Abstract
Maintaining an archive of all non-dominated points is a standard task in multi-objective optimization. Sometimes it is sufficient to store all evaluated points and to obtain the non-dominated subset in a post-processing step. Alternatively the non-dominated set can be updated on the fly. While keeping track of many non-dominated points efficiently is easy for two objectives, we propose an efficient algorithm based on a binary space partitioning (BSP) tree for the general case of three or more objectives. Our analysis and our empirical results demonstrate the superiority of the method over the brute-force baseline method, as well as graceful scaling to large numbers of objectives.
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Notes
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This is usually sufficient for the needs of evolutionary optimization. In data base query problems larger sets must be processed. Hence in some applications memory consumption is still a concern.
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For \(a>0\) the values \(a=0.1\), \(a=0.2\), \(a=0.5\), and \(a=1\) were used with \(m=2\), \(m=3\), \(m=5\), and \(m=10\) objectives, respectively.
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Glasmachers, T. (2017). A Fast Incremental BSP Tree Archive for Non-dominated Points. In: Trautmann, H., et al. Evolutionary Multi-Criterion Optimization. EMO 2017. Lecture Notes in Computer Science(), vol 10173. Springer, Cham. https://doi.org/10.1007/978-3-319-54157-0_18
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DOI: https://doi.org/10.1007/978-3-319-54157-0_18
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