Solving the pre-marshalling problem to optimality with A* and IDA*

Abstract

We present a novel solution approach to the container pre-marshalling problem using the A* and IDA* algorithms combined with several novel branching and symmetry breaking rules that significantly increases the number of pre-marshalling instances that can be solved to optimality. A* and IDA* are graph search algorithms that use heuristics combined with a complete graph search to find optimal solutions to problems. The container pre-marshalling problem is a key problem for container terminals seeking to reduce delays of inter-modal container transports. The goal of the container pre-marshalling problem is to find the minimal sequence of container movements to shuffle containers in a set of stacks such that the resulting stacks are arranged according to the time each container must leave the stacks. We evaluate our approach on three well-known datasets of pre-marshalling problem instances, solving over 500 previously unsolved instances to optimality, which is nearly twice as many instances as the current state-of-the-art method solves. e

ASlib: A benchmark library for algorithm selection

“…The container pre-marshalling problem (CPMP) is an NP-hard container stacking problem from the container terminals literature [96]. We constructed an algorithm selection scenario from two recent A* and IDA* approaches for solving the CPMP presented in [106], using instances from the literature. The scenario is described in detail in [105].…”

A new effective unified model for solving the Pre-marshalling and Block Relocation Problems

“…The authors did not propose further improvements to the basic A * framework, provided their work focuses in the development of a new randomized greedy heuristic relying in a collection of rules and a new set of instances. In a subsequent, more elaborate work, Tierney et al (2016) also developed an exact procedure for the pmp by further exploring the A * and IDA * frameworks. In order to reduce the search space of the problem, the authors embedded in their algorithms dominance rules and memory management procedures for preventing the inspection of suboptimal solutions.…”

“…The instance set of were used for benchmarking their algorithms, and they are able to solve instances of small to medium size. Recently, Tanaka & Tierney (2018), building upon the work of Tierney et al (2016), proposed an iterative depending B&B algorithm that solves instances of medium and relatively large size. The lower bound procedures and branching rules embedded in their B&B method are similar to those introduced in Tierney et al (2016).…”

“…Recently, Tanaka & Tierney (2018), building upon the work of Tierney et al (2016), proposed an iterative depending B&B algorithm that solves instances of medium and relatively large size. The lower bound procedures and branching rules embedded in their B&B method are similar to those introduced in Tierney et al (2016). Up to this date, these two algorithms achieve the best results for the pmp in terms of instances solved to optimal-ity.…”

“…In order to deal with larger instances, the authors implemented a heuristic based on their formulation. All the methods proposed by Lee & Hsu (2007), Tierney et al (2016) and Tanaka & Tierney (2018) (2015) and Zehendner et al (2015) proposed corrections and improvements for the r-brp model presented by Caserta et al (2012). Galle et al (2018) recently put forward a new MIP formulation for the r-brp which explores a binary representation that was initially described on the work of .…”