Evolving problems to learn about particle swarm and other optimisers

We use evolutionary computation (EC) to automatically find problems which demonstrate the strength and weaknesses of modern search heuristics. In particular we analyse Particle Swarm Optimization (PSO) and Differential Evolution (DE). Both evolutionary algorithms are contrasted with a robust deterministic gradient based searcher (based on Newton-Raphson). The fitness landscapes made by genetic programming (GP) are used to illustrate difficulties in GAs and PSOs thereby explaining how they work and allowing us to devise better extended particle swarm systems (XPS).