Krzysztof Krawiec


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Metrics are essential for geometric semantic genetic programming. On one hand, they structure the semantic space and govern the behavior of geometric search operators; on the other, they determine how fitness is calculated. The interactions between these two types of metrics are an important aspect that to date was largely neglected. In this paper, we investigate these interactions and analyze their consequences. We provide a systematic theoretical analysis of the properties of abstract geometric semantic search operators under Minkowski metric of an arbitrary order. For nine combinations of popular metrics (city-block, Euclidean, and Chebyshev) used in fitness function and by search operators, we derive pessimistic bounds on fitness change. We also define three types of progress properties (weak, potential, and strong) and verify them for operators under those metrics. The analysis allows us to determine the combinations of metrics that are most attractive in terms of progress properties and deterioration bounds.

@ARTICLE { Pawlak:2015:GPEM,
    YEAR = { 2015 },
    ISSN = { 1389-2576 },
    JOURNAL = { Genetic Programming and Evolvable Machines },
    DOI = { 10.1007/s10710-015-9252-6 },
    TITLE = { Progress properties and fitness bounds for geometric semantic search operators },
    URL = { http://dx.doi.org/10.1007/s10710-015-9252-6 },
    PUBLISHER = { Springer US },
    KEYWORDS = { Geometric semantic genetic programming; Theory; Metric; Fitness landscape; Fitness bounds; Guarantees of progress },
    AUTHOR = { Pawlak, Tomasz P. and Krawiec, Krzysztof },
    PAGES = { 1-19 },
    ABSTRACT = { Metrics are essential for geometric semantic genetic programming. On one hand, they structure the semantic space and govern the behavior of geometric search operators; on the other, they determine how fitness is calculated. The interactions between these two types of metrics are an important aspect that to date was largely neglected. In this paper, we investigate these interactions and analyze their consequences. We provide a systematic theoretical analysis of the properties of abstract geometric semantic search operators under Minkowski metric of an arbitrary order. For nine combinations of popular metrics (city-block, Euclidean, and Chebyshev) used in fitness function and by search operators, we derive pessimistic bounds on fitness change. We also define three types of progress properties (weak, potential, and strong) and verify them for operators under those metrics. The analysis allows us to determine the combinations of metrics that are most attractive in terms of progress properties and deterioration bounds. },
}


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