Efficient multiple objective optimal control of dynamic systems with integer controls

In practical optimal control problems both integer control variables and multiple objectives can be present. The current paper proposes a generic and efficient solution strategy for these multiple objective mixed-integer optimal control problems (MO-MIOCPs) based on deterministic approaches. Hereto, alternative scalar multiple objective optimisation techniques as normal boundary intersection and normalised normal constraint are used to convert the original problem into a series of parametric single objective optimisation problems. These single objective mixed-integer optimal control problems are then efficiently solved through direct multiple shooting techniques which exploit convex relaxations of the original problem. Moreover, these relaxations enable to quickly approximate the final solution to any desired accuracy (without the need of solving integer problems). Consequently, the set of Pareto optimal solutions of the MO-MIOCP can be accurately obtained in highly competitive computation times. The proposed method is illustrated on (i) a testdrive case study with a complex car model which includes different gears and conflicting minimum time–minimum fuel consumption objectives, and (ii) a jacketed tubular reactor case study with conflicting conversion, heat recovery and installation costs.