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Title of Journal: Numer Algor

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Abbravation: Numerical Algorithms

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Springer US

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DOI

10.1016/0022-4405(76)90046-7

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1572-9265

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Tracing the Pareto frontier in biobjective optimi

Authors: Andreas Potschka Filip Logist Jan F Van Impe Hans Georg Bock
Publish Date: 2010/10/20
Volume: 57, Issue: 2, Pages: 217-233
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Abstract

In this paper we present a deterministic method for tracing the Pareto frontier in nonlinear biobjective optimization problems with equality and inequality constraints We reformulate the biobjective optimization problem as a parametric singleobjective 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 ODE NNEC method and demonstrate numerically that it can yield the entire Pareto frontier to high accuracy Moreover due to event detection capabilities available for common ODE integrators changes in the active constraints can be automatically detected The features of the current algorithm are illustrated for two case studies whose Matlab® code is available as Electronic Supplementary Material to this article

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