Analyzing Evolutionary Algorithms for Dynamic Optimization Problems Based on the Dynamical Systems Approach

Abstract

The study of evolutionary algorithms for dynamic optimization problems (DOPs) has attracted a rapidly growing interest in recent years. However, few work has addressed the theory in this domain. In this chapter, we use the exact model (or dynamical systems approach) to describe the standard genetic algorithm as a discrete dynamical system for DOPs. Based on this dynamical system model, we define some properties and classes of DOPs and analyze some DOPs used by researchers in the dynamic evolutionary optimization area. The analysis of DOPs via the dynamical systems approach allows explaining some behaviors observed in experimental results. The theoretical analysis of the properties of well-known DOPs is important to understand the results obtained in experiments and to analyze the similarity of such problems to other DOPs.