STABILITY ANALYSIS IN MULTICRITERIA OPTIMIZATION Tallinn 2010 Karelkina Olga University of Turku Department of Mathematics.

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STABILITY ANALYSIS IN MULTICRITERIA OPTIMIZATION Tallinn 2010 Karelkina Olga University of Turku Department of Mathematics

2 R EASONS FOR UNCERTAINTY  inaccuracy of initial data  non-adequacy of models to real processes  errors of numerical methods  absence or lack of precise and reliable information SET OF OPTIMAL SOLUTIONS PERTURBED MULTICRITERIA OPTIMIZATION PROBLEM PERTURBATIONS UNCERTAINTY G ENERAL SCHEME OF STABILITY ANALYSIS INITIAL MULTICRITERIA OPTIMIZATION PROBLEM ? ? ? SET OF OPTIMAL SOLUTIONS

3 BASIC APPROACHES OPTIMALITY PRINCIPLES  Qualitative Stability criteria “...stable if and only if..."  Pareto optimality  Lexicographic optimality  Nash equilibrium  Quantitative Stability radius “...maximal perturbation level..."

4 TARGETED PROBLEMS  Integer programming problem Computer Science Journal of Moldova, 2005  Finite cooperative strategic games Discrete Mathematics and Applications, 2009  Center and median location problems Otto-von-Guericke University Magdeburg Preprint, 2009  Combinatorial problem with non-linear criteria Computer Science Journal of Moldova, 2009 P ROSPECTIVE RESEARCH  Efficient algorithms for stability radius calculation  Stability analysis in real-life applications