Real-world optimisation problems are often very complex. Population-based metaheuristics, such as evolutionary algorithms and particle swarm optimisation (PSO) algorithms, have been successful in solving many of these problems, but it is well known that they sometimes fail. Over the last few decades the focus of research in the field has been largely on the algorithmic side with relatively little attention being paid to the study of the problems. Questions such as ‘Which algorithm will most accurately solve my problem?’ or ‘Which algorithm will most quickly produce a reasonable answer to my problem?’ remain unanswered.
This thesis contributes to the understanding of optimisation problems and what makes them hard for algorithms, in particular PSO algorithms. Fitness landscape analysis techniques are developed to characterise continuous optimisation problems and it is shown that this characterisation can be used to predict PSO failure. An essential feature of this approach is that multiple problem characteristics are analysed together, moving away from the idea of a single measure of problem hardness. The resulting prediction models not only lead to a better understanding of the algorithms themselves, but also takes the field a step closer towards the goal of informed decision-making where the most appropriate algorithm is chosen to solve any new complex problem.