Title: Characterising continuous optimisation landscapes via networks
Abstract.
A local optima network (LON) is a compact abstract representation of a search landscape using a graph. Initially inspired by work on the structure of search spaces for chemical energy landscapes, it is a technique to expose the underlying structure of an optimisation/search problem. It has gained in popularity over the last 17 years due to its succinct graphical representation of a number of landscape properties (such as modes, basins, and connectivity). The cognitive load for problem owners using LONs is not too high – particularly as the recent growth of data science means graphs/networks are now a common approach to view information which many people are now familiar with. Additionally, for complex rugged landscapes one can also apply various network analyses (compactness, connectivity, out-degree, etc.) to extract further properties. Traditionally LONs have been developed for (and applied to) combinatorial spaces. In this talk we set out approaches for generating LONs for continuous spaces. These include derivatives-based local search, discretisation, and, more recently, our work using quasi-random sampling which emulates the landscape of an Evolution Strategy (ES). The talk will also cover using networks to visualise multi-objective landscapes, and recent work integrating problem constraints into LONs (and the additional landscape features they induce).
