Pathfollowing methods for nonlinear multiobjective optimization problems

Guddat, J.; Vázquez, F. Guerra; Nowack, Dieter; Rückmamr, Jan-J.

doi:10.1080/17509653.2007.10671019

Cited by 2 publications

(1 citation statement)

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“…Typical challenges these methods face are ensuring a homogeneous distribution of the computed points on the Pareto front, as well as capturing non-convex Pareto fronts. An alternative approach are path-following methods resulting from numerical continuation theory, which have been suggested in literature (Rakowska et al, 1991;Lundberg and Poore, 1993;Seferlis and Hrymak, 1996;Hillermeier, 2001;Gudat et al, 2007;Harada et al, 2007;Potschka et al, 2011;Ringkamp et al, 2012) but so far hardly have been applied to large-scale optimization problems resulting from the optimization of dynamic systems. Path-following methods are able to easily calculate non-convex Pareto fronts.…”

Section: Introductionmentioning

confidence: 99%

Bi-objective optimization of dynamic systems by continuation methods

Keßler

Logist

Mangold

2017

Computers & Chemical Engineering

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As a proof of concept the properties of path-following methods are studied for multi-objective optimization problems involving dynamic systems (also called multi-objective dynamic optimization or multi-objective optimal control problems), which have never been presented before. Two case studies with two objectives are considered to cover convex, as well as non-convex trade-off curves or Pareto sets. In order for the method to be applicable, the infinite dimensional dynamic problems have to be discretized and scalarization parameters have to be introduced, which leads to large-scale parametric nonlinear optimization problems. For both the chemical tubular reactor and the fed-batch bioreactor case study it is found that a path-following continuation approach is able to compute the Pareto fronts accurately and efficiently. A branch switching technique is required whenever a constraint switches from active to inactive or vice versa. When dealing with non-convex problems, a technique for detecting inflection points is required. Simple switching techniques are suggested and have been tested successfully.

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