A numerical method for nonconvex multi-objective optimal control problems

Authors:
C. Yalçın Kaya;Helmut Maurer
Affiliations:
School of Information Technology and Mathematical Sciences, University of South Australia, Mawson Lakes, Australia 5095;Institut für Numerische und Angewandte Mathematik, Westfälische Wilhelms-Universität Münster, Münster, Germany
Venue:
Computational Optimization and Applications
Year:
2014

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Abstract

A numerical method is proposed for constructing an approximation of the Pareto front of nonconvex multi-objective optimal control problems. First, a suitable scalarization technique is employed for the multi-objective optimal control problem. Then by using a grid of scalarization parameter values, i.e., a grid of weights, a sequence of single-objective optimal control problems are solved to obtain points which are spread over the Pareto front. The technique is illustrated on problems involving tumor anti-angiogenesis and a fed-batch bioreactor, which exhibit bang---bang, singular and boundary types of optimal control. We illustrate that the Bolza form, the traditional scalarization in optimal control, fails to represent all the compromise, i.e., Pareto optimal, solutions.