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Article(id=1322164775333770000, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164546295410919, articleNumber=null, orderNo=null, doi=null, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1728662400000, receivedDateStr=2024-10-12, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1793158247072, onlineDateStr=2026-10-28, pubDate=1764000000000, pubDateStr=2025-11-25, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1793158247072, onlineIssueDateStr=2026-10-28, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1793158247072, creator=13701087609, updateTime=1793158247072, updator=13701087609, issue=Issue{id=1322164546295410919, tenantId=1146029695717560320, journalId=1225396423026438145, year='2025', volume='45', issue='11', pageStart='1', pageEnd='284', issueExtLink='null', onlineDate='null', pubDate='1764000000000', pubDateStr='2025-11-25', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1793158192465, creator='13701087609', updateTime=1793158905697, updator='13701087609', preIssue=null, nextIssue=null, articleTotal=null, ext={EN=IssueExt(id=1322167537857573862, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164546295410919, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1322167537861768167, tenantId=1146029695717560320, journalId=1225396423026438145, issueId=1322164546295410919, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null, downloadFileDto=null}, startPage=250, endPage=257, ext={EN=ArticleExt(id=1322164775509930769, articleId=1322164775333770000, tenantId=1146029695717560320, journalId=1225396423026438145, language=EN, title=Research on Mine Intelligent Ore Blending Technology Based on Improved Beluga Whale Optimization Algorithm, columnId=null, journalTitle=Mining Research and Development, columnName=null, runingTitle=null, highlight=null, articleAbstract=

To enhance the efficiency of mine ore blending and resource utilization, based on the beluga whale optimization algorithm (BWO), an improved beluga whale optimization algorithm (IBWO) combining chaotic mapping and Levy flight strategy was proposed, and compared with POS algorithm, WOA algorithm, SSA algorithm and BWO algorithm. The results show that compared with the other four algorithms, the IBWO algorithm has obvious advantages in convergence speed and global optimal solution search ability, and the convergence speed is increased by 31.2％－165.9％. The numerical simulation results of ore blending optimization show that the average profit of IBWO algorithm is 25.06 million yuan at 31 iterations, and the profit is increased by 14.69％－17.93％. The research results provide a new solution path for the optimization of mine ore blending, and are expected to provide a theoretical basis for the efficient utilization of resources and the improvement of economic benefits in mining production.

, authors=Yanbin WANG1, Shufang LI2, Jingqi GAO2, Lei ZHANG1, authorsList=Yanbin WANG, Shufang LI, Jingqi GAO, Lei ZHANG, authorCompany=null, correspAuthors=Shufang LI, authorNote=null, correspAuthorsNote=null, copyrightStatement=null, copyrightOwner=null, extLink=null, articleAbsUrl=null, sourceXml=null, magXml=null, pdfUrl=null, pdf=null, pdfFileSize=null, pdfExtLink=null, richHtmlUrl=null, mobilePdfUrl=null, reviewReport=null, pdfFirstPage=null, abstractGraph=null, abstractGraphContent=null, abstractVideo=null, citation=null, cebUrl=null, magXmlContent=null, mapNumber=null, fund=null), CN=ArticleExt(id=1322164787451114331, articleId=1322164775333770000, tenantId=1146029695717560320, journalId=1225396423026438145, language=CN, title=基于改进白鲸优化算法的矿山智能配矿技术研究, columnId=1226462295946085268, journalTitle=矿业研究与开发, columnName=矿山机电与矿业智能化, runingTitle=null, highlight=null, articleAbstract=

为了提升矿山配矿效率和资源利用率，以白鲸优化算法（Beluga Whale Optimization，BWO）为基础算法，提出了一种结合混沌映射和Levy飞行策略的改进白鲸优化算法（IBWO），并与POS算法、WOA算法、SSA算法及BWO算法的性能进行对比。结果表明，相较于其他4种算法，IBWO算法的收敛速度和全局最优解搜索能力上表现出明显优势，收敛速度提升了31.2％~165.9％。配矿优化数值仿真试验结果表明，IBWO算法在迭代31次时平均利润为25.06万元，利润提高了14.69％~17.93％。研究结果为矿山配矿优化提供了新的解决路径，有望为矿业生产中的资源高效利用和经济效益提升提供理论基础。

, authors=王彦斌1, 李树芳2, 高婧琦2, 张磊1, authorsList=王彦斌, 李树芳, 高婧琦, 张磊, authorCompany=null, correspAuthors=李树芳, authorNote=

王彦斌（1982—），男，陕西府谷县人，硕士，工程师，主要从事信息化管理、5G在能源行业的应用及项目管理工作。E-mail：

, correspAuthorsNote=
李树芳（1993—），女，山西忻州人，工程师，主要研究方向为矿山安全、应急救援。E-mail：
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王彦斌（1982—），男，陕西府谷县人，硕士，工程师，主要从事信息化管理、5G在能源行业的应用及项目管理工作。E-mail：

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王彦斌（1982—），男，陕西府谷县人，硕士，工程师，主要从事信息化管理、5G在能源行业的应用及项目管理工作。E-mail：

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journalId=1225396423026438145, articleId=1322164775333770000, xref=1., ext=[AuthorCompanyExt(id=1322164787803435869, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, companyId=1322164787782464348, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.Guoneng Shendong Coal Intelligent Technology Center, Yulin, Shaanxi 719315, China), AuthorCompanyExt(id=1322164787816018782, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, companyId=1322164787782464348, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1.神东煤炭集团智能技术中心，陕西 榆林市　719315)]), AuthorCompany(id=1322164787912487775, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, xref=2., ext=[AuthorCompanyExt(id=1322164787933459296, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, companyId=1322164787912487775, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.China Academy of Safety Science and Technology, Beijing 100012, China), AuthorCompanyExt(id=1322164787958625121, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, companyId=1322164787912487775, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2.中国安全生产科学研究院，北京　100012)])], figs=[ArticleFig(id=1322164792442336128, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.1, caption=Process of BWO algorithm, figureFileSmall=Ycv8HpCHpwKARWadjj10VQ==, figureFileBig=7jgkhnx0B948rVT7GxRRiA==, tableContent=null), ArticleFig(id=1322164792534610817, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图1, caption=BWO算法流程, figureFileSmall=Ycv8HpCHpwKARWadjj10VQ==, figureFileBig=7jgkhnx0B948rVT7GxRRiA==, tableContent=null), ArticleFig(id=1322164792769491842, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.2, caption=Convergence curves of Rosenbrock function, figureFileSmall=1a/aJCKipWL22kp5ZU1tMg==, figureFileBig=CiMHGqaE61/TWlrPHRc72A==, tableContent=null), ArticleFig(id=1322164792836600707, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图2, caption=Rosenbrock函数收敛曲线, figureFileSmall=1a/aJCKipWL22kp5ZU1tMg==, figureFileBig=CiMHGqaE61/TWlrPHRc72A==, tableContent=null), ArticleFig(id=1322164792920486788, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.3, caption=Convergence curves of Rastrigin function, figureFileSmall=L5HiNd08Ll4o3pYjeybw7A==, figureFileBig=eGNC4FZqN70OU61PMP3PHg==, tableContent=null), ArticleFig(id=1322164792995984261, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图3, caption=Rastrigin函数收敛曲线, figureFileSmall=L5HiNd08Ll4o3pYjeybw7A==, figureFileBig=eGNC4FZqN70OU61PMP3PHg==, tableContent=null), ArticleFig(id=1322164793071481734, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.4, caption=Convergence curves of Schaffer function, figureFileSmall=Fl7J2P/TE5DYF6YDRTPzVg==, figureFileBig=A+IB50uneehRJZ3r96Rwag==, tableContent=null), ArticleFig(id=1322164793163756423, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图4, caption=Schaffer函数收敛曲线, figureFileSmall=Fl7J2P/TE5DYF6YDRTPzVg==, figureFileBig=A+IB50uneehRJZ3r96Rwag==, tableContent=null), ArticleFig(id=1322164793239253896, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.5, caption=Convergence curves of Sphere function, figureFileSmall=/NI54Ug5eNzyarhR5u6CQQ==, figureFileBig=X4IiqUKPaWJg5P4gARXkXQ==, tableContent=null), ArticleFig(id=1322164794908586891, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图5, caption=Sphere函数收敛曲线, figureFileSmall=/NI54Ug5eNzyarhR5u6CQQ==, figureFileBig=X4IiqUKPaWJg5P4gARXkXQ==, tableContent=null), ArticleFig(id=1322164794979890060, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.6, caption=Convergence curves of Griewank function, figureFileSmall=HTngGhn0mLKzvCSa6ocUTg==, figureFileBig=kkfVymD33NlXOc/vWfR7Yw==, tableContent=null), ArticleFig(id=1322164795046998925, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图6, caption=Griewank函数收敛曲线, figureFileSmall=HTngGhn0mLKzvCSa6ocUTg==, figureFileBig=kkfVymD33NlXOc/vWfR7Yw==, tableContent=null), ArticleFig(id=1322164795156050830, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Fig.7, caption=Simulation results of each algorithm, figureFileSmall=X8UfrzKP1/Dm670SPFY/Aw==, figureFileBig=t3LmX02aiz6JZlso9dQ2sQ==, tableContent=null), ArticleFig(id=1322164795235742607, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=图7, caption=各算法的模拟结果, figureFileSmall=X8UfrzKP1/Dm670SPFY/Aw==, figureFileBig=t3LmX02aiz6JZlso9dQ2sQ==, tableContent=null), ArticleFig(id=1322164795344794512, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Table 1, caption=

Individual coding

, figureFileSmall=null, figureFileBig=null, tableContent=
采区采场编码
1#采区1#采场X1
2#采场X2
3#采场X3
4#采场X4
2#采区1#采场X5
2#采场X6
3#采场X7
4#采场X8
……
K#采区1#采场XN－3
2#采场XN－2
3#采场XN－1
4#采场XN
), ArticleFig(id=1322164795416097681, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=表1, caption=

个体编码

, figureFileSmall=null, figureFileBig=null, tableContent=
采区采场编码
1#采区1#采场X1
2#采场X2
3#采场X3
4#采场X4
2#采区1#采场X5
2#采场X6
3#采场X7
4#采场X8
……
K#采区1#采场XN－3
2#采场XN－2
3#采场XN－1
4#采场XN
), ArticleFig(id=1322164795499983762, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Table 2, caption=

Algorithm test parameters

, figureFileSmall=null, figureFileBig=null, tableContent=
种群数量/个最大迭代次数/次重复试验次数/次
501 00030
), ArticleFig(id=1322164795583869843, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=表2, caption=

算法测试参数设置

, figureFileSmall=null, figureFileBig=null, tableContent=
种群数量/个最大迭代次数/次重复试验次数/次
501 00030
), ArticleFig(id=1322164795760030612, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=EN, label=Table 3, caption=

Distribution of resources in mining areas

, figureFileSmall=null, figureFileBig=null, tableContent=
采区采场实际数量/t单价/（元/t）开采量/t
1#矿物2#矿物3#矿物
AA13 208.6362 581.73051.3220.2354.506
A26 898.7572 581.73054.9670.1103.898
A3545.9183 598.77550.9150.3931.709
BB1797.5511 877.62248.3960.2535.153
B22 079.6224 615.82028.2110.0640.022
B3204.5364 615.82027.9450.0940.019
CC11 962.6782 659.96440.7130.3606.135
C2260.019972.45222.7510.9080.049
DD1344.5751 237.66617.0710.5510.053
D21 129.9841 591.28418.7760.8640.055
D32 185.5832 510.69331.1140.5991.258
), ArticleFig(id=1322164795852305301, tenantId=1146029695717560320, journalId=1225396423026438145, articleId=1322164775333770000, language=CN, label=表3, caption=

矿区资源分布情况

, figureFileSmall=null, figureFileBig=null, tableContent=
采区采场实际数量/t单价/（元/t）开采量/t
1#矿物2#矿物3#矿物
AA13 208.6362 581.73051.3220.2354.506
A26 898.7572 581.73054.9670.1103.898
A3545.9183 598.77550.9150.3931.709
BB1797.5511 877.62248.3960.2535.153
B22 079.6224 615.82028.2110.0640.022
B3204.5364 615.82027.9450.0940.019
CC11 962.6782 659.96440.7130.3606.135
C2260.019972.45222.7510.9080.049
DD1344.5751 237.66617.0710.5510.053
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基于改进白鲸优化算法的矿山智能配矿技术研究
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王彦斌 1 , 李树芳 2 , 高婧琦 2 , 张磊 1
矿业研究与开发 | 矿山机电与矿业智能化 2025,45(11): 250-257
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矿业研究与开发 |矿山机电与矿业智能化 2025 , 45 (11) : 250 -257
基于改进白鲸优化算法的矿山智能配矿技术研究
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王彦斌（1982—），男，陕西府谷县人，硕士，工程师，主要从事信息化管理、5G在能源行业的应用及项目管理工作。E-mail：

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王彦斌1 , 李树芳2 , 高婧琦2, 张磊1
作者信息
  • 1.神东煤炭集团智能技术中心，陕西 榆林市　719315
  • 2.中国安全生产科学研究院，北京　100012
通讯作者:
李树芳（1993—），女，山西忻州人，工程师，主要研究方向为矿山安全、应急救援。E-mail：
作者简介:

王彦斌（1982—），男，陕西府谷县人，硕士，工程师，主要从事信息化管理、5G在能源行业的应用及项目管理工作。E-mail：

Research on Mine Intelligent Ore Blending Technology Based on Improved Beluga Whale Optimization Algorithm
Yanbin WANG1 , Shufang LI2 , Jingqi GAO2, Lei ZHANG1
Affiliations
  • 1.Guoneng Shendong Coal Intelligent Technology Center, Yulin, Shaanxi 719315, China
  • 2.China Academy of Safety Science and Technology, Beijing 100012, China
出版时间: 2025-11-25
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摘要
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为了提升矿山配矿效率和资源利用率，以白鲸优化算法（Beluga Whale Optimization，BWO）为基础算法，提出了一种结合混沌映射和Levy飞行策略的改进白鲸优化算法（IBWO），并与POS算法、WOA算法、SSA算法及BWO算法的性能进行对比。结果表明，相较于其他4种算法，IBWO算法的收敛速度和全局最优解搜索能力上表现出明显优势，收敛速度提升了31.2％~165.9％。配矿优化数值仿真试验结果表明，IBWO算法在迭代31次时平均利润为25.06万元，利润提高了14.69％~17.93％。研究结果为矿山配矿优化提供了新的解决路径，有望为矿业生产中的资源高效利用和经济效益提升提供理论基础。

矿山配矿  /  白鲸优化算法  /  混沌映射  /  Levy飞行策略  /  数值仿真

To enhance the efficiency of mine ore blending and resource utilization, based on the beluga whale optimization algorithm (BWO), an improved beluga whale optimization algorithm (IBWO) combining chaotic mapping and Levy flight strategy was proposed, and compared with POS algorithm, WOA algorithm, SSA algorithm and BWO algorithm. The results show that compared with the other four algorithms, the IBWO algorithm has obvious advantages in convergence speed and global optimal solution search ability, and the convergence speed is increased by 31.2％－165.9％. The numerical simulation results of ore blending optimization show that the average profit of IBWO algorithm is 25.06 million yuan at 31 iterations, and the profit is increased by 14.69％－17.93％. The research results provide a new solution path for the optimization of mine ore blending, and are expected to provide a theoretical basis for the efficient utilization of resources and the improvement of economic benefits in mining production.

Mine ore blending  /  Beluga whale optimization algorithm  /  Chaotic mapping  /  Levy flight strategy  /  Numerical simulation
王彦斌, 李树芳, 高婧琦, 张磊. 基于改进白鲸优化算法的矿山智能配矿技术研究. 矿业研究与开发, 2025 , 45 (11) : 250 -257 .
Yanbin WANG, Shufang LI, Jingqi GAO, Lei ZHANG. Research on Mine Intelligent Ore Blending Technology Based on Improved Beluga Whale Optimization Algorithm[J]. Mining Research and Development, 2025 , 45 (11) : 250 -257 .
正文
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0　引言
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随着矿产资源的不断消耗和矿产勘探难度的增加，矿业生产面临着越来越严峻的挑战。为了应对资源短缺和环保压力，不仅需要提高矿石开采的效率和资源利用率，还需尽可能降低对环境的影响[1]。配矿是指在矿山开采过程中，根据矿石的化学成分、物理性质、市场需求和生产工艺等因素，对不同类型的矿石进行合理组合和配置，以达到提升产品质量水平、增加资源利用效率、降低企业生产成本的效果。配矿是一个动态的过程，需要根据矿石的变化、市场需求的波动以及生产条件的变化进行实时调整，这要求矿山企业具备灵活的生产管理能力。现代配矿通常依赖于先进的技术和方法，包括数学模型、优化算法、数据分析等，通过合理配置矿石以减少废料和对环境的负面影响，促进矿业可持续发展[1-3]。
配矿是矿业生产中的重要环节，随着技术的进步和市场需求的变化，国内外配矿领域的发展现状呈现出不同的特点和趋势[4]。澳大利亚、加拿大和南非等国家积极引入和发展智能优化技术[5]，国内配矿技术也得到了迅速提升，配矿技术的研究与应用已取得了显著进展。李宁等[6]开发了一种基于遗传算法的配矿优化模型，通过对矿石成分的分析，实现配矿方案的优化，有效提高了矿石的资源利用效率，该研究结果表明，采用智能优化算法可以有效提高配矿效率和经济效益。何小龙等[7]基于遗传算法，设计了一种智能矿山自动配矿系统，实现了配矿后矿石多种成分含量与矿石质量标准偏差的最小化，该系统在满足出矿量、出矿比例等约束的同时，确定了各个采矿点的配矿比例。
尽管国内在配矿领域已取得了诸多进展，但仍面临着一些挑战。在技术方面，尽管智能优化算法的应用逐渐增多，但数据获取和处理的难题仍有待解决，以确保配矿决策的准确性和实时性。此外，配矿模型的复杂性和多样性也使得算法的设计和实现亟需进一步探究。因此，本文基于智能配矿优化技术，提出了一种结合混沌映射和Levy飞行策略的改进白鲸优化（Improved Beluga Whale Optimization，IBWO）算法，为矿山配矿优化提供了新的解决路径，同时也为矿业生产中的资源高效利用和经济效益提升提供了理论基础。
1　配矿优化模型构建
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配矿的主要目的是为了实现降本增效。本文以企业利润、能耗等为目标函数，同时考虑出矿量、设备生产能力和矿石需求等约束条件，构建了矿山配矿优化模型[8]。
（1）利润最大目标函数Pmax计算如式（1）所示。
式中：n为矿石的总类别（n＝1，2，3，…，M）；pn为第n种矿石的价格，元/t；xn为第n种矿石的开采量，t。
（2）能耗最小目标函数Emin计算如式（2）所示。
式中，en为第n种矿石的平均耗电量，（kW•h）/t。
（3）出矿量约束条件如式（3）和式（4）所示。在进行配矿的过程中，需考虑各个采区、采场出矿量的实际约束条件。每个采区、场区可以根据其生产资料和以往生产计划评估出最大出矿能力，配矿时受出矿能力的约束，分配给每个场区的出矿任务小于其预估的最大出矿量[4]。
式中：i为矿石的第i个采区（i＝1，2，3，…，I）；j为某采区第j个采场（j ＝1，2，3，…，J）；xi，j为第i个采区第j个采场的出矿量，t；Pi，j为第i个采区第j个采场的最大出矿量，t；Qi为第i个采区的最大出矿量，t。
（4）设备生产能力约束条件如式（5）所示。各类生产设备的性能对矿石的开采量有着显著的制约效果。设备的生产能力决定了一定时间内的开采效率，出矿点的铲装设备决定着矿石的产出量，破碎站的设备决定着矿石的处理速度。为了在达到任务需求的同时避免造成堆积，在配矿过程中，分配给每个采场的任务量需控制在设备产能之内[9]。
式中，Mi，j表示第i个采区第j个采场的生产设备单位开采周期内的最大产能，t。
（5）矿石需求约束条件如式（6）所示。配矿的根本目的是要通过合理搭配来达到预期的需求目标，各类矿石在各采区、采场的总量应该不小于该类矿石的总需求。
式中：rijk表示第i个采区第j个采场的第k类矿石的含量；Dk表示第k类矿石的总需求量。
2　BWO算法及其改进
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2.1　BWO算法构建
BWO算法是一种新兴的群体智能优化算法[9]。该算法的灵感来源于白鲸的社会行为和捕食策略，通过模拟白鲸的自然行为来解决复杂的优化问题。
社会行为：白鲸是一种高度社会化的动物，通常以群体形式生活，利用集体的智慧来寻找食物和避开捕食者。BWO算法模拟了这种群体行为，通过群体中的个体相互协作来探索解空间。
捕食策略：白鲸在捕食时会使用不同的策略，包括追逐猎物和利用声呐定位猎物。通过模拟捕食行为，BWO算法在解空间开展高效搜索，从而使该算法能够更有效地找到全局最优解。
位置更新机制：BWO算法通过特定的数学模型来更新个体（即白鲸）的位置信息，结合个体的历史信息和当前最优解的信息，以实现更高效的搜索。
BWO算法流程如图1所示，主要步骤如下。
（1）参数设置：首先需要设置算法的超参数，BWO算法的超参数主要有最大迭代次数Tmax、种群规模P、平衡因子Bf和鲸落概率Wf。
（2）种群初始化：根据设计的编码，使用初始化算子从解空间中随机生成一定数量符合约束条件的随机解，每个解代表一个白鲸个体。
（3）适应度计算：对于每个白鲸个体，根据设计的适应度函数逐个计算其适应度值，适应度越高代表白鲸个体越优秀，通过适应度对种群进行选择和更新。
（4）更新位置：更新位置包含了勘探、开发和鲸落3个阶段，BWO算法通过这3个阶段的操作不断更新每个白鲸的位置，从而实现了白鲸种群的移动，即随机解集合在解空间中的移动。
（5）更新最优解：在每次对白鲸个体进行位置更新时，检查位置更新后白鲸个体的适应度值，如果位置更新后的适应度值优于当前全体种群的适应度值，则将该位置更新后的白鲸个体作为全局最优个体，即全局最优解。
（6）迭代过程：重复步骤（3）至步骤（5），直到达到最大迭代次数或满足其他设置时停止条件。
BWO算法通过模拟白鲸的捕食和社会行为，结合个体和群体的动态调整，能够有效地在复杂的优化问题中寻找出最优解。
2.1.1　个体编码
根据实际配矿作业，对配矿方案采用实数编码。为保证普遍性，同时考虑K个采区，每个采区有N个采场，按照顺序逐个展开形成一维序列，并进行编码，个体编码情况见表1。
由表1可知，共有N个采场，对应的一个白鲸个体的编码如式（7）所示。
每个采场对应的开采量为Xn（n＝1，2，3，…，N）。例如：白鲸个体的编码为X＝[10，20，10，9，10]，则代表1#采场开采10 t，2#采场开采20 t，3#采场开采10 t，4#采场开采9 t，5#采场开采10 t。
2.1.2　种群初始化
白鲸搜索算法是一种随机进化算法，运用随机初始化的原理，具体步骤如下：
（1）根据设定的约束条件得到每个采场开采量的上下限；
（2）使用均匀分布得到一个随机解；
（3）检查步骤（2）产生的解是不是满足全部的约束条件；
（4）如果满足约束条件，则将解加入到初始种群中，如果不满足则舍弃；
（5）如果初始种群中的解达到了种群数量，则停止，否则重复步骤（2）至步骤（4）。
2.1.3　适应度函数
分别求两个目标函数属于多目标优化问题，相对比较复杂，为简化模型，采用线性加权法将两个目标函数进行融合，得到适应度函数如式（8）所示：
式中，P为单位电价，元/（kW•h）。
2.1.4　勘探算子
白鲸可以在不同的动作下进行社会性行为，比如两只白鲸可以同步行动也可以镜像行动，因此，勘探阶段的位置更新公式如式（9）和式（10）所示。
式中：表示更新后个体a在第b维上的取值；r是一个随机整数，表示随机选择一个个体；p是一个随机整数，表示随机选择一个维度；r1，r2均表示服从标准均匀分布的随机数。
2.1.5　开发算子
开发阶段描述了白鲸的捕食行为，白鲸在捕食时会相互分享位置信息，靠近猎物的白鲸会引导整个白鲸群体向着猎物的方向移动，如式（11）所示。
式中：表示更新后个体a；表示当代最优的个体；C1表示随机跳跃的强度；Lf表示Levy分布的随机数；r3，r4表示服从标准均匀分布的随机数。
2.1.6　鲸落算子
在白鲸算法中，白鲸有下坠的可能性，白鲸的下坠称为鲸落，鲸落算子则用来描述白鲸下坠的过程，如式（12）至式（15）所示。
式中：xstep为鲸落的步长；C2为下坠过程中随机跳跃的强度；UB为取值上限；LB为取值下限；Q是种群数量；t是当前迭代次数；T是最大迭代次数；r5，r6，r7均为服从标准均匀分布的随机数。
2.2　IBWO算法
为进一步提高BWO算法的性能，引入混沌系统来改进初始化算子，提高初始化种群分布的均匀性，同时通过引入Levy飞行策略，进一步提高BWO算法在进化过程中的搜索能力，最后通过一系列测试函数验证改进算法的有效性。
2.2.1　混沌映射初始化策略
混沌系统是指在一定条件下表现出高度不确定性和复杂行为的动态系统。尽管该系统的行为是由确定的规则（如微分方程）所驱动，但由于其具有敏感的初始条件和复杂的相互作用，导致难以预测长期行为。
混沌系统的基本特征主要有以下4点。
（1）敏感性。混沌系统对参数的初始值极为敏感，即某个参数的初始值发生极小的改变，也会导致混沌系统的演化发生巨大的变化，类似于“蝴蝶效应”。
（2）非线性。混沌系统通常呈现非线性特征，这表明系统的输出不是输入的简单线性组合。非线性特性使得系统的行为更加复杂。
（3）不确定性。混沌系统虽然由明确的方程描述，但其长期行为却是不可预测的，表现出随机性。
（4）自相似性。混沌系统的某些特征在不同的时间尺度上具有相似性，这种现象称为自相似性，可通过分形几何来描述。
混沌映射（如Logistic映射、Henon映射、Tent映射等）可以生成具有良好分布特性的随机数。这些映射的输出通常具有均匀性和不可预测性，适合作为初始化解的生成器[10-15]。Logistic映射如式（16）所示。
式中：X（h）、X（h+1）分别表示系统在h、h+1时刻的二维横坐标，X（h）在[0，1]区间内；X（h+1）表示第h步状态迭代得到的第h+1步状态；r为一个控制参数，r＝[0，4]，当r在[3.57，4]之间时，系统表现出混沌行为。
Henon映射是一个经典的二维离散混沌映射，具有自相似性和吸引子结构，其定义如式（17）和式（18）所示。
式中：Y（h）、Y（h+1）分别表示系统在h、h+1时刻的二维纵坐标；A和B为映射参数，通常取A＝1.4和B＝0.3。
Chebyshev映射定义如式（19）所示。
式中，c是映射参数，通常取c＝4。
在优化算法中，初始化算子的作用是生成初始解或解的种群。混沌系统的改进初始化算子通过利用混沌行为特性，生成多样化且均匀分布的初始解，有效提高了优化算法的全局搜索能力，避免了算法过早陷入局部最优解。
2.2.2　Levy飞行策略
Levy飞行是一种随机游走模型，可描述复杂系统中的随机运动，一般运用于生物学、物理学和优化算法中。Levy飞行的特点是其步长的分布遵循Levy分布，这种分布具有厚尾特性，意味着偶尔会出现非常长的步长，这使得其在探索大规模解空间时非常有效[16-17]。
Levy飞行的步长通常遵循Levy分布，其偶尔会进行长距离移动，这使得它能够有效地探索解空间，避免陷入局部最优解。Levy飞行在不同的时间尺度上表现出相似的行为，这种自相似性使其在复杂系统中具有广泛的适用性。
Levy飞行的生成可以通过以下步骤实现。
生成Levy分布的步长，利用Levy分布生成随机步长l，如式（20）所示。
式中：u和v是独立的随机变量，通常从标准正态分布中生成；β和α为调整参数。
更新当前位置x，其公式如式（21）所示。
式中，θ为单位向量，表示移动的方向。
Levy飞行通过长距离移动能够有效探索全局解空间，避免陷入局部最优。Levy飞行是一种强大的随机搜索策略，具有独特的长距离移动特性，适用于多种复杂系统的建模和优化。通过有效地探索解空间，Levy飞行在优化算法中的应用越来越受到重视。
2.3　算法性能对比
2.3.1　测试函数
测试函数是优化、数学分析和数值计算等领域中常用的概念，通常用于评估和比较优化算法的性能。测试函数是具有已知最优解的函数，可用于验证优化算法的有效性和效率。
测试函数是指在特定优化问题中选用的函数，通常具有以下特征：一是具有已知的最优解，测试函数的最优解是已知的，便于算法性能的评估；二是测试函数具有凸性、非凸性、平滑性、非平滑性等不同特性，可全面评估算法的性能；三是测试函数可为单变量或多变量，可用于测试算法在不同维度下的表现。通过选取5种测试函数对IBWO算法进行测试，具体使用函数如式（22）至式（26）所示。
Rosenbrock函数：
Rastrigin函数：
Schaffer函数：
Sphere函数：
Griewank函数：
2.3.2　测试结果分析
为了验证改进算法的有效性，对运行粒子群算法（PSO）、灰狼优化算法（WOA）、麻雀搜索算法（SSA）、BWO算法和使用混沌映射、Levy飞行等策略改进的IBWO算法在多个测试函数上进行测试，并进行横向对比，以此验证改进后算法的有效性。具体测试参数设置见表2。
本次试验使用的编程语言为Matlab 2023a。记录各个算法每一次独立运行的收敛曲线，将多次独立重复试验的结果取平均值，得到各个算法的平均收敛曲线。
Rosenbrock函数收敛曲线如图2所示。由图2可知，所有算法都在迭代过程中逐渐降低了适应度值，但收敛速度和最终达到的适应度值有所不同。其中，IBWO算法在前期下降趋势最快，迭代次数为600次时适应度值为1×10－22，而PSO算法的下降速度最慢，表明其在Rosenbrock函数上的性能较差。
Rastrigin函数收敛曲线如图3所示。由图3可知，5种算法都成功地找到了Rastrigin函数的近似最优解，其中，IBWO算法表现最好，迭代15次内适应度值就下降至1×10－4，表明其在寻找全局最优点方面非常高效，同时IBWO算法适应度值随迭代次数变化的曲线线性程度较好，表明IBWO算法运算过程稳定。
图4为Schaffer函数在不同优化算法下的测试平均收敛曲线。由图4可知，IBWO算法在初期有一个快速的下降过程，后期开始缓慢下降，在迭代761次后达到所有算法中的最低适应度值，此时IBWO算法适应度值随迭代次数变化的曲线线性程度较好。
Sphere函数收敛曲线如图5所示。由图5可知，IBWO算法在迭代600次时适应度值为1×10－167，小于其他算法迭代1 000次时的适应度值，表明IBWO算法表现最佳，BWO算法和SSA算法次之，PSO算法和WOA算法的性能较差。
Griewank函数测试平均收敛曲线如图6所示。由图6可知，在初始阶段（迭代次数<100），所有算法的适应度值都较高，说明各算法离最优解还有较大差距。在中期阶段（100≤迭代次数<600），随着迭代的进行，IBWO算法性能逐步提升，并显示出较强的竞争力。迭代1 000次时，适应度值约为3.1×10－5。IBWO算法优化效果较好，在整个迭代过程中始终保持着最快的下降速度，并最终实现了最低的适应度值。BWO、SSA、WOA和PSO算法虽然也有所改善，但它们的收敛速度和最终达到的适应度水平均不及IBWO算法。
综合分析可知，将采用混沌映射、Levy飞行等策略改进的IBWO算法和常用的PSO算法、WOA算法、SSA算法以及BWO算法进行横向对比，IBWO算法在5个测试函数上均取得最好的收敛效果。从收敛曲线上来看，IBWO算法的收敛速度相对其他算法也明显更快。
3　配矿优化仿真分析
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以某矿生产实际数据为例，验证IBWO算法在配矿优化方面的有效性。该矿各采区及采场的出矿能力见表3。
分别使用IBWO算法、PSO算法、WOA算法、SSA算法及BWO算法对配矿案例进行优化。其中，种群数量设置为100，迭代次数为200次，得到不同算法下的模拟结果如图7所示。由图7可知，IBWO算法在迭代31次时平均利润为25.06万元，相较于其他4种优化算法，利润提高了14.69％~17.93％，其搜索效率和搜索结果也明显优于其他算法，表明IBWO算法在搜索速度、最优解及稳定性方面均产生了优化效果。
4　结论
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（1）提出一种结合混沌映射和Levy飞行策略的IBWO算法，该算法结合了勘探、开发、鲸落等优化算子，有效提升了矿石开采方案的合理性和适应性。改进后IBWO算法的全局搜索能力得到了有效提升。
（2）将IBWO算法与POS算法、WOA算法、SSA算法及BWO算法的性能进行对比，发现IBWO算法的收敛速度提升了31.2％~165.9％，有效地缩短了优化时间，提升了全局最优解的准确度。
（3）在配矿优化的数值仿真试验中，IBWO算法在迭代了31次后平均利润为25.06万元，相较于其他4种配矿优化算法，利润提升了14.69％~17.93％。
（4）在矿山矿石资源调度中应用IBWO算法，尤其适用于应对矿石资源复杂布局和开发过程中存在的多目标优化问题。未来将结合实际矿山数据进行更深入的验证，以进一步提升矿山开采方案的合理性与实施效果。
基金
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  • 中国神华能源股份有限公司神东煤炭分公司科技创新项目(E210100270)
文献
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2025年第45卷第11期
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  • 接收时间：2024-10-12
  • 首发时间：2026-10-28
  • 出版时间：2025-11-25
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  • 收稿日期：2024-10-12
基金
中国神华能源股份有限公司神东煤炭分公司科技创新项目(E210100270)
作者信息
    1.神东煤炭集团智能技术中心，陕西 榆林市　719315
    2.中国安全生产科学研究院，北京　100012

通讯作者:

李树芳（1993—），女，山西忻州人，工程师，主要研究方向为矿山安全、应急救援。E-mail：
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2种不同金属材料的力学参数
科
Family		 属数
Number of
genus		 种数
Number of
species		 占总种数比例
Percentage of
total species (%)		 属
Genus		 种数
Number of
species		 占总种数比例
Percentage of total
species (%)
鹅膏菌科Amanitaceae 2 11 5.26 鹅膏菌属 Amanita 10 4.78
小菇科 Mycenaceae 2 12 5.74 丝盖伞属 Inocybe 5 2.39
多孔菌科 Polyporaceae 8 14 6.70 蜡蘑属 Laccaria 5 2.39
红菇科 Russulaceae 3 23 11.00 小皮伞属 Marasmius 6 2.87
小菇属 Mycena 11 5.26
光柄菇属 Pluteus 5 2.39
红菇属 Russula 17 8.13
栓菌属 Trametes 5 2.39
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