In this paper, a new evolutionary strategy is proposed for minimizing uni- modal functions. Main characteristic of the strategy is that the classical mutation operator-Gaussian distribution is substituted by an unifor...In this paper, a new evolutionary strategy is proposed for minimizing uni- modal functions. Main characteristic of the strategy is that the classical mutation operator-Gaussian distribution is substituted by an uniform distribution. Theoretical analysis and numerical experiments indicate that convergence rate of the new strategy is superior to the classical one in most cases. Criteria of adoption of parent population and verification of step-length are also studied, and computa- tional efficiency of evolutionary strategies, in which crossover operator is employed or unemployed, is compared.展开更多
In this paper we consider a parallel algorithm that detects the maximizer of unimodal function f(x) computable at every point on unbounded interval (0, ∞). The algorithm consists of two modes: scanning and detecting....In this paper we consider a parallel algorithm that detects the maximizer of unimodal function f(x) computable at every point on unbounded interval (0, ∞). The algorithm consists of two modes: scanning and detecting. Search diagrams are introduced as a way to describe parallel searching algorithms on unbounded intervals. Dynamic programming equations, combined with a series of liner programming problems, describe relations between results for every pair of successive evaluations of function f in parallel. Properties of optimal search strategies are derived from these equations. The worst-case complexity analysis shows that, if the maximizer is located on a priori unknown interval (n-1], then it can be detected after cp(n)=「2log「p/2」+1(n+1)」-1 parallel evaluations of f(x), where p is the number of processors.展开更多
For any continuous function f on the interval I=[0, 1] and any m, n≥1, let N(n, f)denote the number of n-periodic orbits in f. Put N(n, m)=min{N(n, f):f is a continuousfunction on I, and N(m, f)≥1}. The famous Sarko...For any continuous function f on the interval I=[0, 1] and any m, n≥1, let N(n, f)denote the number of n-periodic orbits in f. Put N(n, m)=min{N(n, f):f is a continuousfunction on I, and N(m, f)≥1}. The famous Sarkovskii’s theorem can be stated as follows:If n?m, then N(n,m)≥1. In this paper, we further obtain analytic expressions of the precisevalue of N(n, m) for all positive integers m and n, which are convenient for computing.展开更多
Replete unimodal function and other conceptions are defined. It is proved that for any continuous function φ, if φ has a unimodal orbit , then φ has all unimodal orbits whose types precede the orbit type of. They a...Replete unimodal function and other conceptions are defined. It is proved that for any continuous function φ, if φ has a unimodal orbit , then φ has all unimodal orbits whose types precede the orbit type of. They are altogether distributed on a compact subset X of I. The restriction φ|X of φ to X is a replete unimodal function. Moreover, an ordered classification φ of the function space C°(I,R) is given. It is a refinement of the famous Sarkovskii’s ordered classification F, and also a generalization of the conclusion obtained by Bhatia and Egerland not long ago.展开更多
文摘In this paper, a new evolutionary strategy is proposed for minimizing uni- modal functions. Main characteristic of the strategy is that the classical mutation operator-Gaussian distribution is substituted by an uniform distribution. Theoretical analysis and numerical experiments indicate that convergence rate of the new strategy is superior to the classical one in most cases. Criteria of adoption of parent population and verification of step-length are also studied, and computa- tional efficiency of evolutionary strategies, in which crossover operator is employed or unemployed, is compared.
文摘In this paper we consider a parallel algorithm that detects the maximizer of unimodal function f(x) computable at every point on unbounded interval (0, ∞). The algorithm consists of two modes: scanning and detecting. Search diagrams are introduced as a way to describe parallel searching algorithms on unbounded intervals. Dynamic programming equations, combined with a series of liner programming problems, describe relations between results for every pair of successive evaluations of function f in parallel. Properties of optimal search strategies are derived from these equations. The worst-case complexity analysis shows that, if the maximizer is located on a priori unknown interval (n-1], then it can be detected after cp(n)=「2log「p/2」+1(n+1)」-1 parallel evaluations of f(x), where p is the number of processors.
基金Project supported by the National Natural Science Foundation of China.
文摘For any continuous function f on the interval I=[0, 1] and any m, n≥1, let N(n, f)denote the number of n-periodic orbits in f. Put N(n, m)=min{N(n, f):f is a continuousfunction on I, and N(m, f)≥1}. The famous Sarkovskii’s theorem can be stated as follows:If n?m, then N(n,m)≥1. In this paper, we further obtain analytic expressions of the precisevalue of N(n, m) for all positive integers m and n, which are convenient for computing.
基金Project supported by the National Natural Science Foundation of China.
文摘Replete unimodal function and other conceptions are defined. It is proved that for any continuous function φ, if φ has a unimodal orbit , then φ has all unimodal orbits whose types precede the orbit type of. They are altogether distributed on a compact subset X of I. The restriction φ|X of φ to X is a replete unimodal function. Moreover, an ordered classification φ of the function space C°(I,R) is given. It is a refinement of the famous Sarkovskii’s ordered classification F, and also a generalization of the conclusion obtained by Bhatia and Egerland not long ago.
