Article(id=1240655024133559230, tenantId=1146029695717560320, journalId=1240618002186551303, issueId=1240655017040991028, articleNumber=null, orderNo=null, doi=10.3969/j.issn.1000-4653.2025.04.011, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1726675200000, receivedDateStr=2024-09-19, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1773724808009, onlineDateStr=2026-03-17, pubDate=1766592000000, pubDateStr=2025-12-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1773724808009, onlineIssueDateStr=2026-03-17, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1773724808009, creator=13701087609, updateTime=1773724808009, updator=13701087609, issue=Issue{id=1240655017040991028, tenantId=1146029695717560320, journalId=1240618002186551303, year='2025', volume='48', issue='4', pageStart='1', pageEnd='199', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1773724806318, creator=13701087609, updateTime=1773725219619, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1240656750618145316, tenantId=1146029695717560320, journalId=1240618002186551303, issueId=1240655017040991028, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1240656750618145317, tenantId=1146029695717560320, journalId=1240618002186551303, issueId=1240655017040991028, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=93, endPage=102, ext={EN=ArticleExt(id=1240655024418771912, articleId=1240655024133559230, tenantId=1146029695717560320, journalId=1240618002186551303, language=EN, title=Berth allocation in container terminals under fuzzy uncertain conditions, columnId=1240655021705065434, journalTitle=Navigation of China, columnName=Port and Waterway Engineering, runingTitle=null, highlight=null, articleAbstract=

The arrival and handling times of vessels are subject to significant uncertainty. Triangular fuzzy numbers, characterized by upper and lower bounds and a most likely value, provide an effective means of representing such imprecise information. In this context, this paper first establishes a fuzzy integer programming model for berth allocation at container terminals, aiming to minimize the total departure delay time of vessels. An improved Multi-Verse Optimizer (MVO) algorithm is then proposed to solve the model, incorporating solution repair and breakout strategies. Comparative analysis shows that, in contrast to deterministic berth allocation schemes, the proposed fuzzy berth allocation approach demonstrates notable advantages in reducing total departure delay time and exhibits greater effectiveness in handling uncertainty. Moreover, the improved MVO algorithm achieves solution speed improvements of 59.9%, 44%, and 26.1% in small, medium, and large scale experiments, respectively, compared to the standard multi-verse optimizer. These results indicate that the proposed algorithm can efficiently solve the fuzzy integer programming model for berth allocation and offers valuable decision-making support for addressing berth allocation problems under fuzzy uncertainty.

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船舶到港时间和装卸作业时间具有明显的不确定性，而三角模糊数能够通过其上、下界及其最可能值三个参数有效描述难以用精确数值描述的信息。基于此，文章首先以最小化船舶总离港延误时间为目标，建立集装箱码头泊位分配模糊整数规划模型；其次，提出基于解修复策略和跳出策略的改进多元宇宙算法求解模糊整数规划模型。最后，通过与确定性泊位分配方案对比，证明模糊泊位分配方案可减少总离港延误时间，在面对不确定性更具有优势。同时，相较于标准多元宇宙算法，文章提出的改进多元宇宙算法在小、中、大规模试验下，其求解速度分别提高59.9%、44%、26.1%，说明该算法可以有效求解泊位分配模糊整数规划模型，为处理模糊不确定性条件下的泊位分配问题提供决策依据。

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