Problems with solutions represented by permutations are very prominent in combinatorial optimization. Thus, in recent decades, a number of evolutionary algorithms have been proposed to solve them, and among them, those based on probability models have received much attention. In that sense, most efforts have focused on introducing algorithms that are suited for solving ordering/ranking nature problems. However, when it comes to proposing probability-based evolutionary algorithms for assignment problems, the works have not gone beyond proposing simple and in most cases univariate models. In this paper, we explore the use of Doubly Stochastic Matrices (DSM) for optimizing matching and assignment nature permutation problems. To that end, we explore some learning and sampling methods to efficiently incorporate DSMs within the picture of evolutionary algorithms. Specifically, we adopt the framework of estimation of distribution algorithms and compare DSMs to some existing proposals for permutation problems. Conducted preliminary experiments on instances of the quadratic assignment problem validate this line of research and show that DSMs may obtain very competitive results, while computational cost issues still need to be further investigated.

翻译：解以排列形式表示的问题在组合优化中非常突出。因此，近几十年来，人们提出了许多进化算法来解决这类问题，其中基于概率模型的算法受到了广泛关注。在这方面，大多数工作集中于引入适用于求解排序/顺序性质问题的算法。然而，在针对分配问题提出基于概率的进化算法方面，相关工作并未超越提出简单且多数情况下为单变量模型的范畴。本文探讨了利用双随机矩阵优化匹配与分配性质的排列问题。为此，我们研究了一些学习和采样方法，以高效地将双随机矩阵纳入进化算法的框架中。具体而言，我们采用了分布估计算法的框架，并将双随机矩阵与现有的一些针对排列问题的算法进行了比较。在二次分配问题实例上进行的初步实验验证了这一研究方向，结果表明双随机矩阵可能获得非常有竞争力的结果，但其计算成本问题仍需进一步研究。