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

TL;DR

This paper introduces a systematic, problem-independent method to characterize and cluster neighborhoods in multi-neighborhood local search algorithms, improving parameter tuning efficiency by reducing complexity without losing search effectiveness.

Contribution

The authors propose a novel neighborhood characterization and clustering approach that adapts to solution quality regions, aiding automated parameter tuning in local search algorithms.

Findings

Clustering neighborhoods reduces tuning complexity.

Behavioral characterization reflects changes across solution quality regions.

Method is applicable across different problem instances.

Abstract

We consider a multi-neighborhood local search algorithm 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 are considered as parameters of the algorithm. Given a set of instances, off-line tuning of the algorithm's parameters can be done by automated algorithm configuration tools (e.g., SMAC). However, the large number of neighborhoods can make the tuning expensive and difficult 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. 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.