Predicting Stochastic Search Algorithm Performance using Landscape State Machines

A landscape state machine (LSM) is a Markov model describing the transition probabilities between the fitness ´levels´ of an optimization problem, when a given neighbourhood (or mutation) operator is applied. Although most optimization problems cannot be modeled precisely by an LSM, an approximate LSM can always be constructed by sampling, and can be used, subsequently, in place of real fitness evaluations in order to model the performance of any search algorithm using the given neighbourhood operator. In this paper, we provide empirical evidence that (a) LSMs constructed by simulated annealing-based sampling of a problem landscape make accurate models in few evaluations; (b) LSMs can accurately rank the performance of diverse algorithms including EAs with/without niching and SA; (c) the LSM approach works on diverse problems from MAX-SAT to NKp; (d) convergence of the LSM can be used as a guide to stopping the sampling phase; and, (e) a single LSM constructed using a low mutation-rate sample is sufficient to accurately rank the performance of search algorithms run at multiples of this mutation rate.