Towards Hybrid Methods for Solving Hard Combinatorial Optimization Problems

Combinatorial Optimization is a branch of optimization in applied mathematics and computer science, related to operations research, algorithm theory and computational complexity theory that sits at the intersection of many fields, such as artificial intelligence,mathematics and software engineering. Combinatorial optimization problems commonly imply finding values to a set of variables which are restricted by a set of constraints, in some cases in order to optimize a certain function (optimization) and in others only to find a valid solution (satisfaction). Combinatorial optimization algorithms solve instances of problems that are believed to be hard in general by exploiting the usually large solution space of these instances. They can achieve this by reducing the effective size of the search space and by exploiting it efficiently. In this talk I will focus on Combinatorial Optimization Algorithms which fall into the field of Artificial Intelligence (although the line that separates this field from Operations Research is very fine), instead of algorithms from the Operations Research field. My goal is to show that different approaches can be better suited for different problems, and that hybrid techniques which include mechanisms from different frameworks can benefit from their advantages while minimizing their drawbacks. The last part of the talk will be devoted to introduce the application of these techniques to problems within the computational biology field.