Progress properties and fitness bounds for geometric semantic search operators

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.

Genetic programming with semantic equivalence classes

“…In [15], the importance of metrics for GSGP was discussed. According to the authors, two main types of metrics can be identified: measures that structure the semantic space and govern the behavior of geometric search operators and metrics that determine how fitness is calculated.…”

“…According to the authors, two main types of metrics can be identified: measures that structure the semantic space and govern the behavior of geometric search operators and metrics that determine how fitness is calculated. The first kind of metrics is clearly very important for the work presented here, while for the second kind of metric, this work differs from [15] given that no type of error between calculated values and targets is used here to assess the quality of the evolving individuals. An idea that can be considered as orthogonal to the one of the alignment in the error space is the one presented in [16], where a new type of crossover called subtree semantic geometric crossover (SSGC) was proposed.…”

Solving the exponential growth of symbolic regression trees in geometric semantic genetic programming

“…e motivation for choosing GSX E over GSX M for GSGP-Red comes from the fact that GSX M multiplies the parents by a randomly generated function-contrary to the linear combination performed by GSX E -which would imply in additional complexity in time and space to store and manipulate a function instead of a constant. Notice that the usage of the GSX E over the GSX M or vice versa is an open discussion in the literature, with some works defending the usage of GSX M , given empirical analysis [16], and others defending the usage of GSX E , given its progression properties [21].…”