The Directed Search Method for Unconstrained Parameter Dependent Multi-objective Optimization Problems

Adrián Sosa Hernández V, Lara A, Trautmann H, Rudolph G, Schütze O

Abstract
In this chapter we present the adaptions of the recently proposed Directed Search method to the context of unconstrained parameter dependent multi-objective optimization problems (PMOPs). The new method, called λ-DS, is capable of performing a movement both toward and along the solution set of a given differentiable PMOP. We first discuss the basic variants of the method that use gradient information and describe subsequently modifications that allow for a gradient free realization. Finally, we show that λ-DS can be used to understand the behavior of stochastic local search within PMOPs to a certain extent which might be interesting for the development of future local search engines, or evolutionary strategies, for the treatment of such problems. We underline all our statements with several numerical results indicating the strength of the novel approach.

Keywords
Parameter dependent multi-objective optimization; Local search; Descent method; Continuation method; Stochastic local search; Evolutionary algorithms