Heuristics for sampling repetitions in noisy landscapes with fitness caching

For many large-scale combinatorial search/optimization problems, meta-heuristic algorithms face noisy objective functions, coupled with computationally expensive evaluation times. In this work, we consider the interaction between the technique of "fitness caching" and the straightforward noise reduction approach of "fitness averaging" by repeated sampling. Fitness caching changes how noise affects a fitness landscapes, as noisy values become frozen in the cache. Assuming the use of fitness caching, we seek to develop heuristic methods for predicting the optimal number of sampling replications for fitness averaging. We derive two analytic measures for quantifying the effects of noise on a cached fitness landscape (probabilities of creating "false switches" and "false optima"). We empirically confirm that these measures correlate well with observed probabilities on a set of four well-known test-bed functions (sphere, Rosenbrock, Rastrigin, Schwefel). We also present results from a preliminary experimental study on these landscapes, investigating four possible heuristic approaches for predicting the optimal sampling, using a random-mutation hill-climber with fitness caching.