  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.

Neural and Evolutionary Computing