Characterization of neighborhood behaviours in a multi-neighborhood local search algorithm

Abstract

We consider a multi-neighborhood local search framework with a large number of possible neighborhoods. Each neighborhood is accompanied by a weight value which represents the probability of being chosen at each iteration. These weights are fixed before the algorithm runs, and can be tuned by off-the-shelf off-line automated algorithm configuration tools (e.g., SMAC). However, the large number of parameters might deteriorate the tuning tool’s efficiency, especially in our case where each run of the algorithm is not computationally cheap, even when the number of parameters has been reduced by some intuition. In this work, we propose a systematic method to characterize each neighborhood’s behaviours, representing them as a feature vector, and using cluster analysis to form similar groups of neighborhoods. The novelty of our characterization method is the ability of reflecting changes of behaviours according to hardness of different solution quality regions based on simple statistics collected during any algorithm runs. We show that using neighborhood clusters instead of individual neighborhoods helps to reduce the parameter configuration space without misleading the search of the tuning procedure. Moreover, this method is problem-independent and potentially can be applied in similar contexts.