Tunably Rugged Landscapes With Known Maximum and Minimum

We propose NM landscapes as a new class of tunably rugged benchmark problems. NM landscapes are well defined on alphabets of any arity, including both discrete and real-valued alphabets, include epistasis in a natural and transparent manner, are proven to have known value and location of the global maximum and, with some additional constraints, are proven to also have a known global minimum. Empirical studies are used to illustrate that, when coefficients are selected from a recommended distribution, the ruggedness of NM landscapes is smoothly tunable and correlates with several measures of search difficulty. We discuss why these properties make NM landscapes preferable to both NK landscapes and Walsh polynomials as benchmark landscape models with tunable epistasis.