Container Relocation Problem Research Articles

Real-Time Batch Optimization for the Stochastic Container Relocation Problem

The container relocation problem (CRP) is an important factor affecting the operation efficiency of container terminal yards, and it has attracted much attention for decades. The CRP during the pickup operations of import containers is still an intractable problem for two reasons: the first is that the solution efficiency of the algorithms developed in the existing literature cannot meet the real-time operation requirements; the second is that the pre-optimized operation plan cannot cope with the changes in the real-time operation scenarios caused by the uncertainty of the arrival time of external trucks. This paper proposes an optimization method for the real-time operation scenario which aims to solve the most reasonable operation plan quickly according to the arrivals of external trucks, in which a dynamic upper bound of the optimal solution is derived based on the dynamic programming model of the import containers’ CRP, and an approximate optimal solution can be obtained by minimizing this dynamic upper bound. A heuristic algorithm based on three relocation rules is developed to implement this method, considering the adjustment of the pickup sequence of the target containers. Numerical experiments show that (1) when the number of a batch of target containers is less than 10 (excluding target containers that can be directly picked up), the method proposed in this paper can solve the problem quickly to meet the demand of optimizing real-time pickup operations; (2) compared with other outstanding algorithms, the quality of the solutions obtained by this method is also improved; and (3) this method can be applied to the most container terminals for optimizing real-time pickup operations.

Designing relocation rules with genetic programming for the container relocation problem with multiple bays and container groups

The container relocation problem (CRP) is an NP-hard combinatorial optimisation problem that arises in yard management. The problem is concerned with loading all containers from the storage yard to the ship in a certain order. The yard layout consists of bays where containers are placed in stacks on top of each other, and each container has a due date that determines their retrieval order. Due to its complexity, heuristic methods are used to solve CRP, ranging from relocation rules to metaheuristics. Relocation rules (RRs) are used when the goal is to obtain a solution of acceptable quality in short time. Manually designing RRs is difficult and time-consuming, which motivates the use of different methods to automatically design RRs. In this study, we investigate the application of genetic programming (GP) to design RRs for CRP with multiple bays and container groups. The GP algorithm was adapted for generating RRs by proposing a new set of terminals and several solution construction methods. The proposed method was evaluated on an extensive benchmark of existing problems. The results obtained with automatically developed RRs were compared with the results of manually designed RRs and it was found that the automatically designed RRs performed significantly better in all cases.

Automated design of relocation rules for minimising energy consumption in the container relocation problem

The container relocation problem (CRP) is a combinatorial optimisation problem in which the sequence of container relocations must be determined to retrieve all containers from the yard while optimising a given objective. Prior to now, the primary objective of CRP was to minimise the number of container relocations; however, due to environmental concerns, optimising energy consumption is gaining importance. This criterion was not considered extensively in the literature about CRP; therefore, there is a lack of suitable methods to tackle this problem variant. Primarily, there is a lack of relocation rules (RRs), simple heuristics that efficiently solve large problems in negligible time. Unfortunately, RRs are challenging to design manually since this process requires significant domain knowledge and is time-consuming. Using hyperheuristics to evolve new RRs automatically is one way to circumvent this problem. In this study, we evolved new RRs that aim to minimise energy consumption using genetic programming. We consider both the scenario in which only energy consumption is optimised and a multi-objective scenario where energy consumption is optimised together with the number of container relocations. The proposed approach is compared with an existing approach from the literature that uses a genetic algorithm to design RRs. The results show that RRs designed using genetic programming perform significantly better than the existing method, especially in multi-objective scenarios.

Enhancing Metaheuristic Optimization: A Novel Nature-Inspired Hybrid Approach Incorporating Selected Pseudorandom Number Generators

In this paper, a hybrid nature-inspired metaheuristic algorithm based on the Genetic Algorithm and the African Buffalo Optimization is proposed. The hybrid approach adaptively switches between the Genetic Algorithm and the African Buffalo Optimization during the optimization process, leveraging their respective strengths to improve performance. To improve randomness, the hybrid approach uses two high-quality pseudorandom number generators—the 64-bit and 32-bit versions of the SIMD-Oriented Fast Mersenne Twister. The effectiveness of the hybrid algorithm is evaluated on the NP-hard Container Relocation Problem, focusing on a test set of restricted Container Relocation Problems with higher complexity. The results show that the hybrid algorithm outperforms the individual Genetic Algorithm and the African Buffalo Optimization, which use standard pseudorandom number generators. The adaptive switch method allows the algorithm to adapt to different optimization problems and mitigate problems such as premature convergence and local optima. Moreover, the importance of pseudorandom number generator selection in metaheuristic algorithms is highlighted, as it directly affects the optimization results. The use of powerful pseudorandom number generators reduces the probability of premature convergence and local optima, leading to better optimization results. Overall, the research demonstrates the potential of hybrid metaheuristic approaches for solving complex optimization problems, which makes them relevant for scientific research and practical applications.

Automated design of heuristics for the container relocation problem using genetic programming

The container relocation problem is a challenging combinatorial optimisation problem tasked with finding a sequence of container relocations required to retrieve all containers by a given order. Due to the complexity of this problem, heuristic methods are often applied to obtain acceptable solutions in a small amount of time. These include relocation rules (RRs) that determine the relocation moves that need to be performed to efficiently retrieve the next container based on certain yard properties. Such rules are often designed manually by domain experts, which is a time-consuming and challenging task. This paper investigates the application of genetic programming (GP) to design effective RRs automatically. Experimental results show that RRs evolved by GP outperform several existing manually designed RRs. Additional analyses of the proposed approach demonstrate that the evolved rules generalise well across a wide range of unseen problems and that their performance can be further enhanced. Therefore, the proposed method presents a viable alternative to existing manually designed RRs and opens a new research direction in the area of container relocation problems.

Service fairness and value of customer information for the stochastic container relocation problem under flexible service policy

This paper considers the optimization of service efficiency and service fairness in a Stochastic Container Relocation Problem (SCRP) under flexible service policies at a container terminal. Under the flexible service policy, the external trucks arriving within the same time window can be served out of sequence, which may raise a concern of service fairness. We incorporate the concept of service fairness into the SCRP in two phases. In phase 1, we propose a multiple sub-time windows-based flexible service policy, under which each time window will be divided into multiple sub-time windows and the flexible service policy is only applied to each individual sub-time window. In phase 2, the SCRP is formulated as a dynamic programming model with two lexicographically ordered objectives representing both relocation efficiency and service fairness, which is solved via a hierarchical iterative approach. In addition, we investigate whether the information of trucks’ arrival probability over the time window (which represents the customer preference information) would add value to the terminal operators. Extensive computational experiments are conducted to evaluate the impacts of the number of sub-time windows and to examine the impacts and value of customer preference information in various scenarios. The results show interesting trade-offs between efficiency and fairness. As the number of sub-time windows increases, the service fairness is generally improving (but not guaranteed) while the expected number of relocations is increasing. It is found that the customer preference information can be valuable in some circumstances, especially when each truck indicates a certain arrival sub-time window.

Solving the Integrated Multi-Port Stowage Planning and Container Relocation Problems with a Genetic Algorithm and Simulation

The greater flow of containers in global supply chains requires ever-increasing productivity at port terminals. The research found in the literature has focused on optimizing specific parts of port operations but has ignored important features, such as the stack-wise organization of containers in a container ship and port yard and the effects of interconnection among the operations in both places. The objective of this paper is to show the importance of designing an integrated plan of the container relocation problem at the port yard with the stowage planning problem for loading and unloading a ship through ports. Both individual problems are NP-Complete, and exact approaches for each problem are only able to find optimal or feasible solutions for small instances. We describe a simulation-optimization methodology that combines simulation, a genetic algorithm, and a new solution representation based on rules. The test results show that the solution from the integrated plan is mutually beneficial for port yards and ship owners.

Solving the Container Relocation Problem by Using a Metaheuristic Genetic Algorithm

Maritime transport is the backbone of international trade of goods. Therefore, seaports are of great importance for maritime transport. Container transport plays an important role in maritime transport and is increasing year by year. Containers transported to a container terminal are stored in container yards side by side and on top of each other, forming blocks. If a container that is not on top of the block has to be retrieved, the containers that are above the required container must be relocated before the required container is retrieved. These additional container relocations, which block the retrieval of the required container, slow down the entire retrieval process. The container relocation problem, also known as the block relocation problem, is an optimization problem that involves finding an optimal sequence of operations for retrieving blocks (containers) from a container yard in a given order, minimizing additional relocations of blocking containers. In this paper, the focus is on the two-dimensional, static, offline and the restricted container relocation problem of real-size yard container bays. A new method for resolving the container relocation problem that uses a genetic algorithm is proposed to minimize the number of relocations within the bay. The method is evaluated on well-known test instances, and the obtained results are compared with the results of various relevant models for resolving the container relocation problem. The results show that the proposed method achieves the best or the second-best result for each test instance within the test set.

The realization-independent reallocation heuristic for the stochastic container relocation problem

The realization-independent reallocation heuristic for the stochastic container relocation problem

An exact algorithm for the unrestricted container relocation problem with new lower bounds and dominance rules

The container relocation problem, also known as the block(s) relocation problem, is one of the most studied optimization problems in container terminals. The problem aims at minimizing the total number of relocations for retrieving containers from a storage yard according to a specific order. The purpose of this study is to develop an efficient iterative deepening branch-and-bound algorithm for exactly solving one of the most practical variants of the problem, namely the unrestricted container relocation problem with duplicate priorities, which has received less attention in the literature. To improve the search efficiency of the proposed algorithm, we design two new lower bounds that can be computed quickly to incorporate them into the branch-and-bound algorithm. We also present a set of mutually consistent dominance rules to reduce the search space while avoiding over-pruning. The performance of the proposed algorithm is evaluated by extensive computational experiments on three commonly used benchmark datasets. The results show that the proposed algorithm outperforms the state-of-the-art exact algorithm for the unrestricted container relocation problem with distinct priorities, although our algorithm is applicable to a more general variant of the problem. Moreover, it can still provide competitive results for small- and medium-sized instances under a strict time limit of one second in comparison to existing metaheuristic approaches.

Coordinating truck appointments with container relocations and retrievals in container terminals under partial appointments information

This paper introduces a new scheduling approach that optimizes truck appointments, truck service order, and container relocations at the yard through a bi-objective IP model with a lexicographical objective function. The proposed approach serves as a proactive decision support system that coordinates truck appointments with container handling operations to avoid excessive delays caused by container relocations. The performance of the approach is compared to existing practices of the online container relocation using a case study involving an operational Japanese container terminal. A rule-based heuristic for the online container relocation problem is formulated and compared to our proposed optimization approach. Taking into account a number of essential practical aspects, including trucking company preferences, container delivery schedules, yard capacity, and appointment levels, our proposed optimization approach has the potential to significantly reduce the number of relocations in the yard while making minimal shifts in the preferred container pickup times.

GA for Optimization in the Container Relocation Problem. Improvements in Solving Time and Quality of Results

GA for Optimization in the Container Relocation Problem. Improvements in Solving Time and Quality of Results

An exact approach to the restricted block relocation problem based on a new integer programming formulation

This study addresses the block(s) relocation problem (BRP), also known as the container relocation problem. This problem considers individually retrieving blocks piled up in tiers according to a predetermined order. When the block to be retrieved next is not at the top, we have to relocate the blocks above it because we can access only the topmost blocks. The objective is to retrieve all the blocks with the smallest number of relocations. In this study, a novel exact algorithm is proposed for the restricted BRP, a class of the problem where relocatable blocks are restricted. The proposed algorithm computes lower and upper bounds iteratively by solving the corresponding integer programming problems until the optimality gap is reduced to zero. The novelty of the algorithm lies in the formulations based on complete and truncated relocation sequences of the individual blocks. We examine the effectiveness of the proposed algorithm through computational experiments for benchmark instances from the literature. In particular, we report that, for the first time, all the instances with up to 100 blocks are solved to proven optimality.

A New Heuristic Reinforcement Learning for Container Relocation Problem

Many research efforts on reinforcement learning (RL) is dedicated to solving challenging combinatorial optimization problems, including the container relocation problem (CRP) arising from maritime industry. In CRP, large and heavy containers are stacked on top of each other, those above the target container should be relocated elsewhere before retrieving it. This problem, which minimizes the number of relocations in the retrieval process, is NP-hard, while existing RL studies do not provide satisfactory results yet. We study the structure of CRP problem and design a new heuristic RL framework. On a set of commonly used examples, our RL demonstrates a performance almost equivalent to the most famous results.

The stochastic container relocation problem with flexible service policies

This paper investigates the Stochastic Container Relocation Problem in which a flexible service policy is adopted in the import container retrieval process. The flexible policy allows the terminal operators to determine the container retrieval sequence to some extent, which provides more opportunity for reducing the number of relocations and the truck waiting times. A more general probabilistic model that captures customers’ arrival preference is presented to describe the randomness for external truck arrivals within their appointed time windows. Being a multi-stage stochastic sequential decision-making problem, it is first formulated into a stochastic dynamic programming (SDP) model to minimize the expected number of relocations. Then, the SDP model is extended considering a secondary objective representing the truck waiting times. Tree search-based algorithms are adapted to solve the two models to their optimality. Heuristic algorithms are designed to seek high-quality solutions efficiently for larger problems. A discrete-event simulation model is developed to evaluate the optimal solutions and the heuristic solutions respectively on two performance metrics. Extensive computational experiments are performed based on instances from literature to verify the effectiveness of the proposed models and algorithms.

G-CREM: A GRASP approach to solve the container relocation problem for multibays

The Container Relocation Problem for multiple bays consists of finding the minimum number of moves to load a set of stacked containers on a ship according to a given loading sequence, and in minimizing the crane’s working time for an entire yard of multiple bays. This is a crucial problem for every commercial port in the world given the maximum time requirements and the costs associated with the containers’ retrieval. In this paper, we propose a Greedy Randomized Adaptive Search Procedure to solve this problem. We use a myopic function specially designed to produce feasible candidate solutions with a structure that allows a local search procedure to optimize relocations. In order to validate our approach, we use a large set of well-known Container Relocation Problems for multiples bays, as well as a statistical analysis of our results. Our experiments show new bounds for various instances.

Machine learning-driven algorithms for the container relocation problem

The container relocation problem is one of important issues in seaport terminals which could bring a significant saving on the operating cost even with a slight improvement due to the huge number of containers processed across the world each year. Given a specific layout and container retrieval priorities, the container relocation problem aims to find the optimal movement sequence to minimize the total number of container relocation operations. In this paper, we propose novel machine learning-driven algorithms, which integrate optimization methods and machine learning techniques, to solve the problem. More specifically, we propose a new upper bound method called MLUB that incorporates branch pruners. These pruners are derived from some machine learning techniques through using the optimal solution values of many small-scale instances. The tightened upper bounds generated by MLUB are used subsequently both in the exact branch-and-bound algorithm called IB&B and the hybrid beam search heuristic called MLBS. Moreover, we also provide a tighter lower bound for the problem by additionally considering the interaction between consecutive target containers. Based on the benchmark data published recently in the literature, extensive experiments are conducted to test the performance of the proposed algorithms. The experimental results demonstrate that the proposed algorithms outperform the state-of-the-art algorithms reported in the literature, and some managerial insights regarding the load intensity of the bay and some algorithm parameters such as the look-ahead depth and the beam width are drawn from the results.

OPTIMIZATION OF CONTAINER RELOCATION OPERATIONS IN PORT CONTAINER TERMINALS

The relocation of containers is a crucial operation in container ports all around the world. The Container Relocation Problem (CRP) is focused upon to find a sequence of container retrievals in a defined order from a single yard container bay with a minimum number of relocations. The goal of this paper is to find out if Genetic Algorithm (GA) can give new insights in the problem of solving the CRP. In this paper we focus on the two-dimensional, static, offline and restricted CRP of real-world yard container bays. Four rules are proposed for determining the position of relocated containers. We applied GA to find the best sequence of container retrievals according to these four rules in order to minimize the number of relocations within the bay. The experimental testing was run on a total of 800 different instances with varying bay sizes and number of containers. The given results are compared with the results of different authors using other heuristic methods. The results show that the proposed model solves CRP and achieves near optimal solutions.

Optimizing pre-processing and relocation moves in the Stochastic Container Relocation Problem

In container terminals, containers are often moved to other stacks in order to access containers that need to leave the terminal earlier. We propose a new optimization model in which the containers can be moved in two different phases: a pre-processing and a relocation phase. To solve this problem, we develop an optimal branch-and-bound algorithm. Furthermore, we develop a local search heuristic because the problem is NP-hard. Besides that, we give a rule-based method to estimate the number of relocation moves in a bay. The local search heuristic produces solutions that are close to the optimal solution. Finally, for instances in which the benefits of moving containers in the two different phases are in balance, the solution of the heuristic yields significant improvement compared to the existing methods in which containers are only moved in one of the two phases.

On the integer programming formulation for the relaxed restricted container relocation problem

In a recent paper entitled “A new binary formulation of the restricted container relocation problem based on a binary encoding of configurations”, Galle, Barnhart and Jaillet (2018) introduced a new variant of the container relocation problem (CRP), named the relaxed restricted CRP, where every container can be relocated at most once for retrieving each target container. The authors also proposed a binary integer programming model for formulating the relaxed restricted CRP. In this paper, it is first shown that the proposed model contains two deficiencies in formulating the “last in, first out” (LIFO) policy. These deficiencies will cause the solutions obtained by the model to correspond to infeasible configurations or infeasible relocation sequences. Then, the LIFO policy is analyzed in detail and reformulated as linear constraints correctly. Lastly, the corrected integer programming formulation is presented. Computational experiments show that the corrected model dramatically reduces complexity and improves performance.