Multiobjective Optimisation (NOPT017), summer semester 2017/2018

The lecture is scheduled on Tuesday at 10:40 in the corridor of KAM on the 3rd floor.

Done:

 27.2. Introduction and motivation. Efficient and proper efficient solutions. Scalarization and relation to (proper) efficient solution set. 6.3. Convex multiobjective optimization: relation between (proper) efficient solutions and optimal solutions of scalarizations (Geoffrion theorem). Karush-Kuhn-Tucker optimality conditions for multiobjective problems: necessary conditions and sufficient conditions. 13.3. Multiobjective linear programming: test of efficiency of a feasible point (Charnes & Cooper), characterization of efficient solutions via scalarization (Isermann), topology of the efficient solution set. 20.3. Multiobjective linear programming and relation to parametric programming. Methods of type III.: Geoffrion method, STEM, algorithms of dialogs (Guddat, Wendler). 27.3. Methods of type I.: Methods of global objective function and Benson's method. 3.4. Methods of type II.: goal attainment, epsilon-constraints, lexicografical method, goal programming. 11.4. Methods of type IV.: Inner and outer approximation, Normal-Boundary Intersection method. General utility function approach. 17.4. Combinatorial multiobjective optimization: Shortest path and minimum spanning tree problems with multiple criteria. 24.4. Cone efficiency and dominance. DEA (Data Envelopment Analysis). 15.5. Interval multiobjective linear programming: possibly efficiency and necessary efficiency, computational complexity, characterization, geometry of the efficient solution set. 22.5. AHP (Analytic Hierarchy Process): comparison matrix and its algebraic properties, consistency, hierarchy, examples.

Homework exercises: PDF

### Software

Dostupné v počítačové laborce (Karlín K10 nebo Malá Strana rotunda unix):
• MATLAB: cílové programování (funkce fgoalattain), minimax (funkce fminimax), metoda nejmenších čtverců (funkce lsqnonlin),
Normal-Boundary Intersection - volně dostupný balík k Matlabu
On-line optimalizace: Další software:

### Odkazy

anglické:

"Experientia est optima rerum magistra."