Optimizing single-finger keyboard layouts on smartphones

•We propose a simple yet efficient metaheuristic for the problem.•The results obtained are extremely competitive with the best ones available.•The first single-finger keyboard layout for Portuguese is provided.•The problem is also solved for newly generated bilingual instances.•We evaluate the gains of adopting optimized layouts when compared to default ones. 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.