The goal of this project is to develop new formal techniques and computational tools for optimization and   satisfiability problems paying special emphasis on those of combinatorial flavour. We shall focus our attention on the study and implementation of new strategies to successfully tackle formal problems which may be extended to practical situations from industry. We propose to combine the use of several metaheuristics (such as evolutionary algorithms, state space search, adaptive greedy algorithms or local search) with other techniques coming from the fields of  Mathematics and Computational Intelligence with the purpose of generating new hybrid methodologies to deal with complex problems and to extend and improve other existing ones. On the one hand, our aim is to transfer results from the corpus of Mathematics (such as linear algebra, numerical calculus, probability and approximation) and Computational Learning Theory to the field of heuristics and evolutionary computation. By the other hand, we seek to adapt and adjust these general methods to real problem solving, to enable technology transfer to society. This double transfer is in the nucleus of project AEDRHOS.