Reduction of function evaluation in differential evolution using nearest neighbor comparison

Abstract

Approximation models have recently been introduced to differential evolution (DE) to reduce expensive fitness evaluation in function optimization. These models basically require additional control parameters and/or external storage for the learning process. Depending on the choice of the additional parameters, the strategies may have different levels of efficiency. The present paper introduces an alternative way for reducing function evaluations in differential evolution, which does not require additional control parameter and external archive. The algorithm uses a nearest neighbor in the search population to judge whether a new point is worth evaluating, so that unnecessary evaluations can be avoided. The performance of this new scheme of differential evolution, known as differential evolution with nearest neighbor comparison (DE-NNC), is demonstrated and compared with that of standard DE as well as approximation models including differential evolution using k-nearest neighbor predictor (DE-kNN), differential evolution using speeded-up k-nearest neighbor estimator (DE-EkNN) and DE with estimated comparison method through some test functions. The results show that DE-NNC can produce considerable reduction of actual function calls compared to DE and is competitive to DE-kNN, DE-EkNN and DE with estimated comparison.