Abstract
Abstract Previously a theoretical study of the average convergence rate was conducted for discrete optimisation. This paper extends it to a further analysis for continuous optimisation. 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 positive-adaptive generators is asymptotically positive, but that of algorithms using landscape-invariant generators and zero-adaptive generators asymptotically converges to zero. A case study is made to validate the applicability of theoretical results. Besides the theoretical study, numerical simulations are presented to show the feasibility of the average convergence rate in practical applications. In case of unknown optimum, an alternative definition of the average convergence rate is also considered.KeywordsEvolutionary algorithmsContinuous optimisationConvergence rateMarkov chainsApproximation errorSearch strategies
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