The Bounded Beam Search algorithm for the Block Relocation Problem

TL;DR

This paper introduces a new lower bound and a bounded beam search heuristic for the Block Relocation Problem, demonstrating improved performance over existing methods on standard and large-scale instances.

Contribution

A novel polynomial-time computable lower bound and a bounded beam search heuristic that outperform previous algorithms for the Block Relocation Problem.

Findings

The new lower bound is provably better than some existing bounds.

The heuristic approach outperforms other algorithms on most benchmark instances.

New large instances of the problem are introduced for testing.

Abstract

In this paper we deal with the restricted Block Relocation Problem. We present a new lower bound and a heuristic approach for the problem. The proposed lower bound can be computed in polynomial time and it is provably better than some previously known lower bounds. We use it within a bounded beam search algorithm to solve the Block Relocation Problem and show that the considered heuristic approach outperforms the other existing algorithms on most of the instances in the literature. In order to test the approaches on real-size dimensions, new large instances of the Block Relocation Problem are also introduced.