A faster branch-and-bound algorithm for the block relocation problem

Tanaka, Shotaro; Takii, Kenta

doi:10.1109/coase.2014.6899296

Cited by 12 publications

(42 citation statements)

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“…The numerical experiments showed that these dominance properties enable us to reduce the number of nodes in a branch-and-bound algorithm. However, the algorithm is still less efficient than that for the restricted problem [4]. Moreover, the dominance properties are not applicable to the problem with duplicate priorities where some blocks share the same priority.…”

Section: Discussionmentioning

confidence: 97%

“…In the restricted version of the problem, only a specific topmost block is relocatable, while in the unrestricted version of the problem, any topmost blocks are relocatable. In [1][2][3][4], dedicated exact algorithms based on the branch-andbound algorithm were proposed for the restricted problem. However, we can further reduce the number of necessary relocation operations if we solve the unrestricted problem.…”

Section: Introductionmentioning

confidence: 99%

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Extension of the dominance properties for the unrestricted block relocation problem

Tanaka

2015

2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

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The block (container) relocation problem is an optimization problem that typically arises in container terminals. Its objective is to minimize the number of relocation operations necessary for retrieving all blocks (containers) stacked in tiers according to a given order. In our previous study, we considered the unrestricted version of the problem where no restriction is imposed on relocatable blocks, and proposed two dominance properties for it. However, they considered only two successive operations. The purpose of this study is to extend them for any two operations. They enable us to improve the efficiency of the branch-and-bound algorithm for the problem, which will be verified by numerical experiment.

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Section: Discussionmentioning

confidence: 97%

Section: Introductionmentioning

confidence: 99%

Extension of the dominance properties for the unrestricted block relocation problem

Tanaka

2015

2015 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM)

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“…It is worth noting that our framework is applicable to those small-scale but complicated sequencing problems, while it would be more suitable to apply other exact or heuristic approaches to handle large-scale problems. For the future research, we can apply the proposed enhanced B&B to find the optimal solutions of other practical sequencing problems, e.g., disassembly sequencing problem [16], [20], [39], heterogeneous traveling salesman problem [21], [26], [30], and block relocation problem [38], [46]. In addition, more advanced searching techniques, such as different branching rules [1], problem-specific dominance checkers, incremental bounding [25], and other caching methods, can be studied for further improving the performance of the proposed framework.…”

Section: Discussionmentioning

confidence: 99%

Enhanced Branch-and-Bound Framework for a Class of Sequencing Problems

Zhang

Teng

Zhou

et al. 2021

IEEE Trans. Syst. Man Cybern, Syst.

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In this paper, we propose an enhanced branch-andbound (B&B) framework for a class of sequencing problems, which aim to find a permutation of all involved elements to minimize a given objective function. We require that the sequencing problems satisfy three conditions: 1) incrementally computable; 2) monotonic; and 3) overlapping subproblems. Our enhanced B&B framework is built on the classical B&B process by introducing two techniques, i.e., dominance rules and caching search states. Following the enhanced B&B framework, we conduct empirical studies on three typical and challenging sequencing problems, i.e., quadratic traveling salesman problem, traveling repairman problem, and talent scheduling problem. The computational results demonstrate the effectiveness of our enhanced B&B framework when compared to classical B&B and some exact approaches, such as dynamic programming and constraint programming. Additional experiments are carried out to analyze different configurations of the algorithm. Index Terms-Branch-and-bound (B&B), caching states, dominance rules, dynamic programming (DP), talent scheduling problem, traveling salesman/repairman problem. I. INTRODUCTION T HE SEARCH techniques for solving combinatorial optimization problems (COPs) have been widely studied in the communities of artificial intelligence, industrial engineering, and operations research during the last century. The simplest and standard framework for solving COPs is to use branch-and-bound (B&B) algorithms [3], [8], [14]. Its basic idea is to systematically and implicitly enumerate all possible candidate solutions, where large subsets of fruitless candidates Manuscript

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“…The procedure implemented for providing tight upper bounds on the number of relocations (parameter T ) for the brp models is based on the B&B algorithm for the Restricted BRP of Tanaka & Takii (2016). This algorithm can handle the r-brp with unique and grouped container priorities.…”

Section: Estimating Parameter T For the Brp Modelsmentioning

confidence: 99%

“…This algorithm can handle the r-brp with unique and grouped container priorities. The branch-and-bound implemented differs from the one presented in the paper of Tanaka & Takii (2016) by using a simpler lower bounding method.…”

Section: Estimating Parameter T For the Brp Modelsmentioning

confidence: 99%

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

Silva

Toulouse

Calvo

2018

European Journal of Operational Research

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Container terminals are exchange hubs that interconnect many transportation modes and facilitate the flow of containers. Among other elements, terminals include a yard which serves as temporary storage space. In the yard, containers are piled up by cranes to form blocks of stacks. During the shipment process, containers are carried from the stacks to ships following a given sequence. Hence, if a high priority container is placed below low priority ones, such obstructing containers have to be moved (relocated) to other stacks. Given a set of stacks and a retrieval sequence, the aim in the Pre-marshalling Problem (pmp) is to sort the initial configuration according to the retrieval sequence using a minimum number of relocations, so that no new relocations are needed during the shipment. The objective in the Block Relocation Problem (brp) is to retrieve all the containers according to the retrieval sequence by using a minimum number of relocations. This paper presents a new unified integer programming model for solving the pmp, the brp, and the Restricted brp (r-brp) variant. The new formulations are compared with existing mathematical models for these problems, as well as with other exact methods that combines combinatorial lower bounds and the branch-and-bound (B&B) framework, by using a large set of instances available in the literature. The numerical experiments * Corresponding author: Tel. +33 1 4940 4082.show that the proposed models are able to outperform the approaches based on mathematical programming. Nevertheless, the B&B algorithms achieve the best results both in terms of computation time and number of instances solved to optimality.

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A faster branch-and-bound algorithm for the block relocation problem

Cited by 12 publications

References 10 publications

Extension of the dominance properties for the unrestricted block relocation problem

Extension of the dominance properties for the unrestricted block relocation problem

Enhanced Branch-and-Bound Framework for a Class of Sequencing Problems

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

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