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.
The first author was supported by the National Science Foundation of China (NSFC) under Grant No. 61303028; The second author was supported by EPSRC under Grant No. EP/I009809/1.
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Notes
- 1.
We don’t add a converge order because for discrete optimisation, \(e_t\) converges linearly to 0 according to [15, Theorem 1]. For continuous optimisation, a conjecture is that \(e_t\) also converges linearly unless gradient information is used in the search.
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Chen, Y., He, J. (2020). Average Convergence Rate of Evolutionary Algorithms II: Continuous Optimisation. In: Li, K., Li, W., Wang, H., Liu, Y. (eds) Artificial Intelligence Algorithms and Applications. ISICA 2019. Communications in Computer and Information Science, vol 1205. Springer, Singapore. https://doi.org/10.1007/978-981-15-5577-0_3
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