Fitness landscapes were proposed in 1932 as an abstract notion for understanding biological evolution and were later used to explain evolutionary algorithm behaviour. The last ten years has seen the field of fitness landscape analysis develop from a largely theoretical idea in evolutionary computation to a practical tool applied in optimisation in general and more recently in machine learning. With this widened scope, new types of landscapes have emerged such as multiobjective landscapes, violation landscapes, dynamic and coupled landscapes and error landscapes. This survey is a follow-up from a 2013 survey on fitness landscapes and includes an additional 11 landscape analysis techniques. The paper also includes a survey on the applications of landscape analysis for understanding complex problems and explaining algorithm behaviour, as well as algorithm performance prediction and automated algorithm configuration and selection. The extensive use of landscape analysis in a broad range of areas highlights the wide applicability of the techniques and the paper discusses some opportunities for further research in this growing field.

A major unsolved problem in the field of optimisation and computational intelligence is how to determine which algorithms are best suited to solving which problems. This research aims to analytically characterise individual problems as a first step towards attempting to link problem types with the algorithms best suited to solving them. In particular, an information theoretic technique for analysing the ruggedness of a fitness landscape with respect to neutrality was adapted to work in continuous landscapes and to output a single measure of ruggedness. Experiments run on test functions with increasing ruggedness show that the proposed measure of ruggedness produced relative values consistent with a visual inspection of the problem landscapes. Combined with other measures of complexity, the proposed ruggedness measure could be used to more broadly characterise the complexity of fitness landscapes in continuous domains.

A number of fitness landscape analysis approaches are based on random walks through discrete search spaces. Applying these approaches to real-encoded problems requires the notion of a random walk in continuous space. This paper proposes a progressive random walk algorithm and the use of multiple walks to sample neighbourhood structure in continuous multi-dimensional spaces. It is shown that better coverage of a search space is provided by progressive random walks than simple unbiased random walks.