘This paper is a continuation of our previous work [Front. Math. China, 2016, 11（6）： 1379-1418] where an efficient algorithm for computing the maximal eigenpalr was introduced first for tridiagonal matrices and then extended to the irreducible matrices with nonnegative off-diagonal elements. This paper introduces mainly two global algorithms for computing the maximal eigenpair in a rather general setup, including even a class of real （with some negative off-diagonal elements） or complex matrices.
基金This work was supported in part by the National Natural Science Foundation of China(Grant No.11771046)the Project from the Ministry of Education in China,and the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions.
文摘This paper is a continuation of our previous paper[Front.Math.China,2017,12(5):10231043]where global algorithms for computing the maximal cigcnpair were introduced in a rather general setup.The efficiency of the global algorithms is improved in this paper in terms of a good use of power iteration and two quasi-symmetric techniques.Finally,the new algorithms are applied to Hua’s economic optimization model.
文摘The Firefly Algorithm(FA)is a highly efficient population-based optimization technique developed by mimicking the flashing behavior of fireflies when mating.This article proposes a method based on Differential Evolution(DE)/current-to-best/1 for enhancing the FA's movement process.The proposed modification increases the global search ability and the convergence rates while maintaining a balance between exploration and exploitation by deploying the global best solution.However,employing the best solution can lead to premature algorithm convergence,but this study handles this issue using a loop adjacent to the algorithm's main loop.Additionally,the suggested algorithm’s sensitivity to the alpha parameter is reduced compared to the original FA.The GbFA surpasses both the original and five-version of enhanced FAs in finding the optimal solution to 30 CEC2014 real parameter benchmark problems with all selected alpha values.Additionally,the CEC 2017 benchmark functions and the eight engineering optimization challenges are also utilized to evaluate GbFA’s efficacy and robustness on real-world problems against several enhanced algorithms.In all cases,GbFA provides the optimal result compared to other methods.Note that the source code of the GbFA algorithm is publicly available at https://www.optim-app.com/projects/gbfa.
文摘In this paper, we develop a new theoretical framework by means of the absorbing Markov process theory for analyzing some stochastic global optimization algorithms. Applying the framework to the pure random search, we prove that the pure random search converges to the global minimum in probability and its time has geometry distribution. We also analyze the pure adaptive search by this framework and turn out that the pure adaptive search converges to the global minimum in probability and its time has Poisson distribution.
文摘This paper presents a new stochastic algorithm for box constrained global optimization problem. Bacause the level set of objective function is always not known, the authors designed a region containing the current minimum point to replace it, and in order to fit the level set well, this region would be walking and contracting in the running process. Thus, the new algorithm is named as region's walk and contraction(RWC). Some numerical experiments for the RWC were conducted, which indicate good property of the algorithm.
基金the National Natural Science Foundation of China(Nos.51779135 and 51009087)the Natural Science Foundation of Shanghai(No.14ZR1419500)。
文摘Rankine source method,optimization technology,parametric modeling technology,and improved multiobjective optimization algorithm were combined to investigate the multiobjective optimization design of hull form.A multiobjective and multilevel optimization design framework was constructed for the comprehensive navigation performance of ships.CAESES software was utilized as the optimization platform,and nondominated sorting genetic algorithm II(NSGA-II)was used to conduct multiobjective optimization research on the resistance and sea-keeping performance of the ITTC Ship A-2 fishing vessel.Optimization objectives of this study are heave/pitch response amplitude and wave-making resistance.Taking the displacement and the length between perpendiculars as constraints,we optimized the profile of the hull.Analytic hierarchy process(AHP)and technique for order preference by similarity to ideal solution(TOPSIS)were used to sort and select Pareto solutions and determine weight coefficient of each navigation performance objective in the general objective.Finally,the hydrodynamic performance before and after the parametric deformation of the hull was compared.The results show that both the wave-making resistance and heave/pitch amplitude of the optimized hull form are reduced,and the satisfactory optimal hull form is obtained.The results of this study have a certain reference value for the initial stage of multiobjective optimization design of hull form.
文摘A modification of evolutionary programming or evolution strategies for ndimensional global optimization is proposed. Based on the ergodicity and inherentrandomness of chaos, the main characteristic of the new algorithm which includes two phases is that chaotic behavior is exploited to conduct a rough search of the problem space in order to find the promising individuals in Phase I. Adjustment strategy of steplength and intensive searches in Phase II are employed. The population sequences generated by the algorithm asymptotically converge to global optimal solutions with probability one. The proposed algorithm is applied to several typical test problems. Numerical results illustrate that this algorithm can more efficiently solve complex global optimization problems than evolutionary programming and evolution strategies in most cases.
基金Supported by National Natural Science Foundation of P.R.China(50275150)National Research Foundation for the Doctoral Program of Higher Education of P.R.China(20040533035)
文摘A new dynamical evolutionary algorithm (DEA) based on the theory of statistical mechanics is presented. This algorithm is very different from the traditional evolutionary algorithm and the two novel features are the unique of selecting strategy and the determination of individuals that are selected to crossover and mutate. We use DEA to solve a lot of global optimization problems that are nonlinear, multimodal and multidimensional and obtain satisfactory results.
文摘Evolutionary computation is a kind of adaptive non--numerical computation method which is designed tosimulate evolution of nature. In this paper, evolutionary algorithm behavior is described in terms of theconstruction and evolution of the sampling distributions over the space of candidate solutions. Iterativeconstruction of the sampling distributions is based on the idea of the global random search of generationalmethods. Under this frame, propontional selection is characterized as a gobal search operator, and recombination is characerized as the search process that exploits similarities. It is shown-that by properly constraining the search breadth of recombination operators, weak convergence of evolutionary algorithms to aglobal optimum can be ensured.
文摘A new genetic algorithm (GA) is developed. It features three new operations: restoration, reconstruction and recording the better, so as to produce a limited monotonic sequence of fitness value, to realize a globally optimal choosing, and to converge to a globally optimal solution through a perfectly stochastic process. Practical examples are given to illustrate the superiority of this new GA.
基金supported by the National Natural Science Foundation of China(60870004)
文摘A novel heuristic search algorithm called seeker op- timization algorithm （SOA） is proposed for the real-parameter optimization. The proposed SOA is based on simulating the act of human searching. In the SOA, search direction is based on empir- ical gradients by evaluating the response to the position changes, while step length is based on uncertainty reasoning by using a simple fuzzy rule. The effectiveness of the SOA is evaluated by using a challenging set of typically complex functions in compari- son to differential evolution （DE） and three modified particle swarm optimization （PSO） algorithms. The simulation results show that the performance of the SOA is superior or comparable to that of the other algorithms.
文摘This paper discusses the algorithms for achieving global states and self-stabilizationfor communication protocols. It first describes a primary algorithm including its suitability forachieving global states and limitation of self-stabilization for communication protocols, and thenpresents an improved algorithm that can be suitable to achieve global states and can be also usedto self-stabilizing communication protocols. Filially, it gives the proof of correctness and analysis ofcomplexity of the improved algorithm, and verifies its availability and efficiency by illustrating anexample protocol.
文摘Selection, crossover, and mutation are three main operators of the canonical genetic algorithm (CGA). This paper presents a new approach to the genetic algorithm. This new approach applies only to mutation and selection operators. The paper proves that the search process of the non-crossover genetic algorithm (NCGA) is an ergodic homogeneous Markov chain. The proof of its convergence to global optimum is presented. Some nonlinear multi-modal optimization problems are applied to test the efficacy of the NCGA. NP-hard traveling salesman problem (TSP) is cited here as the benchmark problem to test the efficiency of the algorithm. The simulation result shows that NCGA achieves much faster convergence speed than CGA in terms of CPU time. The convergence speed per epoch of NCGA is also faster than that of CGA.
基金This project is supported by Provincial Science Foundation of Hebei (No.01213553).
文摘An extended crowding genetic algorithm (ECGA) is introduced for solvingoptimal pump configuration problem, which was presented by T. Westerlund in 1994. This problem hasbeen found to be non-convex, and the objective function contained several local optima and globaloptimality could not be ensured by all the traditional MINLP optimization method. The concepts ofspecies conserving and composite encoding are introduced to crowding genetic algorithm (CGA) formaintain the diversity of population more effectively and coping with the continuous and/or discretevariables in MINLP problem. The solution of three-levels pump configuration got from DICOPT++software (OA algorithm) is also given. By comparing with the solutions obtained from DICOPT++, ECPmethod, and MIN-MIN method, the ECGA algorithm proved to be very effective in finding the globaloptimal solution of multi-levels pump configuration via using the problem-specific information.
文摘This paper is dedicated to virtual world exploration techniques, which have to help a human being to understand a 3D scene. A new method to compute a global view of a scene is presented in the paper. The global view of a scene is determined by a “good” set off points of view. This method is based on a genetic algorithm. The “good” set of points of view is used to compute a camera path around the scene.
文摘A trust region algorithm for equality constrained optimization is given in this paper.The algorithm does not enforce strict monotonicity of the merit function for every iteration.Global convergence of the algorithm is proved under the same conditions of usual trust region method.
文摘Making use of the theory of continuous homotopy and the relation betweensymmetric polynomtal and polynomtal in one variable the arthors devoted ims article to constructing a regularly homotopic curve with probability one. Discrete tracingalong this honlotopic curve leads 10 a class of Durand-Kerner algorithm with stepparameters. The convergernce of this class of algorithms is given, which solves theconjecture about the global property of Durand-Kerner algorithm. The.problem forsteplength selection is thoroughly discussed Finally, sufficient numerical examples areused to verify our theory
