A numerical method for nonconvex multi-objective optimal control problems

作者：Kaya C Yalcin^*; Maurer Helmut

来源：Computational Optimization and Applications, 2014, 57(3): 685-702.

DOI：10.1007/s10589-013-9603-2

• Multi-objective optimization
• Optimal control
• Pareto front
• Numerical methods
• Tumor anti-angiogenesis
• Fed-batch bioreactor

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.

• 出版日期2014-4