Discrete stochastic optimization with continuous auxiliary variables

Slides of a talk given at Dortmund University, Dept. of Statistics, on March 2015 the 11th. Invitation by Prof. Sonja Kuhnt.Many discrete optimization problems formulated at a detailed level can be approximated by continuous variables at a less detailed level. Under the assumption that a numerically efficient mapping exists from the detailed discrete variables to their continuous counterparts, a global stochastic optimization algorithm has been proposed in 2006, the Double Distribution Optimization Algorithm (DDOA, Grosset et al., SMO, 2006). DDOA takes advantage of the continuous approximated formulation to increase the efficiency of the search. In these slides, we revisit DDOA, interpreting its sampling distribution as a distribution conditioned on the value of the continuous variables. An analytical Gaussian example is given. New tests in the field of composite structures design are provided