Use of parametric sensitivities for multi-objective optimisation

Abstract

When controlling automated systems, the combination of several different objectives becomes increasingly important. These objectives represent goals of the process like driving as close as possible to a final position or minimising the energy consumption. Integrating these objectives into an automated system can become complicated. This thesis aims at investigating how parametric sensitivities can be utilised to provide the developer of automated systems with a better insight into the structure of the underlying multi-objective problem. For this, the Pascoletti-Serafini approach is used. In this approach, the Lagrange multiplier represents a linearisation of the Pareto front at a computed sample. Based on this, the Pareto front is interpolated locally around a computed sample. The parametric sensitivities of the Lagrange multiplier are used to extend this approach to a quadratic approximation. A third approach is formulated by using the parametric sensitivities of the variables to create an approximation in variable space. Next, the local approximations are used to define a continuous approximation of the whole Pareto front by defining a polynomial interpolation using the samples and derivative information. Next, the MOSQP algorithm is introduced as a method to investigate multi-objective problems with less necessity for a-priori knowledge than methods like the Pascoletti-Serafini scalarisation. The algorithm is improved by replacing the internal cleanup strategy between iterations by the strategy from the heuristic NSGA-II algorithm. In this way, fewer points are deleted from the intermediate set in early iterations, which improves the overall spread. Finally, the introduced methods are applied to a bi-objective example of autonomous ship control from the research project GALILEOnautic 2 using the dynamical model of a real ship. The methods are evaluated for their usability within the development process of a trajectory optimisation module.