论文标题
基于K-Pareto的最佳分类，最大化选择
k-Pareto Optimality-Based Sorting with Maximization of Choice
论文作者
论文摘要
拓扑排序是众多实用应用中的一项重要技术，例如信息检索，推荐系统，优化等。在本文中，我们引入了一个广义拓扑排序的问题，即最大化选择的最大化，即选择预定尺寸的项目的子集，其中包含相同优选选项（物品）相对于统治的最大优先选择的数量。我们以非常抽象的形式提出这个问题，并证明通过K-Pareto最优性排序可以产生有效的解决方案。接下来，我们表明所提出的理论在实践中可能很有用。我们在遗传优化的选择步骤中应用它，并证明所得算法的表现优于NSGA-II和NSGA-III等现有的最新方法。我们还证明，提供的一般公式允许发现有趣的关系并将开发理论应用于不同的应用。
Topological sorting is an important technique in numerous practical applications, such as information retrieval, recommender systems, optimization, etc. In this paper, we introduce a problem of generalized topological sorting with maximization of choice, that is, of choosing a subset of items of a predefined size that contains the maximum number of equally preferable options (items) with respect to a dominance relation. We formulate this problem in a very abstract form and prove that sorting by k-Pareto optimality yields a valid solution. Next, we show that the proposed theory can be useful in practice. We apply it during the selection step of genetic optimization and demonstrate that the resulting algorithm outperforms existing state-of-the-art approaches such as NSGA-II and NSGA-III. We also demonstrate that the provided general formulation allows discovering interesting relationships and applying the developed theory to different applications.
