细胞自动机多数问题的适应度景观：来自Olympus的观点
Fitness landscape of the cellular automata majority problem: View from the Olympus
摘要：
在本文中，我们研究了执行计算多数任务的细胞自动机（CA）。这个任务是一个很好的例子，说明了复杂系统中的涌现现象是什么。我们感兴趣的原因，使这一特定的健身景观是一个困难的。第一个目标是研究景观本身，因此它在理想情况下独立于用于搜索空间的实际地理学。然而，第二个目标是了解这个特定问题空间的好搜索技术应该具备的功能。我们以各种方式统计量化搜索这一景观的难度。由于中立性，很难对整个景观进行基于抽样技术的调查。所以我们从顶部开始探索这片土地。虽然已经证明，没有CA可以完美地执行这个任务，几个有效的CA为这个task.Exploiting这些CA和对称性之间的相似性的景观，我们定义的奥林巴斯景观被认为是“天堂的家”的最佳局部最优已知（blok）。然后我们测量这个子空间的几个性质。虽然在这个子空间中找到相关的CA比在整体景观中更容易，但有结构性原因阻止了一个搜索者在Olympus中找到过度拟合的CA。最后，我们在Olympus上研究了遗传算法的动力学和性能，以证实我们的分析，并找到有效的CA与低计算成本的多数问题。
英文摘要：
In this paper we study cellular automata (CAs) that perform the computational Majority task. This task is a good example of what the phenomenon of emergence in complex systems is. We take an interest in the reasons that make this particular fitness landscape a difficult one. The first goal is to study the landscape as such, and thus it is ideally independent from the actual heuristics used to search the space. However, a second goal is to understand the features a good search technique for this particular problem space should possess. We statistically quantify in various ways the degree of difficulty of searching this landscape. Due to neutrality, investigations based on sampling techniques on the whole landscape are difficult to conduct. So, we go exploring the landscape from the top. Although it has been proved that no CA can perform the task perfectly, several efficient CAs for this task have been found. Exploiting similarities between these CAs and symmetries in the landscape, we define the Olympus landscape which is regarded as the ''heavenly home'' of the best local optima known (blok). Then we measure several properties of this subspace. Although it is easier to find relevant CAs in this subspace than in the overall landscape, there are structural reasons that prevent a searcher from finding overfitted CAs in the Olympus. Finally, we study dynamics and performance of genetic algorithms on the Olympus in order to confirm our analysis and to find efficient CAs for the Majority problem with low computational cost.
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