The partial Latin square extension problem is to fill as many as possible empty cells of a partially filled Latin square. This problem is a useful model for a wide range of applications in diverse domains. This paper presents the first massively parallel evolutionary algorithm algorithm for this computationally challenging problem based on a transformation of the problem to partial graph coloring. The algorithm features the following original elements. Based on a very large population (with more than $10^4$ individuals) and modern graphical processing units, the algorithm performs many local searches in parallel to ensure an intensive exploitation of the search space. The algorithm employs a dedicated crossover with a specific parent matching strategy to create a large number of diversified and information-preserving offspring at each generation. Extensive experiments on 1800 benchmark instances show a high competitiveness of the algorithm compared to the current best performing methods. Competitive results are also reported on the related Latin square completion problem. Analyses are performed to shed lights on the roles of the main algorithmic components. The code of the algorithm will be made publicly available.

翻译：部分拉丁平方延伸问题是填充部分填充的拉丁方形中尽可能多的空单元格。 这个问题是不同领域广泛应用的有用模型。 本文展示了第一个基于问题转换成部分图形颜色的、 计算具有挑战性的问题的大规模平行进化算法算法。 算法具有以下原始元素。 基于众多人口( 超过 10+4美元的个人) 和现代图形处理器, 算法同时进行许多本地搜索, 以确保对搜索空间的密集利用 。 算法与特定的父对齐策略专门交叉, 以在每一代人中创建大量多样化和保存信息的后代。 在1800个基准实例上进行的广泛实验显示算法相对于当前最佳运行方法具有很高的竞争力 。 还报告了相关的拉丁方形完成问题的竞争结果 。 进行了分析, 以亮亮出主要算法组成部分的作用 。 算法的代码将被公诸于众 。