Benchmarking plays a major role in the development and analysis of optimization algorithms. As such, the way in which the used benchmark problems are defined significantly affects the insights that can be gained from any given benchmark study. One way to easily extend the range of available benchmark functions is through affine combinations between pairs of functions. From the perspective of landscape analysis, these function combinations smoothly transition between the two base functions. In this work, we show how these affine function combinations can be used to analyze the behavior of optimization algorithms. In particular, we highlight that by varying the weighting between the combined problems, we can gain insights into the effects of added global structure on the performance of optimization algorithms. By analyzing performance trajectories on more function combinations, we also show that aspects such as the scaling of objective functions and placement of the optimum can greatly impact how these results are interpreted.

翻译：基准测试在优化算法的开发与分析中扮演着重要角色。因此，所使用的基准问题的定义方式显著影响着从任何给定基准研究中获得的见解。扩展可用基准函数范围的一种简单方法是通过函数对之间的仿射组合。从景观分析的角度来看，这些函数组合在两个基础函数之间平滑过渡。在本工作中，我们展示了如何利用这些仿射函数组合来分析优化算法的行为。特别地，我们强调通过改变组合问题之间的权重，可以深入了解新增全局结构对优化算法性能的影响。通过分析更多函数组合上的性能轨迹，我们还表明目标函数的缩放和最优点的放置等方面可能会极大地影响这些结果的解释方式。