Chance-constrained problems involve stochastic components in the constraints which can be violated with a small probability. We investigate the impact of different types of chance constraints on the performance of iterative search algorithms and study the classical maximum coverage problem in graphs with chance constraints. Our goal is to evolve reliable chance constraint settings for a given graph where the performance of algorithms differs significantly not just in expectation but with high confidence. This allows to better learn and understand how different types of algorithms can deal with different types of constraint settings and supports automatic algorithm selection. We develop an evolutionary algorithm that provides sets of chance constraints that differentiate the performance of two stochastic search algorithms with high confidence. We initially use traditional approximation ratio as the fitness function of (1+1)~EA to evolve instances, which shows inadequacy to generate reliable instances. To address this issue, we introduce a new measure to calculate the performance difference for two algorithms, which considers variances of performance ratios. Our experiments show that our approach is highly successful in solving the instability issue of the performance ratios and leads to evolving reliable sets of chance constraints with significantly different performance for various types of algorithms.

翻译：机会约束问题涉及约束条件中的随机成分，这些约束可以以较小概率被违反。我们研究了不同类型机会约束对迭代搜索算法性能的影响，并探讨了带机会约束的经典图最大覆盖问题。我们的目标是为给定图演化出可靠的机会约束设置，使得算法性能不仅在期望值上存在显著差异，而且能以高置信度区分。这有助于更好地理解和学习不同类型算法如何处理不同约束设置，并支持自动算法选择。我们开发了一种进化算法，能够以高置信度生成能区分两种随机搜索算法性能的机会约束集合。我们最初采用传统近似比作为(1+1)~EA的适应度函数来演化问题实例，但发现其无法生成可靠实例。为解决此问题，我们引入了一种考虑性能比方差的新度量方法来计算两种算法的性能差异。实验表明，我们的方法能有效解决性能比不稳定的问题，成功演化出能为各类算法产生显著不同性能的可靠机会约束集合。