Vectorial Genetic Programming (Vec-GP) extends GP by allowing vectors as input features along regular, scalar features, using them by applying arithmetic operations component-wise or aggregating vectors into scalars by some aggregation function. Vec-GP also allows aggregating vectors only over a limited segment of the vector instead of the whole vector, which offers great potential but also introduces new parameters that GP has to optimize. This paper formalizes an optimization problem to analyze different strategies for optimizing a window for aggregation functions. Different strategies are presented, included random and guided sampling, where the latter leverages information from an approximated gradient. Those strategies can be applied as a simple optimization algorithm, which itself ca be applied inside a specialized mutation operator within GP. The presented results indicate, that the different random sampling strategies do not impact the overall algorithm performance significantly, and that the guided strategies suffer from becoming stuck in local optima. However, results also indicate, that there is still potential in discovering more efficient algorithms that could outperform the presented strategies.

翻译：向量遗传编程（Vec-GP）通过允许向量作为输入特征（与常规标量特征共同使用）扩展了遗传编程，其采用按分量算术运算或通过聚合函数将向量聚合成标量的方式。Vec-GP还允许仅对向量的有限分段而非整体进行聚合，这虽提供了巨大潜力，但也引入了遗传编程须优化的新参数。本文形式化了一个优化问题，用于分析不同策略在优化聚合函数窗口时的表现。提出了包括随机采样与引导采样在内的多种策略，其中后者利用近似梯度信息。这些策略可应用于简单的优化算法，该算法本身可在遗传编程内嵌的专用变异算子中实现。结果表明，不同随机采样策略对整体算法性能无显著影响，而引导策略容易陷入局部最优。然而，结果同样表明，仍有潜力发现能够超越现有策略的更高效算法。