Scalable Local Optima Networks for Continuous Search Spaces

This chapter delves into the construction of scalable local optima networks (LONs) for continuous search spaces, a technique that provides a compact, graphical representation of search landscapes. The author introduces a novel sampling procedure that emulates the landscape experienced by an Evolution Strategy, offering a faster convergence to the underlying landscape compared to existing methods. The chapter explores the advantages of using directed graphs to represent search landscapes, which are easily manipulable and have a low cognitive load for users. It also discusses the limitations of current methods, such as discretising the space or using derivatives-based approaches, and presents a new framework that allows for a predetermined function evaluation budget and better global view of the landscape. The author illustrates the proposed method with various test problems and compares it with basin-hopping generated LONs, demonstrating the growth in complexity and connectivity of the networks. The chapter concludes with a discussion on the efficiency and accuracy of the proposed approach, highlighting its potential for identifying the degree of ruggedness of the landscape more quickly than other methods.