Average Convergence Rate of Evolutionary Algorithms II: Continuous Optimization

by   Yu Chen, et al.

A good convergence metric must satisfy two requirements: feasible in calculation and rigorous in analysis. The average convergence rate is proposed as a new measurement for evaluating the convergence speed of evolutionary algorithms over consecutive generations. Its calculation is simple in practice and it is applicable to both continuous and discrete optimization. Previously a theoretical study of the average convergence rate was conducted for discrete optimization. This paper makes a further analysis for continuous optimization. First, the strategies of generating new solutions are classified into two categories: landscape-invariant and landscape-adaptive. Then, it is proven that the average convergence rate of evolutionary algorithms using landscape-invariant generators converges to zero, while the rate of algorithms using positive-adaptive generators has a positive limit. Finally, two case studies, the minimization problems of the two-dimensional sphere function and Rastrigin function, are made for demonstrating the applicability of the theory.


page 1

page 2

page 3

page 4


Average Convergence Rate of Evolutionary Algorithms

In evolutionary optimization, it is important to understand how fast evo...

An Analytic Expression of Relative Approximation Error for a Class of Evolutionary Algorithms

An important question in evolutionary computation is how good solutions ...

Novel Analysis of Population Scalability in Evolutionary Algorithms

Population-based evolutionary algorithms (EAs) have been widely applied ...

A Theoretical Framework of Approximation Error Analysis of Evolutionary Algorithms

In the empirical study of evolutionary algorithms, the solution quality ...

Distributed Evolution Strategies for Black-box Stochastic Optimization

This work concerns the evolutionary approaches to distributed stochastic...

A Revisit of Infinite Population Models for Evolutionary Algorithms on Continuous Optimization Problems

Infinite population models are important tools for studying population d...

On the Genotype Compression and Expansion for Evolutionary Algorithms in the Continuous Domain

This paper investigates the influence of genotype size on evolutionary a...

Please sign up or login with your details

Forgot password? Click here to reset