Multiobjective Optimization

Objectives: This course introduces the main concepts, results and methods in multiobjective optimization in general, with an emphasis on multiobjective combinatorial optimization. 

We focus on the exact or approximate determination of either the non-dominated set or a best compromise solution according to the decision maker's preferences.

Several real-world applications will be introduced.

Contents:

• Motivation, main concepts (decision space, criterion space, efficient solutions, non-dominated points,...),
• Interest and limitations of the main scalarizing functions (Weighted sum, Tchebychev, reference point,...)
• Multiobjective combinatorial optimization – Specific difficulties (intractability...)
• Exact methods for enumérating the non-dominated set (generic methods, specific methods)
• Approximate methods with a priori guarantee
• General approaches for determining a best compromise solution

Bibliography

• M. Ehrgott, Multicriteria Optimization, Springer, 2005, 2nd edition.
• Steuer, R. 1985. Multiple Criteria Optimization: Theory, Computation and Application. New York: John Wiley and Sons.
• Vanderpooten, D.  Multiobjective Programming: Basic Concepts and Approaches. In R. Slowinski and J. Teghem, editors, Stochastic versus Fuzzy Approaches to Multiobjective Mathematical Programming under Uncertainty, pages 7-22, 1990. Kluwer Academic, Dordrecht.