Section: New Results
We have a small theoretical research activity that is a by-product of our main work and is regrouped in this section.
Development of Optimization techniques : the knapsack problem
Large scale bioinformatics also relies on a clever use of advanced optimization techniques (like Dynamic Programing (DP), Branch&Bounds (B&B), Lagrangian Relaxation (LR), diverse Heuristics etc). The result in  presents a new approach for exactly solving the Unbounded Knapsack Problem (UKP) and proposes a new bound that was proved to dominate the previous bounds on a special class of UKP instances. Integrating bounds within the framework of sparse dynamic programming led to the creation of an efficient and robust hybrid algorithm, called EDUK2. This algorithm takes advantage of the majority of the known properties of UKP, particularly the diverse dominance relations and the important periodicity property. Extensive computational results show that, in all but a very few cases, EDUK2 significantly outperforms both MTU2 and EDUK, the currently available UKP solvers, as well the well-known general purpose mathematical programming optimizer CPLEX of ILOG. These experimental results demonstrate that the class of hard UKP instances needs to be redefined, and the authors offer their insights into the creation of such instances.
Quality of association rules in Data Mining
In the field of Data Mining, one fundamental objective consists in building asymmetrical association rule measures. The interest of a rule A -> B may be evaluated with the LLA approach using an implication index (measure) that evaluates in a certain way the propensity of B, knowing A. This method directly uses asymmetrical similarities and build an oriented ascendant binary hierarchical classification. New extensive analysis including formal logical and statistical aspects of this original construction is provided in  .