Abstract This paper concerns the design of optimized single-finger keyboard layouts on smartphones. In the literature, the optimization problem associated with assigning characters to keys on a single-finger keyboard is denoted as single-finger keyboard layout problem (SK-QAP), which can be seen as a variant of the quadratic assignment problem (QAP), a classical combinatorial optimization problem. To solve it, we propose a simple yet effective local search-based metaheuristic which is composed of three neighborhood structures. Two of them were previously applied to solve the SK-QAP, whereas the third one consists of an adaptation of a QAP neighborhood and it was introduced in this work. In addition, two perturbation mechanisms were developed as diversification procedures and together with the latter neighborhood structure, they revealed to be highly beneficial for improving the performance of the algorithm. Computational experiments were carried out on benchmark instances for English, French, Italian and Spanish. The results obtained were extremely competitive both in terms of solution quality and CPU time, such that all best known solutions were found in a matter of seconds. Moreover, we developed and solved benchmark instances for Portuguese, which currently has more than 230 million speakers, as a first or second language, and also uses the Latin alphabet. We have also proposed and solved bilingual instances, combining English, one of the top spoken languages in the world, with each of the remaining four ones. In addition, we quantify the potential practical benefits of adopting alternative and smartphone-oriented optimized single-finger keyboards, when compared to well-known layouts, namely QWERTY and AZERTY, for the five languages and bilingual variants considered. Finally, we show the efficiency of the proposed algorithm when generating layouts based on other existing arrangements, namely Metropolis and FITALY.

中文翻译：

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优化智能手机的单指键盘布局

摘要 本文涉及智能手机上优化的单指键盘布局的设计。在文献中，与为单指键盘上的键分配字符相关的优化问题表示为单指键盘布局问题（SK-QAP），它可以看作是二次分配问题（QAP）的变体，一个经典的组合优化问题。为了解决这个问题，我们提出了一个简单而有效的基于局部搜索的元启发式算法，它由三个邻域结构组成。其中两个以前用于解决 SK-QAP，而第三个由 QAP 邻域的改编组成，并在这项工作中引入。此外，还开发了两种扰动机制作为多样化程序，并与后者的邻域结构一起，他们发现这对提高算法的性能非常有益。在英语、法语、意大利语和西班牙语的基准实例上进行了计算实验。获得的结果在解决方案质量和 CPU 时间方面都极具竞争力，因此所有最著名的解决方案都可以在几秒钟内找到。此外，我们开发并解决了葡萄牙语的基准实例，葡萄牙语目前拥有超过 2.3 亿的使用者，作为第一或第二语言，并且还使用拉丁字母。我们还提出并解决了双语实例，将世界上最流行的语言之一英语与其余四种语言中的每一种相结合。此外，我们量化了采用替代和面向智能手机的优化单指键盘的潜在实际好处，与所考虑的五种语言和双语变体的著名布局（即 QWERTY 和 AZERTY）相比。最后，我们展示了在基于其他现有安排（即 Metropolis 和 FITALY）生成布局时所提出算法的效率。