Example landscapes to support analysis of multimodal optimisation

Abstract

Theoretical analysis of all kinds of randomised search heuristics has been and keeps being supported and facilitated by the use of simple example functions. Such functions help us understand the working principles of complicated heuristics. If the function represents some properties of practical problem landscapes these results become practically relevant. While this has been very successful in the past for optimisation in unimodal landscapes there is a need for generally accepted useful simple example functions for situations where unimodal objective functions are insufficient: multimodal optimisation and investigation of diversity preserving mechanisms are examples. A family of example landscapes is defined that comes with a limited number of parameters that allow to control important features of the landscape while all being still simple in some sense. Different expressions of these landscapes are presented and fundamental properties are explored.