Bi-objective optimization of dynamic systems by continuation methods. (4th March 2017)

• Record Type: Journal Article
• Authors: Keßler, Tobias; Logist, Filip; Mangold, Michael
• Is Part Of: Computers & chemical engineering. Volume 98(2017)
• Page Start: 89
• Page End: 99
• Publication Date: 2017-03-04
• Subjects: Multi-objective optimization -- Continuation techniques -- Karush–Kuhn–Tucker conditions -- Fritz–John conditions -- Scalarization -- Pareto front; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2016.11.025
• Languages: English
• ISSNs: 0098-1354

Abstract

Abstract : Highlights: A novel approach for solving multi-objective optimization problems is proposed. The algorithm is able to compute non-convex as well as convex Pareto fronts of large-scale dynamical optimization problems. Problems induced by inequality constraints are handled. The algorithm is tested successfully on two case studies. Abstract: 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.