Model-based Gradient Search for Permutation Problems

Global random search algorithms are characterized by using probability distributions to optimize problems. Among them, generative methods iteratively update the distributions by using the observations sampled. For instance, this is the case of the well-known Estimation of Distribution Algorithms. Although successful, this family of algorithms iteratively adopts numerical methods for estimating the parameters of a model or drawing observations from it. This is often a very time-consuming task, especially in permutation-based combinatorial optimization problems. In this work, we propose using a generative method, under the model-based gradient search framework, to optimize permutation-coded problems and address the mentioned computational overheads. To that end, the Plackett-Luce model is used to define the probability distribution on the search space of permutations. Not limited to that, a parameter-free variant of the algorithm is investigated. Conducted experiments, directed to validate the work, reveal that the gradient search scheme produces better results than other analogous competitors, reducing the computational cost and showing better scalability.