Article ID: | iaor20115135 |
Volume: | 57 |
Issue: | 2 |
Start Page Number: | 217 |
End Page Number: | 233 |
Publication Date: | Jun 2011 |
Journal: | Numerical Algorithms |
Authors: | Logist Filip, Potschka Andreas, Van Impe F, Bock Georg |
Keywords: | differential equations |
In this paper we present a deterministic method for tracing the Pareto frontier in non‐linear bi‐objective optimization problems with equality and inequality constraints. We reformulate the bi‐objective optimization problem as a parametric single‐objective optimization problem with an additional Normalized Normal Equality Constraint (NNEC) similar to the existing Normal Boundary Intersection (NBI) and the Normalized Normal Constraint method (NNC). By computing the so called Defining Initial Value Problem (DIVP) for segments of the Pareto front and solving a continuation problem with a standard integrator for ordinary differential equations (ODE) we can trace the Pareto front. We call the resulting approach