Multi-scale search, modular variation, and adaptive neighbourhoods

This paper investigates a framework for multi-scale search, which makes use of automatically defined multi-variable groupings to search over multiple scales of organisation. We show how this method redefines the variational neighbourhood visible to the search process to efficiently find high quality optima. We use a transparent two-scale modular problem to provide a clear explanation of when and how this approach works, supporting this with analysis of expected runtimes. This problem has an obvious and familiar modular structure but, unlike previous test problems used for existing model-building methods, the size of the modules are not constant but scale as a function of problem size. We show that this problem class requires multi-scale search to be solved in polynomial time