2189. Decision and Objective Space Representations (DO-REP) in Continuous Multi-objective Optimization
Invited abstract in session TC-5: Multiobjective Optimization 2: Continuous Problems, stream Decision Theory and Multi-criteria Decision Making.
Thursday, 11:45-13:15Room: H7
Authors (first author is the speaker)
| 1. | Lara Löhken
|
| Department of Mathematics and Informatics, University of Wuppertal | |
| 2. | Kathrin Klamroth
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| Department of Mathematics and Informatics, University of Wuppertal | |
| 3. | Serpil Sayin
|
| College of Administrative Sciences and Economics, Koc University |
Abstract
Representation algorithms aim to provide a discrete subset of solutions of a multi-objective optimization problem (MOP). The solution set, referred to as a representation, must ensure a particular quality with respect to a chosen measure/indicator. While recent research on representations and representation measures focuses mainly on the objective space of MOP, we aim at finding a representation of high quality both in the decision and objective space for continuous MOP.
By stating optimality conditions for weighted sum scalarizations, the Pareto front is described as a surface parameterized by the weight vector. Investigating its sensitivity wrt. variations of the weights yields a system of differential equations. Its solution is a function (depending on the weight vector) that satisfies first-order optimality conditions. Under appropriate assumptions, it yields the set of Pareto optimal solutions. Numerical solvers for differential equations are applied to approximate this function and hence the Pareto set.
The determination of solutions at specific grid points can be interpreted as a representation of the Pareto front. The resulting approximation method contrasts with other common representation approaches as it operates in the decision rather than the objective space. By using different discretization strategies (grid points, search directions, and step-lengths) in the decision space, we derive different representations that are evaluated wrt. their approximation and representation quality. Suitable quality indicators are incorporated in the approximation scheme. We analyze the effect (wrt. representation quality indicators) in the objective space when applying different discretization strategies in the decision space and thus interrelations between the two.
Keywords
- Multi-Objective Programming
- Continuous Optimization
Status: accepted
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