Motivated by the celebrated paper of Hooker (J Heuristics 1(1): 33–42, 1995) published in the first issue of this journal, and by the relative lack of progress of both approximation algorithms and fixed-parameter algorithms for the classical decision and optimization problems related to covering edges by vertices, we aimed at developing an approach centered in augmenting our intuition about what is indeed needed. We present a case study of a novel design methodology by which algorithm weaknesses will be identified by computer-based and fixed-parameter tractable algorithmic challenges on their performance. Comprehensive benchmarkings on all instances of small size then become an integral part of the design process. Subsequent analyses of cases where human intuition “fails”, supported by computational testing, will then lead to the development of new methods by avoiding the traps of relying only on human perspicacity and ultimately will improve the quality of the results. Consequently, the computer-aided design process is seen as a tool to augment human intuition. It aims at accelerating and foster theory development in areas such as graph theory and combinatorial optimization since some safe reduction rules for pre-processing can be mathematically proved via theorems. This approach can also lead to the generation of new interesting heuristics. We test our ideas with a fundamental problem in graph theory that has attracted the attention of many researchers over decades, but for which seems it seems to be that a certain stagnation has occurred. The lessons learned are certainly beneficial, suggesting that we can bridge the increasing gap between theory and practice by a more concerted approach that would fuel human imagination from a data-driven discovery perspective.

受到Hooker的著名论文（J Heuristics 1（1）：33–42，1995）的启发，并且由于经典决策的近似算法和固定参数算法都相对缺乏进展以及与通过顶点覆盖边缘有关的优化问题，我们旨在开发一种以增强我们对实际需求的直觉为中心的方法。我们提供了一个新颖的设计方法的案例研究，该算法将通过基于计算机的固定参数可处理的算法挑战对其性能进行识别。然后，所有小尺寸实例的全面基准测试都将成为设计过程的组成部分。在计算机测试的支持下，对人类直觉“失败”的案例进行后续分析，然后，通过避免仅依靠人类的洞察力而导致新方法的开发，最终将提高结果的质量。因此，计算机辅助设计过程被视为增强人类直觉的工具。它旨在加速和促进图论和组合优化等领域的理论发展，因为可以通过定理在数学上证明一些安全的预处理减法则。这种方法还可以导致产生新的有趣的启发式方法。我们用图论中的一个基本问题测试了我们的想法，这个问题在几十年来已经引起了许多研究者的注意，但是似乎似乎已经出现了某种停滞。吸取的教训当然是有益的