Within the optimization community, the question of how to generate new optimization problems has been gaining traction in recent years. Within topics such as instance space analysis (ISA), the generation of new problems can provide new benchmarks which are not yet explored in existing research. Beyond that, this function generation can also be exploited for solving complex real-world optimization problems. By generating functions with similar properties to the target problem, we can create a robust test set for algorithm selection and configuration. However, the generation of functions with specific target properties remains challenging. While features exist to capture low-level landscape properties, they might not always capture the intended high-level features. We show that a genetic programming (GP) approach guided by these exploratory landscape analysis (ELA) properties is not always able to find satisfying functions. Our results suggest that careful considerations of the weighting of landscape properties, as well as the distance measure used, might be required to evolve functions that are sufficiently representative to the target landscape.

翻译：在优化领域，近年来关于如何生成新的优化问题逐渐引起关注。在实例空间分析（ISA）等课题中，新问题的生成能提供现有研究中尚未探索的新基准。此外，这种函数生成还可用于解决复杂的现实世界优化问题。通过生成与目标问题具有相似特性的函数，我们可以为算法选择与配置构建鲁棒的测试集。然而，生成具有特定目标特性的函数仍然充满挑战。尽管存在用于捕捉低层级景观特征的指标，但这些指标未必总能反映预期的高层级特征。我们证明：由探索性景观分析（ELA）属性指导的遗传编程（GP）方法并非总能找到令人满意的函数。我们的结果表明，为了演化出充分代表目标景观的函数，可能需要仔细权衡景观属性的权重以及所使用的距离度量。