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 metrics of arbitrary order. For nine combinations of popular metrics (city-block, Euclidean, and Chebyshev) used in fitness functions and of 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.
Highlights
Semantic genetic programming (SGP) is a relatively recent research thread in GP, where selected behavioral properties of programs are being exploited for the sake of making program synthesis more efficient and scalable
We provided a systematic theoretical analysis of the key properties of the abstract geometric semantic search operators under the most popular variants of Minkowski metric
We showed which combinations of metrics used by the fitness function and geometric search operators are most beneficial in terms of progress properties and deterioration bounds
Summary
Semantic genetic programming (SGP) is a relatively recent research thread in GP, where selected behavioral properties of programs are being exploited for the sake of making program synthesis more efficient and scalable. The geometric semantic crossover and geometric semantic mutation exactly realize the properties expected from ideal search operators This is achieved by expressing the desirable ‘mixing’ of the parents using the instructions of the programming language of consideration. In effect, those operators are guaranteed to produce offspring with specific geometric properties of semantics, and in turn ensure certain types of progress.
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