Iterative Deepening A* Algorithms for the Container Relocation Problem

Abstract

The container relocation problem, where containers that are stored in bays are retrieved in a fixed sequence, is a crucial port operation. Existing approaches using branch and bound algorithms are only able to optimally solve small cases in a practical time frame. In this paper, we investigate iterative deepening A* algorithms (rather than branch and bound) using new lower bound measures and heuristics, and show that this approach is able to solve much larger instances of the problem in a time frame that is suitable for practical application. We also examine a more difficult variant of the problem that has been largely ignored in existing literature.Note to Practitioners-Container retrieval is an important operation in a container port. When a ship arrives, containers stored in the port yard are first retrieved by yard crane, loaded onto autoguided vehicles, transported to quay cranes, and loaded onto the ship by quay crane. Due to various operational constraints, e.g., maintenance of vessel balance and safety issues, the containers in a storage bay are retrieved one by one in a fixed sequence. When the next container to be retrieved is not at the top of its stack, all other containers above it must then be first relocated onto other stacks within the bay. The relocation of a container is a time-consuming operation that essentially dominates all other aspects of the problem, and therefore it is important that the retrieval plan minimizes the number of such relocations. This study proposes a method to generate a near-optimal retrieval plan for yard cranes. This often arises as a subproblem when devising an overall plan for port operations that maximizes throughput, which involves the coordination of multiple pieces of machinery. Our approach produces significantly better results than all existing approaches.Index Terms-Container relocation problem, container yard operation, iterative deepening A*.

Search space reduction with multiset for effectively solving the container pre-marshalling problem

“…[4], the procedures in this study are specialized for the CPMP whereas the algorithm is specialized for the container relocation problem.…”

“…The implementation of the history check resembles the use of the map shown in Ref. [4] although their matching method is not described. The history check introduced in this paper compares bays based on the equivalence of bays defined in Section 2 to increase the possibility of reduction of search paths.…”

Decreasing the Crane Working Time in Retrieving the Containers from a Bay

“…To decrease the time required to load the containers onto a ship, most of the studies in the literature have attempted to decrease the number of necessary relocations [3][4][5]. Experimental results indicate that there is a high correlation between working time of the crane, denoted by T CW , and the number of relocations, denoted by N MOV [6].…”

“…When N MOV is considered to be minimized, the problem is called the Containers/Blocks Relocation Problem (CRP or BRP) [4,5,7]. Kim and Hong [3] developed a Branch and Bound (B&B) algorithm that made use of the number of blocking containers in the initial layout as a lower bound for the number of required relocations.…”

“…Their computational results proved that this heuristic was highly competitive in comparison with the best known approaches in the literature. Subsequently, Zhu et al [4] employed the iterative deepening A* algorithm, which was based on novel lower-bound measures as well as new heuristics. Their IDA* heuristic was able to nd the optimal or near-optimal solutions for the considered problems in a time-e cient computational e ort.…”