Part II.1 Algorithmic Tools for solving multiobjective optimization methods

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Part II.1 Algorithmic Tools for
solvingmultiobjective optimization methods

• Scalar solution methods
• Population based methods
• Evaluation of algorithms

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Table of contents

• Linear weighting methods
• Utility function methods (Multiattribute Utility
  Theory)
• Distance to a reference point methods
• Min-Max or Tschebyscheff method
• Goal attainment
• Constraint methods
• Compromise programming (e-Constraint methods)
• Goal programming
• Sequential minimization
• Excursus Nash equilibria and Pareto optimiality
• Summary

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Part II Scalarization techniques
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Part II Overview
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Weighted sum scalarization
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Proper efficiency
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Convex Pareto front
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Concave Pareto front
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Example Schaffer problem
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Example Schaffer problem
Source Siarry et al. Multiobjective
Optimization, Springer, Berlin
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Utility functions
f2
Iso-Utility-lines
U 1
U 2
U 1
f1
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Client-Theory by Kahneman and Tversky
Subjective State (e.g. disappointment/excitement)
Objective State (e.g. money won/lost)
e.g. how good are people feeling when
losing/winning money in a horse-race
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Utility functions
F2 (e.g. -speed)
U 1
U 2
U 1
F1 (e.g. cost)
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Keene-Raiffa utility functions
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Cobbs Douglas utility functions
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Distance to a reference point (DRP) method
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Distance functions
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View of DRP as a utility function
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View of DRP as a utility function
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View of DRP as a utility functionWeighted
euclidian distance function
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Tschebyscheff DRP
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Tschebyscheff DRP
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Tschebyscheff DRP
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Lexicographic min-max scalarization
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Choice of reference point
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e-Constraint method
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Volume vs. Surface Tin example
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Goal programming
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Goal programming
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Sequential Multiobjective Optimization
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SummaryScalarization methods