To understand one-dimensional continuous fitness landscapes by drift analysis

This work shows that we could describe the characteristics of easy and hard fitness landscapes in one-dimensional continuous space by drift analysis. The work expends the existing results in the discrete space into the continue space. A fitness landscape, here, is regarded as the behaviour of an evolutionary algorithm on fitness functions. Based on the drift analysis, easy fitness landscapes are thought to be a "short-distance" landscape, which is easy for the evolutionary algorithm to find the optimal point; and hard fitness landscapes then are as a far-distance landscape, which the evolutionary algorithm had to spend a long time to find the optimal point.

[1]  Bart Naudts,et al.  A comparison of predictive measures of problem difficulty in evolutionary algorithms , 2000, IEEE Trans. Evol. Comput..

[2]  Richard L. Tweedie,et al.  Markov Chains and Stochastic Stability , 1993, Communications and Control Engineering Series.

[3]  Terry Jones,et al.  Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms , 1995, ICGA.

[4]  B. Hajek Hitting-time and occupation-time bounds implied by drift analysis with applications , 1982, Advances in Applied Probability.

[5]  Alden H. Wright,et al.  Stability of Vertex Fixed Points and Applications , 1994, FOGA.

[6]  Kalyanmoy Deb,et al.  Long Path Problems , 1994, PPSN.

[7]  Xin Yao,et al.  From an individual to a population: an analysis of the first hitting time of population-based evolutionary algorithms , 2002, IEEE Trans. Evol. Comput..

[8]  Günter Rudolph,et al.  Convergence of non-elitist strategies , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[9]  Xin Yao,et al.  Drift analysis and average time complexity of evolutionary algorithms , 2001, Artif. Intell..

[10]  X. Yao,et al.  An analysis of evolutionary algorithms for finding approximation solutions to hard optimisation problems , 2003, The 2003 Congress on Evolutionary Computation, 2003. CEC '03..

[11]  Yuval Davidor,et al.  Epistasis Variance: A Viewpoint on GA-Hardness , 1990, FOGA.

[12]  Stewart W. Wilson GA-Easy Does Not Imply Steepest-Ascent Optimizable , 1991, ICGA.

[13]  H. Teicher,et al.  Probability theory: Independence, interchangeability, martingales , 1978 .

[14]  Xin Yao,et al.  A study of drift analysis for estimating computation time of evolutionary algorithms , 2004, Natural Computing.

[15]  Xin Yao,et al.  Towards an analytic framework for analysing the computation time of evolutionary algorithms , 2003, Artif. Intell..

[16]  Tim Jones Evolutionary Algorithms, Fitness Landscapes and Search , 1995 .

[17]  David E. Goldberg,et al.  Genetic Algorithm Difficulty and the Modality of Fitness Landscapes , 1994, FOGA.