This project intends to develop optimization algorithms combining exact and heuristic techniques that outperform the state-of-the-art algorithms in optimization problems of three different domains: Economy (portfolio selection), Software Engineering (next release problem and software module clustering), Logistics (location of logistics hubs). In order to obtain an effective combination of techniques, we plan to discover new theoretical results (from elementary landscape theory, submodular functions, matroid theory, etc.) that can be used to reduce the search space or explore it in a more effective way, discarding non-optimal solutions. The optimization problems we will address are multiobjective (several objectives to optimize) and contain uncertainty in their parameters. The latter requires the use of robust optimization techniques. Real instances will be solved for each problem (or instances based on real data). Together with the robustness and multiple objectives, this will increase the interest and impact of the results of the project not only in the scientific community, but also in Industry, since companies can profit from them.

There are many aspects in this project (robustness, multiple objectives, hybrid algorithms, exact techniques, heuristic techniques, theoretical results, real problems, etc.), all of them challenging, that do not usually co-occur in the same research project. This ensures the novelty and impact of the project. Our main hypothesis is that the key ingredient of an effective combination of exact and heuristic techniques is the use of problem knowledge and theoretical results. Although the project will focus on concrete problems, something required in a 1-year project, the design methodology for the algorithms and some theoretical results can be transferred to other optimization problems, increasing the scientific impact of the project.