1.Efficiency and efficacy of a symmetric variant of the Simplex method are in course of evaluation

2.Development of methodologies in learning processes headed by the computer (AUDIP project)

3.Development, implementation and experimentation of global optimization algorithms in order to detect the minimal energy configuration according to the Lennard-Jones potential function as well as for other relevant potentials such as the Morse potential. The minimal energy of a cluster of identical and uncharged atoms, where the energy between any pair of atoms is represented by the Lennard-Jones pair potential or the Morse pair potential, is searched. This problems are widely explored in the literature, they are very challenging from the optimization point of view and have important applications in the field of chemistry.

Currently, the combination of two-phase local searches, previously successully employed, with other methods, such as basin-hopping, is tested with quite encouraging results.

4. Max-clique problems, i.e. finding the maximum clique (the complete subgraph of a graph with highest cardinality) are very challenging optimization problems. An analysis of existing methods based on a continuous formulation of such problem revealed their equivalence with particular combinatorial heuristics. Such heuristics have been further developed and lead to the detection of the global optimum or at least of the best known value for many benchmark problems.

5. Function landscapes have been analyzed in order to better understand why some algorithms perform particularly well on some test functions. During the analysis it has also been revealed that a particular test function (the Griewank function) has the surprisinmg property of becoming easier as its dimension increases. The reason of such behavior has now been explained.