A branch and bound approach for large pre-marshalling problems

Abstract

The container pre-marshalling problem involves the sorting of containers in stacks so that there are no blocking containers and retrieval is carried out without additional movements. This sorting process should be carried out in as few container moves as possible. Despite recent advancements in solving real world sized problems to optimality, several classes of pre-marshalling problems remain difficult for exact approaches. We propose a branch and bound algorithm with new components for solving such difficult instances. We strengthen existing lower bounds and introduce two new lower bounds that use a relaxation of the pre-marshalling problem to provide tight bounds in specific situations. We introduce generalized dominance rules that help reduce the search space, and a memoization heuristic that finds feasible solutions quickly. We evaluate our approach on standard benchmarks of pre-marshalling instances, as well as on a new dataset to avoid overfitting to the available data. Overall, our approach optimally solves many more instances than previous work, and finds feasible solutions on nearly every problem it encounters in limited CPU times.

Pre-processing a container yard under limited available time

“…In Tierney et al (2017), an improved A * algorithm is given in which they make use of the lower bounds for the CPMP of Bortfeld & Forster (2012). The current state-of-the-art algorithm for solving the CPMP to optimality is a branch-and-bound algorithm that is first presented by Tanaka & Tierney (2018) and later improved by Tanaka et al (2019). This method can solve almost all real-sized instances within an hour.…”

A Novelty in Blahut-Arimoto T ype Algorithms: Optimal Control over Noisy Commu nication Channels

“…COROLLARY 1: φ v = 0, ∀v ∈ {1, 2}, in relation to φ 1 I(Y;Ŝ|X, S) − φ 2 I(Y;X|X, S), is in accordance with the 15 Please do not be confused with the principle of −Nash Equilibria, or α−stable [39]. case of an unstable, but detectable-and-stabilisable sysetm.…”

“…In order to design the system model from a mathematicalphysical point-of-view, a multi-objective optimisation (MOO) problem is commonly determined. In an MOO [13], [14], [15], [16], the objective function is a vector set containing some metrics. The Augmented Lagrangian methods [14], [15], [16] such as alternating-direction-method-of-multipliers (ADMM) [14] as well as the Branch-and-Bound (BB) one [15], [16] ACCEPTED in IEEE TVT 2020 be the totally applicable candidates for providing a globally acceptable solution to the MOO problems.…”

A Novelty in Blahut-Arimoto T ype Algorithms: Optimal Control over Noisy Commu nication Channels

“…In order to design the system model from a mathematicalphysical point-of-view, a multi-objective optimisation (MOO) problem is commonly determined. In an MOO [13], [14], [15], [16], the objective function is a vector set containing some metrics. The Augmented Lagrangian methods [14], [15], [16] such as alternating-direction-method-of-multipliers (ADMM) [14] as well as the Branch-and-Bound (BB) one [15], [16] may 2 Low-distortion regime.…”