At the end of the course the student is expected to be able to determine the computational complexity of a given algorithm, to design exact and heuristic approaches for real world combinatorial optimization problems, to master the main multi-criteria analysis approaches and be able to apply them in relation to specific decision problem situations.

Bases of operations research with emphasis on linear programming.

Computational complexity: complexity analysis of polynomial time algorithms with emphasis on basic graph theory algorithms, complexity classes, polynomial time reductions. Combinatorial optimization: exact approaches with emphasis on search-tree algorithms and dynamic programming, heuristic approaches with emphasis on constructive procedures, neighborhood search, meta-heuristics, evolutionary algorithms, mat-heuristics. Multi-criteria analysis: introduction to multiobjective optimization (pareto-optimality, solution approaches) and to multicriteria outranking methods, ELECTRE methods for sorting decision problems.

The exercise classes are related to the topics presented in the course. The flow is such that 2 exercise classes are proposed every 5 teaching classes. Exercise classes are provided both in class and in laboratories. In the laboratories commercial software tools are used to deal with more complex problems.

Slides will be provided directly by the instructors. Reference textbooks that contain part of the topics presented in the course are among others - M.R. Garey, D.S. Johnson (1979), Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Co. - V.Th Paschos (Editor) Concepts of Combinatorial Optimization, 2nd Edition, Wiley-ISTE, 2014. - P. Vincke (1992), Multicriteria decision-Aid, Wiley, Chichester. - L.A. Wolsey (1999), Integer Programming and Combinatorial Optimization, Wiley.

Exam: Written test;

The assessment is composed of two parts: the written test (60% of the final grade and the assignment (40% of the final grade). The assignment consists in the development and implementation by the students subdivided into groups of a heuristic procedure for a given combinatorial optimization problem. The assignment foresees also a description (by means of slides) of the proposed procedure including the relevant complexity analysis. The written test covers the multicriteria analysis part and is an open-book exam consisting of numerical exercises plus questions related to the analysis of applications of multicriteria methods. The typical exam duration is 1.5h.

In addition to the message sent by the online system, students with disabilities or Specific Learning Disorders (SLD) are invited to directly inform the professor in charge of the course about the special arrangements for the exam that have been agreed with the Special Needs Unit. The professor has to be informed at least one week before the beginning of the examination session in order to provide students with the most suitable arrangements for each specific type of exam.