First Steps Towards a Runtime Analysis When Starting With a Good Solution
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arXiv
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| Format: | Preprint |
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2020
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| _version_ | 1866917076817412096 |
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| author | Antipov, Denis Buzdalov, Maxim Doerr, Benjamin |
| author_facet | Antipov, Denis Buzdalov, Maxim Doerr, Benjamin |
| contents | The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible to guess solutions that are better than random ones. We start a mathematical runtime analysis for such situations. We observe that different algorithms profit to a very different degree from a better initialization. We also show that the optimal parameterization of the algorithm can depend strongly on the quality of the initial solutions. To overcome this difficulty, self-adjusting and randomized heavy-tailed parameter choices can be profitable. Finally, we observe a larger gap between the performance of the best evolutionary algorithm we found and the corresponding black-box complexity. This could suggest that evolutionary algorithms better exploiting good initial solutions are still to be found. These first findings stem from analyzing the performance of the $(1+1)$ evolutionary algorithm and the static, self-adjusting, and heavy-tailed $(1 + (λ,λ))$ GA on the OneMax benchmark. We are optimistic that the question how to profit from good initial solutions is interesting beyond these first examples. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_12161 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | First Steps Towards a Runtime Analysis When Starting With a Good Solution Antipov, Denis Buzdalov, Maxim Doerr, Benjamin Neural and Evolutionary Computing 68W50 The mathematical runtime analysis of evolutionary algorithms traditionally regards the time an algorithm needs to find a solution of a certain quality when initialized with a random population. In practical applications it may be possible to guess solutions that are better than random ones. We start a mathematical runtime analysis for such situations. We observe that different algorithms profit to a very different degree from a better initialization. We also show that the optimal parameterization of the algorithm can depend strongly on the quality of the initial solutions. To overcome this difficulty, self-adjusting and randomized heavy-tailed parameter choices can be profitable. Finally, we observe a larger gap between the performance of the best evolutionary algorithm we found and the corresponding black-box complexity. This could suggest that evolutionary algorithms better exploiting good initial solutions are still to be found. These first findings stem from analyzing the performance of the $(1+1)$ evolutionary algorithm and the static, self-adjusting, and heavy-tailed $(1 + (λ,λ))$ GA on the OneMax benchmark. We are optimistic that the question how to profit from good initial solutions is interesting beyond these first examples. |
| title | First Steps Towards a Runtime Analysis When Starting With a Good Solution |
| topic | Neural and Evolutionary Computing 68W50 |
| url | https://arxiv.org/abs/2006.12161 |