Stability of Optimal Solutions: Multi- and Single-Objective Approaches

Abstract

This paper deals with assessing stability of optimal solutions. Two ways are considered: introducing stochastic stability based on Lyapunov's stability as constraints in a single-objective optimization problem and using it as a second objective. The problem from the field of wind energy is taken $optimization of electricity production with a novel wind power concept called Laddermill. Due to the multi-objectiveness of the second approach both problems are programmed with an algorithm based on a modification of Pareto-optimization. The main conclusion is that multi-objectiveness makes problem statement more transparent and also easier to implement and faster to compute which makes multi-objective formulation desirable for the class of robust optimal control problems