Invited Session Mon.3.H 1029

Monday, 15:15 - 16:45 h, Room: H 1029

Cluster 15: Multi-objective optimization [...]

Multi-objective optimization

 

Chair: Emilio Carrizosa

 

 

Monday, 15:15 - 15:40 h, Room: H 1029, Talk 1

Antonio Flores-Tlacuahuac
An utopia-tracking approach to multiobjective predictive control

Coauthors: Morales Pilar, Zavala Victor

 

Abstract:
We propose a multiobjective strategy for model predictive control (MPC) that we term utopia-tracking MPC. The controller minimizes, in some norm, the distance of its cost vector to that of the unreachable steady-state utopia point. Stability is ensured by using a terminal constraint to a selected point along the steady-state Pareto front. One of the key advantages of this approach is that multiple objectives can be handled systematically without having to compute the entire Pareto front or selecting weights. In addition, general cost functions (i.e., economic, regularization) can be used.

 

 

Monday, 15:45 - 16:10 h, Room: H 1029, Talk 2

Wlodzimierz Ogryczak
Fair multiobjective optimization: Models and techniques

 

Abstract:
In systems which serve many users there is a need to respect some fairness rules while looking for the overall efficiency, e.g., in network design one needs to allocate bandwidth to flows efficiently and fairly, in location analysis of public services the clients of a system are entitled to fair treatment according to community regulations. This leads to concepts of fairness expressed by the equitable multiple objective optimization. The latter is formalized with the model of multiple objective optimization of tail averages and the Lorenz order enhancing the Pareto dominance concept. Due to the duality theory, the order is also equivalent to the second order
stochastic dominance representing multiple objective optimization of the mean shortages (mean below-target deviations). Despite equivalent, two orders lead to different computational models though both based on auxiliary linear inequalities and criteria. Moreover, the basic computational models can be differently enhanced. We analyze advantages of various computational models when applied to linear programming and mixed integer programming problems of fair optimization.

 

 

Monday, 16:15 - 16:40 h, Room: H 1029, Talk 3

Kai-Simon Goetzmann
Compromise solutions

Coauthors: Christina B├╝sing, Jannik Matuschke, Sebastian Stiller

 

Abstract:
The most common concept in multicriteria optimization is Pareto optimality. However, in general the number of Pareto optimal solutions is exponential. To choose a single, well-balanced Pareto optimal solution, Yu (1973) proposed compromise solutions.
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A compromise solution is a feasible solution closest to the ideal point. The ideal point is the component-wise optimum over all feasible solutions in objective space.
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Compromise solutions are always Pareto optimal. Using different weighted norms, the compromise solution can attain any point in the Pareto set.
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The concept of compromise solutions (and the slightly more general reference point methods) are widely used in state-of-the-art software tools. Still, there are very few theoretical results backing up these methods.
We establish a strong connection between approximating the Pareto set and approximating compromise solutions. In particular, we show that an approximate Pareto set always contains an approximate compromise solution. The converse is also true if we allow to substitute the ideal point by a sub-ideal reference point. Compromise solutions thus neatly fit with the concept of Pareto optimality.

 

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