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：基准设定在优化算法的开发和分析中起着重要作用。 因此, 界定使用的基准问题的方式会大大影响从任何特定基准研究中获得的洞察力。 容易扩展现有基准功能范围的一种方法是通过对等功能组合。 从景观分析的角度来看, 这些功能将两个基本功能之间的平稳过渡结合起来。 在这项工作中, 我们展示这些对等函数组合如何用来分析优化算法的行为。 我们特别强调, 通过对合并问题进行不同的权衡, 我们就能了解增加的全球结构对优化算法绩效的影响。 通过分析更多功能组合的绩效轨迹, 我们还表明, 目标功能的扩大和最佳功能的定位等方面可以极大地影响这些结果的解释。</s>