Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search an...Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.展开更多
The stationary probability vectors of a second order Markov chain on the(n-1)-dimensional standard simplex are considered.In 2015,Li and Zhang gave a characterization of the second order Markov chain such that every v...The stationary probability vectors of a second order Markov chain on the(n-1)-dimensional standard simplex are considered.In 2015,Li and Zhang gave a characterization of the second order Markov chain such that every vector in the simplex is a stationary vector.A modification of the characterization is presented in the paper.Some sufficient conditions are derived for any facet of the simplex such that every vector of the facet is a stationary vector.展开更多
We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we intr...We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.展开更多
This article addresses the autonomy of joint radio resource management （JRRM） between heterogeneous radio access technologies（RATs） owned by multiple operators. By modeling the inter-operator competition as a gene...This article addresses the autonomy of joint radio resource management （JRRM） between heterogeneous radio access technologies（RATs） owned by multiple operators. By modeling the inter-operator competition as a general-sum Markov game, correlated-Q learning（CE-Q） is introduced to generate the operators＇ pricing and admission policies at the correlated equilibrium autonomically. The heterogeneity in terms of coverage, service suitability, and cell capacity amongst different RATs are considered in the input state space, which is generalized using multi-layer feed-forward neural networks for less memory requirement. Simulation results indicate that the proposed algorithm can produce rational JRRM polices for each network under different load conditions through the autonomic learning process. Such policies guide the traffic toward an optimized distribution and improved resource utilization, which results in the highest network profits and lowest blocking probability compared to other self-learning algorithms.展开更多
Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is...Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is proved that inadequate parameters of mutation and crossover probabilities degenerate standard genetic algorithm to a class of random search algorithms without selection bias toward any solution based on fitness. After introducing elitist reservation, the stochastic matrix of Markov chain of the best-so-far individual with the highest fitness is derived.The average convergence velocity of genetic algorithms is defined as the mathematical expectation of the mean absorbing time steps that the best-so-far individual transfers from any initial solution to the global optimum. Using the stochastic matrix of the best-so-far individual, a theoretic method and the computing process of estimating the average convergence velocity are proposed.展开更多
Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where ...Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.展开更多
This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditio...This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.展开更多
In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
基金Supported by the National Natural Science Foundation of China(60133010,70071042,60073043)
文摘Multi-objective Evolutionary Algorithm (MOEA) is becoming a hot research area and quite a few aspects of MOEAs have been studied and discussed. However there are still few literatures discussing the roles of search and selection operators in MOEAs. This paper studied their roles by solving a case of discrete Multi-objective Optimization Problem (MOP): Multi-objective TSP with a new MOEA. In the new MOEA, We adopt an efficient search operator, which has the properties of both crossover and mutation, to generate the new individuals and chose two selection operators: Family Competition and Population Competition with probabilities to realize selection. The simulation experiments showed that this new MOEA could get good uniform solutions representing the Pareto Front and outperformed SPEA in almost every simulation run on this problem. Furthermore, we analyzed its convergence property using finite Markov chain and proved that it could converge to Pareto Front with probability 1. We also find that the convergence property of MOEAs has much relationship with search and selection operators.
基金National Natural Science Foundation of China(Nos.1167125811371086)
文摘The stationary probability vectors of a second order Markov chain on the(n-1)-dimensional standard simplex are considered.In 2015,Li and Zhang gave a characterization of the second order Markov chain such that every vector in the simplex is a stationary vector.A modification of the characterization is presented in the paper.Some sufficient conditions are derived for any facet of the simplex such that every vector of the facet is a stationary vector.
基金supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Remin University of China(Grant No.10XNJ033)
文摘We characterize A-linear symmetric and contraction module operator semigroup{Tt}t∈R+L(l2(A)),where A is a finite-dimensional C-algebra,and L(l2(A))is the C-algebra of all adjointable module maps on l2(A).Next,we introduce the concept of operator-valued quadratic forms,and give a one to one correspondence between the set of non-positive definite self-adjoint regular module operators on l2(A)and the set of non-negative densely defined A-valued quadratic forms.In the end,we obtain that a real and strongly continuous symmetric semigroup{Tt}t∈R+L(l2(A))being Markovian if and only if the associated closed densely defined A-valued quadratic form is a Dirichlet form.
基金This work is supported by the National Natural Science Foundation of China （60632030）；the Integrated Project of the 6th Framework Program of the European Commission （IST-2005-027714）；the Hi-Tech Research and Development Program of China （2006AA01Z276） ；the China-European Union Science and Technology Cooperation Foundation of Ministry of Science and Technology of China （0516）.
文摘This article addresses the autonomy of joint radio resource management （JRRM） between heterogeneous radio access technologies（RATs） owned by multiple operators. By modeling the inter-operator competition as a general-sum Markov game, correlated-Q learning（CE-Q） is introduced to generate the operators＇ pricing and admission policies at the correlated equilibrium autonomically. The heterogeneity in terms of coverage, service suitability, and cell capacity amongst different RATs are considered in the input state space, which is generalized using multi-layer feed-forward neural networks for less memory requirement. Simulation results indicate that the proposed algorithm can produce rational JRRM polices for each network under different load conditions through the autonomic learning process. Such policies guide the traffic toward an optimized distribution and improved resource utilization, which results in the highest network profits and lowest blocking probability compared to other self-learning algorithms.
文摘Formulizations of mutation and crossover operators independent of representation of solutions are proposed. A kind of precisely quantitative Markov chain of populations of standard genetic algorithms is modeled. It is proved that inadequate parameters of mutation and crossover probabilities degenerate standard genetic algorithm to a class of random search algorithms without selection bias toward any solution based on fitness. After introducing elitist reservation, the stochastic matrix of Markov chain of the best-so-far individual with the highest fitness is derived.The average convergence velocity of genetic algorithms is defined as the mathematical expectation of the mean absorbing time steps that the best-so-far individual transfers from any initial solution to the global optimum. Using the stochastic matrix of the best-so-far individual, a theoretic method and the computing process of estimating the average convergence velocity are proposed.
文摘Let X be a compact metric space and C（X） be the space of all continuous functions on X. In this article, the authors consider the Markov operator T ： C（X）N C（X）N defined by for any f = （f1,f2,… ,fN）, where （pij） is a N x N transition probability matrix and {wij } is an family of continuous transformations on X. The authors study the uniqueness, ergodicity and unidimensionality of T＊-invariant measures where T＊ is the adjoint operator of T.
基金This work is supported by the National Natural Science Foundation of ChinaVisiting Scholar Foundation of Key Lab, in Univers
文摘This paper discusses the convergence rates about a class of evolutionary algorithms in general search spaces by means of the ergodic theory in Markov chain and some techniques in Banach algebra. Under certain conditions that transition probability functions of Markov chains corresponding to evolutionary algorithms satisfy, the authors obtain the convergence rates of the exponential order. Furthermore, they also analyze the characteristics of the conditions which can be met by genetic operators and selection strategies.
文摘In this paper, we give a survey on the PhD thesis of the first author. There theexistence and ergodicity on invariant measures of set-valued mappings are discused.
