PILS: Exploring high-order neighborhoods by pattern mining and injection

TL;DR

PILS is a novel local search strategy that uses pattern mining to explore high-order neighborhoods, improving optimization performance in vehicle routing problems by identifying complex moves beyond traditional enumeration.

Contribution

This paper introduces pattern injection local search (PILS), a new method that leverages pattern mining to efficiently explore high-order neighborhoods in local search algorithms.

Findings

PILS discovers high-order moves like 9-opt and 10-opt that are hard to find by enumeration.

PILS significantly enhances the performance of existing metaheuristics.

The strategy offers a controllable computational time for exploring complex neighborhoods.

Abstract

We introduce pattern injection local search (PILS), an optimization strategy that uses pattern mining to explore high-order local-search neighborhoods, and illustrate its application on the vehicle routing problem. PILS operates by storing a limited number of frequent patterns from elite solutions. During the local search, each pattern is used to define one move in which 1) incompatible edges are disconnected, 2) the edges defined by the pattern are reconnected, and 3) the remaining solution fragments are optimally reconnected. Each such move is accepted only in case of solution improvement. As visible in our experiments, this strategy results in a new paradigm of local search, which complements and enhances classical search approaches in a controllable amount of computational time. We demonstrate that PILS identifies useful high-order moves (e.g., 9-opt and 10-opt) which would otherwise not be found by enumeration, and that it significantly improves the performance of state-of-the-art population-based and neighborhood-centered metaheuristics.