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Article(id=1147999676340630099, tenantId=1146029695717560320, journalId=1146123346816638986, issueId=1147999671055802382, articleNumber=1000-8063(2024)04-0025-08, orderNo=null, doi=10.13426/j.cnki.yky.2024.04.04, pmid=null, cstr=null, oa=null, hot=null, price=null, onlineType=0, articleFormat=0, articleType=null, articleTypeStr=null, receivedDate=1712246400000, receivedDateStr=2024-04-05, revisedDate=null, revisedDateStr=null, acceptedDate=null, acceptedDateStr=null, onlineDate=1751634051642, onlineDateStr=2025-07-04, pubDate=1732032000000, pubDateStr=2024-11-20, doiRegisterDate=null, doiRegisterDateStr=null, onlineIssueDate=1751634051642, onlineIssueDateStr=2025-07-04, onlineJustAcceptDate=null, onlineJustAcceptDateStr=null, onlineFirstDate=null, onlineFirstDateStr=null, sourceXml=null, magXml=null, createTime=1751634051642, creator=13701087609, updateTime=1751634051642, updator=13701087609, issue=Issue{id=1147999671055802382, tenantId=1146029695717560320, journalId=1146123346816638986, year='2024', volume='43', issue='4', pageStart='1', pageEnd='126', issueExtLink='null', onlineDate='null', pubDate='null', beforeIssueId=null, nextIssueId=null, price=null, status=1, issueComplete=1, articleOrder=1, issueType=-1, specialIssue=null, createTime=1751634050380, creator=13701087609, updateTime=1759123758692, updator=13701087609, preIssue=null, nextIssue=null, ext={EN=IssueExt(id=1179413784637617069, tenantId=1146029695717560320, journalId=1146123346816638986, issueId=1147999671055802382, language=EN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=), CN=IssueExt(id=1179413784641811374, tenantId=1146029695717560320, journalId=1146123346816638986, issueId=1147999671055802382, language=CN, specialIssueTitle=, coverIllustrator=null, specialIssueEditor=, specialIssueAbout=)}, issueFiles=null}, startPage=25, endPage=32, ext={EN=ArticleExt(id=1147999676659397222, articleId=1147999676340630099, tenantId=1146029695717560320, journalId=1146123346816638986, language=EN, title=Multi-objective Optimization Method for Ore Blending of Open-pit Mine Based on SPEA2 and Entropy-weighted TOPSIS, columnId=1175805041752556213, journalTitle=Uranium Mining and Metallurgy, columnName=MINING AND HYDROMETALLURGY, runingTitle=null, highlight=null, articleAbstract=

Aiming at the optimization problem of ore blending for multi-metal in open-pit mine, a multi-objective optimization mathematical model for ore blending of multi-metal in open-pit mine is established, which takes the minimum ore grade deviation and the lowest production cost as the optimization objectives, and comprehensively considers various constraints such as production capacity of ore point, ore output, ore grade, oxidation rate, equipment production capacity and quantity, lithology and beneficiation process requirements. A multi-objective optimization method for ore blending of multi-metal in open-pit mine based on SPEA2 and entropy weighted TOPSIS is proposed. The method is applied to the optimization of ore matching in Shangfanggou molybdenum mine. The results show that compared with the original ore blending plan, the ore grade deviation of the optimized ore blending plan is reduced by 73.60%, and the production cost is reduced by 20.99%.

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周晓将(1981—),男,河南洛阳人,学士,高级工程师,主要从事生产及配矿管理工作。

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周晓将(1981—),男,河南洛阳人,学士,高级工程师,主要从事生产及配矿管理工作。

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周晓将(1981—),男,河南洛阳人,学士,高级工程师,主要从事生产及配矿管理工作。

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Energy, 2020,201:117675., articleTitle=Multi-criteria decision based waste to energy technology selection using entropy-weighted topsis technique: the case study of lagos, nigeria, refAbstract=null)], funds=null, companyList=[AuthorCompany(id=1179500572119020214, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, xref=1, ext=[AuthorCompanyExt(id=1179500572127408823, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, companyId=1179500572119020214, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 Luoyang Fuchuan Mining Co., Ltd., Luoyang 471500, China), AuthorCompanyExt(id=1179500572135797432, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, companyId=1179500572119020214, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=1 洛阳富川矿业有限公司, 河南 洛阳 471500)]), AuthorCompany(id=1179500572211294906, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, xref=2, ext=[AuthorCompanyExt(id=1179500572219683514, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, companyId=1179500572211294906, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 China Molybdenum Group Co., Ltd., Luoyang 471500, China), AuthorCompanyExt(id=1179500572223877819, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, companyId=1179500572211294906, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=2 洛阳栾川钼业集团股份有限公司, 河南 洛阳 471500)]), AuthorCompany(id=1179500572282598077, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, xref=3, ext=[AuthorCompanyExt(id=1179500572286792382, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, companyId=1179500572282598077, language=EN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=3 Changsha Dimine Co., Ltd., Changsha 410221, China), AuthorCompanyExt(id=1179500572299375295, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, companyId=1179500572282598077, language=CN, country=null, province=null, city=null, postcode=null, companyName=null, departmentName=null, remark=3 长沙迪迈科技股份有限公司, 湖南 长沙 410221)])], figs=[ArticleFig(id=1179500574572688123, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=EN, label=Fig. 1, caption=Flowchart of multi-objective optimization method for refined ore blending of multiple metals in open-pit mines, figureFileSmall=bqSKB10mTZnWurcc3qtS2w==, figureFileBig=uvabz0q6EAxE5l0UespLRw==, tableContent=null), ArticleFig(id=1179500574627214077, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=CN, label=图1, caption=露天矿多金属精细化配矿多目标优化方法流程图, figureFileSmall=bqSKB10mTZnWurcc3qtS2w==, figureFileBig=uvabz0q6EAxE5l0UespLRw==, tableContent=null), ArticleFig(id=1179500574723683071, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=EN, label=Fig. 2, caption=Top view of Shangfanggou molybdenum mine, figureFileSmall=fX3vPa6G1K9uclIJ76hlcw==, figureFileBig=qMqQAV0muBWe2V6BXZmDOw==, tableContent=null), ArticleFig(id=1179500574803374849, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=CN, label=图2, caption=上房沟钼矿俯视图, figureFileSmall=fX3vPa6G1K9uclIJ76hlcw==, figureFileBig=qMqQAV0muBWe2V6BXZmDOw==, tableContent=null), ArticleFig(id=1179500574929203971, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=EN, label=Table 1, caption=

The mineral grade, lithology and distance from the receiving point of the mining site

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出矿点编号 钼品位/% 磁铁品位/% 滑石品位/% 氧化率/% 岩性 与受矿点的距离/km
24-1215-2-1 0.342 5.72 9.96 8.56 花岗斑岩 1.25
24-1230-3-1 0.240 12.22 15.36 4.16 蚀变碳酸盐岩 1.30
24-1230-5-1 0.081 14.78 15.49 4.95 蚀变碳酸盐岩 1.19
24-1230-6-1 0.086 1.58 11.21 2.12 花岗斑岩 1.15
24-1230-7-1 0.118 5.04 13.93 3.68 蚀变碳酸盐岩 1.15
24-1230-7-3 0.095 15.07 17.67 3.59 蚀变碳酸盐岩 1.20
24-1260-4 0.089 1.80 5.80 10.88 蚀变碳酸盐岩 1.00
24-1275-3 0.113 0.89 9.63 5.61 辉长岩 0.35
24-1335-3 0.067 0.80 7.98 1.77 辉长岩 0.80
24-1335-4 0.102 0.81 6.92 7.50 辉长岩 0.85
), ArticleFig(id=1179500575004701445, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=CN, label=表1, caption=

出矿点的矿物品位、岩性及其与受矿点的距离

, figureFileSmall=null, figureFileBig=null, tableContent=
出矿点编号 钼品位/% 磁铁品位/% 滑石品位/% 氧化率/% 岩性 与受矿点的距离/km
24-1215-2-1 0.342 5.72 9.96 8.56 花岗斑岩 1.25
24-1230-3-1 0.240 12.22 15.36 4.16 蚀变碳酸盐岩 1.30
24-1230-5-1 0.081 14.78 15.49 4.95 蚀变碳酸盐岩 1.19
24-1230-6-1 0.086 1.58 11.21 2.12 花岗斑岩 1.15
24-1230-7-1 0.118 5.04 13.93 3.68 蚀变碳酸盐岩 1.15
24-1230-7-3 0.095 15.07 17.67 3.59 蚀变碳酸盐岩 1.20
24-1260-4 0.089 1.80 5.80 10.88 蚀变碳酸盐岩 1.00
24-1275-3 0.113 0.89 9.63 5.61 辉长岩 0.35
24-1335-3 0.067 0.80 7.98 1.77 辉长岩 0.80
24-1335-4 0.102 0.81 6.92 7.50 辉长岩 0.85
), ArticleFig(id=1179500575067616006, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=EN, label=Table 2, caption=

Pareto-optimal set

, figureFileSmall=null, figureFileBig=null, tableContent=
熵加权
TOPSIS排序		 矿石品位
偏差/%		 运输成本/元 计划类型 熵加权
TOPSIS排序		 矿石品位
偏差/%		 运输成本/元 计划类型
原配矿计划 2.636 7 5 797.25 不脱泥 18 0.520 8 4 595.60 脱泥
1 0.696 0 4 580.28 脱泥 19 0.514 5 4 599.06 脱泥
2 0.680 7 4 582.45 脱泥 20 0.441 2 4 601.41 脱泥
3 0.678 1 4 583.87 脱泥 21 0.210 5 4 607.34 脱泥
4 0.534 5 4 587.62 脱泥 22 0.440 9 4 602.88 脱泥
5 0.675 8 4 585.60 脱泥 23 0 4 614.67 脱泥
6 0.528 3 4 589.16 脱泥 24 0.210 4 4 609.27 脱泥
7 1.030 3 4 577.67 不脱泥 25 0.202 8 4 610.98 脱泥
8 0.525 5 4 590.65 脱泥 26 0.436 4 4 605.69 脱泥
9 0.522 1 4 593.95 脱泥 27 0.202 1 4 612.76 脱泥
), ArticleFig(id=1179500575143113480, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=CN, label=表2, caption=

Pareto最优解集

, figureFileSmall=null, figureFileBig=null, tableContent=
熵加权
TOPSIS排序		 矿石品位
偏差/%		 运输成本/元 计划类型 熵加权
TOPSIS排序		 矿石品位
偏差/%		 运输成本/元 计划类型
原配矿计划 2.636 7 5 797.25 不脱泥 18 0.520 8 4 595.60 脱泥
1 0.696 0 4 580.28 脱泥 19 0.514 5 4 599.06 脱泥
2 0.680 7 4 582.45 脱泥 20 0.441 2 4 601.41 脱泥
3 0.678 1 4 583.87 脱泥 21 0.210 5 4 607.34 脱泥
4 0.534 5 4 587.62 脱泥 22 0.440 9 4 602.88 脱泥
5 0.675 8 4 585.60 脱泥 23 0 4 614.67 脱泥
6 0.528 3 4 589.16 脱泥 24 0.210 4 4 609.27 脱泥
7 1.030 3 4 577.67 不脱泥 25 0.202 8 4 610.98 脱泥
8 0.525 5 4 590.65 脱泥 26 0.436 4 4 605.69 脱泥
9 0.522 1 4 593.95 脱泥 27 0.202 1 4 612.76 脱泥
), ArticleFig(id=1179500575210222345, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=EN, label=Table 3, caption=

Original ore blending plan and optimal ore blending plan

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出矿点编号 计划量/t
原配矿计划 最优配矿计划
24-1215-2-1 750 0
24-1230-3-1 0 331
24-1230-5-1 0 415
24-1230-6-1 0 0
24-1230-7-1 0 1 254
24-1230-7-3 0 0
24-1260-4 1 750 0
24-1275-3 1 000 3 000
24-1335-3 0 0
24-1335-4 1 500 0
), ArticleFig(id=1179500575294108427, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=CN, label=表3, caption=

原配矿计划与最优配矿计划

, figureFileSmall=null, figureFileBig=null, tableContent=
出矿点编号 计划量/t
原配矿计划 最优配矿计划
24-1215-2-1 750 0
24-1230-3-1 0 331
24-1230-5-1 0 415
24-1230-6-1 0 0
24-1230-7-1 0 1 254
24-1230-7-3 0 0
24-1260-4 1 750 0
24-1275-3 1 000 3 000
24-1335-3 0 0
24-1335-4 1 500 0
), ArticleFig(id=1179500575361217293, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=EN, label=Table 4, caption=

The values of various indicators in the ore blending plan

, figureFileSmall=null, figureFileBig=null, tableContent=
项目 矿石品位偏差/% 运输成本/元 钼品位/% 磁铁品位/% 滑石品位/% 氧化率/% 计划类型
原配矿计划 2.636 7 5 797.25 0.135 7 1.909 4 7.526 3 8.464 1 不脱泥
最优配矿计划 0.696 0 4 580.28 0.120 0 3.834 0 11.574 2 4.975 2 脱泥
), ArticleFig(id=1179500575449297679, tenantId=1146029695717560320, journalId=1146123346816638986, articleId=1147999676340630099, language=CN, label=表4, caption=

配矿计划各项指标值

, figureFileSmall=null, figureFileBig=null, tableContent=
项目 矿石品位偏差/% 运输成本/元 钼品位/% 磁铁品位/% 滑石品位/% 氧化率/% 计划类型
原配矿计划 2.636 7 5 797.25 0.135 7 1.909 4 7.526 3 8.464 1 不脱泥
最优配矿计划 0.696 0 4 580.28 0.120 0 3.834 0 11.574 2 4.975 2 脱泥
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基于SPEA2和熵加权TOPSIS的露天矿配矿多目标优化方法
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周晓将 1, 2 , 刘鹏程 1, 2 , 文历学 3 , 赵松阳 1, 2
铀矿冶 | 开采·选冶 2024,43(4): 25-32
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铀矿冶 | 开采·选冶 2024, 43(4): 25-32
基于SPEA2和熵加权TOPSIS的露天矿配矿多目标优化方法
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周晓将1, 2, 刘鹏程1, 2, 文历学3, 赵松阳1, 2
作者信息
  • 1 洛阳富川矿业有限公司, 河南 洛阳 471500
  • 2 洛阳栾川钼业集团股份有限公司, 河南 洛阳 471500
  • 3 长沙迪迈科技股份有限公司, 湖南 长沙 410221

    • 周晓将(1981—),男,河南洛阳人,学士,高级工程师,主要从事生产及配矿管理工作。

Multi-objective Optimization Method for Ore Blending of Open-pit Mine Based on SPEA2 and Entropy-weighted TOPSIS
Xiaojiang ZHOU1, 2, Pengcheng LIU1, 2, Lixue WEN3, Songyang ZHAO1, 2
Affiliations
  • 1 Luoyang Fuchuan Mining Co., Ltd., Luoyang 471500, China
  • 2 China Molybdenum Group Co., Ltd., Luoyang 471500, China
  • 3 Changsha Dimine Co., Ltd., Changsha 410221, China
出版时间: 2024-11-20 doi: 10.13426/j.cnki.yky.2024.04.04
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摘要
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以矿石品位偏差最小、运输成本最低为优化目标,对露天矿多金属精细化配矿问题进行优化,综合考虑出矿点生产能力、矿石产量、矿石品位、氧化率、设备生产能力及其数量、岩性和选矿工艺要求等多种约束条件,建立了露天矿多金属精细化配矿多目标优化数学模型,提出了一种基于SPEA2和熵加权TOPSIS的露天矿多金属精细化配矿多目标优化方法,并将该方法应用于上房沟钼矿的配矿优化。结果表明:与原配矿计划相比,优化后的配矿计划使矿石品位偏差降低了73.60%,运输成本降低了20.99%。
配矿优化  /  SPEA2  /  熵加权TOPSIS  /  多目标优化  /  钼矿  /  多金属矿

Aiming at the optimization problem of ore blending for multi-metal in open-pit mine, a multi-objective optimization mathematical model for ore blending of multi-metal in open-pit mine is established, which takes the minimum ore grade deviation and the lowest production cost as the optimization objectives, and comprehensively considers various constraints such as production capacity of ore point, ore output, ore grade, oxidation rate, equipment production capacity and quantity, lithology and beneficiation process requirements. A multi-objective optimization method for ore blending of multi-metal in open-pit mine based on SPEA2 and entropy weighted TOPSIS is proposed. The method is applied to the optimization of ore matching in Shangfanggou molybdenum mine. The results show that compared with the original ore blending plan, the ore grade deviation of the optimized ore blending plan is reduced by 73.60%, and the production cost is reduced by 20.99%.

ore blending optimization  /  SPEA2  /  entropy-weighted TOPSIS  /  multi-objective optimization  /  molybdenum mine  /  multi-metal mine
周晓将, 刘鹏程, 文历学, 赵松阳. 基于SPEA2和熵加权TOPSIS的露天矿配矿多目标优化方法. 铀矿冶, 2024 , 43 (4) : 25 -32 . DOI: 10.13426/j.cnki.yky.2024.04.04
Xiaojiang ZHOU, Pengcheng LIU, Lixue WEN, Songyang ZHAO. Multi-objective Optimization Method for Ore Blending of Open-pit Mine Based on SPEA2 and Entropy-weighted TOPSIS[J]. Uranium Mining and Metallurgy, 2024 , 43 (4) : 25 -32 . DOI: 10.13426/j.cnki.yky.2024.04.04
正文
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矿石品位直接决定矿石的经济价值,通过配矿可将不同品位、不同组分的矿石进行搭配,从而得到品位稳定且符合选矿工艺需求的矿石产品。通过配矿可以提高资源利用率,减少资源浪费,为矿产企业带来更高的经济效益。另外,运输成本在露天开采生产成本中占比较大,通过配矿可以优化矿石运输方案,减少不必要的运输距离和班次,从而降低矿产企业的生产成本。因此,露天矿配矿优化问题一直是露天开采领域的研究热点。通过科学合理的配矿,可提高矿石品位、实现资源综合利用、降低运输成本、推进矿产企业的可持续发展。
目前露天矿短期配矿优化研究主要以单目标优化为主。赵海云等[1]以企业的综合利润指标最高为目标函数,建立线性规划模型;胡乃联等[2]以采掘和运输作业成本最小为优化目标,构建露天矿生产作业计划模型;王李管等[3]以品位均衡为优化目标,建立基于目标规划的露天矿配矿优化模型。学者大多采用线性规划的方法进行求解[4-6];但该法仅能处理单目标优化问题,且对于约束处理存在限制,使得该法的应用受限。
随着多目标智能优化算法的发展和对配矿要求的不断提高,研究者建立了多目标露天矿配矿优化模型。顾清华等[7]构建了以运输功和配矿品位偏差最小为目标函数的多目标短期配矿模型,并采用其改进的粒子群算法进行求解;顾清华等[8]以品位偏差、矿石岩性百分比偏差、总产量偏差和采掘运输成本为优化目标,构建了基于采选流程的多金属多目标配矿优化数学模型,并提出一种自适应遗传算法进行求解;黄麟淇等[9]以矿石品位波动、采掘运输成本、矿石产量为优化目标,建立多目标精细化配矿模型,并采用Matlab中的自适应遗传算法进行求解。但这些研究大都采用加权法或理想点法(TOPSIS)将多目标优化问题转化为单目标优化,这使得各优化目标的权重设置直接影响优化结果,可能导致更优解被忽略。
基于此,笔者以矿石品位偏差最小、运输成本最低为优化目标,综合考虑出矿点生产能力、矿石产量、矿石品位、氧化率、设备生产能力及其数量、岩性和选矿工艺要求等多种约束条件,建立露天矿精细化配矿多目标优化模型,并提出一种基于SPEA2和熵加权TOPSIS的露天矿多金属精细化配矿多目标优化方法。该方法首先采用SPEA2算法求解多目标优化模型的Pareto最优解集,然后通过熵加权TOPSIS优选出最优配矿方案。
1 露天矿多金属精细化配矿多目标优化模型
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1.1 优化目标
1.1.1 矿石品位偏差最小
配矿的目的是将不同品位、不同组分的矿石进行搭配,以确保输出产品的质量稳定并符合选矿工艺需求。配矿质量的好坏直接关系到磨矿、选矿流程,进而影响整个矿山的生产效率和经济效益。矿石品位偏差(f1)最小可表示为
$\mathrm{m}\mathrm{i}\mathrm{n}{f}_{1}=\frac{\stackrel{l}{\sum _{k=1}}\stackrel{m}{\sum _{i=1}}\stackrel{n}{\sum _{j=1}}\left|({g}_{ik}-{G}_{jk}){x}_{ij}\right|}{\stackrel{m}{\sum _{i=1}}\stackrel{n}{\sum _{j=1}}{x}_{ij}}$
式中:xij为出矿点i到受矿点j的运输量,t;gik为出矿点i中k类矿石的供矿品位,%;Gik为受矿点j中k类矿石的目标品位,%。
1.1.2 运输成本最低
大型露天矿一般有多个出矿点和受矿点,在制定运输方案时,需要综合考虑多种因素。每个出矿点到受矿点的距离不同,运输费用也不同,因此合理安排每个出矿点到受矿点的矿量,对于控制整个生产作业的运输成本至关重要。运输成本(f2)最低可表示为
$\mathrm{m}\mathrm{i}\mathrm{n}{f}_{2}=\stackrel{n}{\sum _{j=1}}\stackrel{n}{\sum _{i=1}}b{L}_{ij}{x}_{ij}+\frac{{x}_{ij}}{d}c{L}_{ij}$
式中:b为重载运输成本,元/(km·t);d为汽车载重量,t;c为空载运输成本,元/(km·t);Lij为出矿点i到受矿点j的距离,km。
1.2 约束条件
1.2.1 出矿点生产能力约束
露天矿山的生产作业需要在保证安全、效率和经济效益之间找到平衡点。为避免超前开采并确保企业的稳定收益,对采场出矿量的控制至关重要。采场的出矿量必须严格控制在最大允许采掘量和最小允许采掘量之间。
${Q}_{i\mathrm{m}\mathrm{i}\mathrm{n}}\le \stackrel{n}{\sum _{j=1}}{x}_{ij}\le {Q}_{i\mathrm{m}\mathrm{a}\mathrm{x}}$
式中:Qimin、Qimax分别为出矿点i的最小和最大允许采掘量,t。
1.2.2 矿石产量约束
在短期的配矿计划中,所采的矿石必须达到作业周期内的目标产量。
$\stackrel{n}{\sum _{j=1}}\stackrel{m}{\sum _{i=1}}{x}_{ij}\ge B$
式中:B为短期配矿计划的矿石产量的目标产量,t。
1.2.3 矿石品位约束
在配矿过程中,需要充分考虑不同矿石品位的差异,通过合理的搭配和混合,使最终输出的矿石品位满足生产要求。矿石的品位需要尽可能处于目标范围内。
${g}_{k\mathrm{m}\mathrm{i}\mathrm{n}}\le \frac{\stackrel{n}{\sum _{j=1}}\stackrel{m}{\sum _{i=1}}{x}_{ij}{g}_{ik}}{\stackrel{n}{\sum _{j=1}}\stackrel{m}{\sum _{i=1}}{x}_{ij}}\le {g}_{k\mathrm{m}\mathrm{a}\mathrm{x}}$
式中:gkmin、gkmax分别为k类矿石的最低品位和最高品位要求,%。
1.2.4 氧化率约束
氧化率是指矿石中金属元素或有用组分因氧化作用而降低的含量比例,它直接关系到矿石的质量、加工难度以及最终产品的价值。因此,在露天矿配矿过程中,必须严格控制氧化率,确保配出的矿石满足生产要求。
$\frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}{O}_{i}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}\le R$
式中:Oi为出矿点i的矿石氧化率,%;R为氧化率允许的最大限值,%。
1.2.5 设备生产能力及其数量约束
设备生产能力决定了在特定时间内可以处理多少矿石,进而影响到配矿的效率和整体生产进度。因此,在配矿过程中,必须充分考虑设备生产能力的约束,以确保配矿工作的顺利进行。
$\stackrel{n}{\sum _{j=1}}{x}_{ij}\le {M}_{i}$
$\stackrel{m}{\sum _{i=1}}{x}_{ij}\le {N}_{j}$
式中:Mi为出矿点i的铲装能力,t;Nj为受矿点j的破碎能力,t。
受到供矿挖机数量的限制,每个计划周期内的出矿点数量必须少于供矿挖机数量。
$\stackrel{m}{\sum _{i=1}}\stackrel{n}{\sum _{j=1}}{e}_{ij}\le E$
${e}_{ij}=\left\{\begin{array}{l}1,{x}_{ij}\ne 0\\ 0,{x}_{ij}=0\end{array}\right.$
式中:eij为出矿点i是否向受矿点j供矿;E为供矿挖机的数量。
1.2.6 岩性约束
不同岩性的矿石具有不同的硬度和强度。岩性的硬度和强度直接影响到碎矿过程中所需的能量消耗以及所选择的破碎设备。受到破碎设备的限制,精细化配矿还需满足岩性约束。
$\frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}Roc{k}_{ip}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}\le {\stackrel{-}{p}}_{jp}$
$Roc{k}_{ip}=\left\{\begin{array}{l}1,\mathrm{出}\mathrm{矿}\mathrm{点}i\mathrm{的}\mathrm{岩}\mathrm{性}\mathrm{是}\mathrm{第}p\mathrm{类}\mathrm{岩}\mathrm{性}\\ 0,\mathrm{出}\mathrm{矿}\mathrm{点}i\mathrm{的}\mathrm{岩}\mathrm{性}\mathrm{不}\mathrm{是}\mathrm{第}p\mathrm{类}\mathrm{岩}\mathrm{性}\end{array}\right.$
式中:Rockip为出矿点i的岩性;pjp为受矿点j允许的第p类矿石的含量,%。
1.2.7 滑石含量约束
受到选矿厂选矿工艺的影响,配矿计划分为不脱泥配矿计划和脱泥配矿计划。不脱泥配矿计划要求滑石含量小于10%,脱泥配矿计划要求滑石含量大于10%。
$\frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}{T}_{i}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}<\mathrm{ }10\mathrm{\%}\mathrm{ }\mathrm{o}\mathrm{r}\frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}{T}_{i}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}\ge 10\mathrm{\%}$
式中:Ti为出矿点i中滑石含量,%。
2 露天矿多金属精细化配矿多目标优化数学模型
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基于SPEA2和熵加权TOPSIS算法建立露天矿精细化配矿多目标优化模型,该模型可以表示为
$\begin{array}{l}\mathrm{m}\mathrm{i}\mathrm{n}F=[{f}_{1},{f}_{2}]\\ \begin{array}{c}s.t.\left\{\begin{array}{l}{Q}_{i\mathrm{m}\mathrm{i}\mathrm{n}}\le \stackrel{n}{\sum _{j=1}}{x}_{ij}\le {Q}_{i\mathrm{m}\mathrm{a}\mathrm{x}}\\ \stackrel{n}{\sum _{j=1}}\stackrel{m}{\sum _{i=1}}{x}_{ij}\ge B\\ {g}_{k\mathrm{m}\mathrm{i}\mathrm{n}}\le \frac{\stackrel{n}{\sum _{j=1}}\stackrel{m}{\sum _{i=1}}{x}_{ij}{g}_{ik}}{\stackrel{n}{\sum _{j=1}}\stackrel{m}{\sum _{i=1}}{x}_{ij}}\le {g}_{k\mathrm{m}\mathrm{a}\mathrm{x}}\\ \frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}{O}_{i}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}\le R\\ \stackrel{n}{\sum _{j=1}}{x}_{ij}\le {M}_{i}\\ \stackrel{m}{\sum _{i=1}}{x}_{ij}\le {N}_{j}\\ \frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}Roc{k}_{ip}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}\le {\stackrel{-}{p}}_{jp}\\ \stackrel{m}{\sum _{i=1}}\stackrel{n}{\sum _{j=1}}{e}_{ij}\le E\\ \frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}{T}_{i}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}<\mathrm{ }10\mathrm{\%}\mathrm{ }\mathrm{o}\mathrm{r}\frac{\stackrel{m}{\sum _{i=1}}{x}_{ij}{T}_{i}}{\stackrel{m}{\sum _{i=1}}{x}_{ij}}\ge 10\mathrm{\%}\end{array}\right.\end{array}\end{array}$。
2.1 SPEA2算法
Zitzler等学者于2001年对SPEA[10](Strength Pareto Evolutionary Algorithm)进行了改进,在适应度分配策略、个体分布性的评估方法,以及非支配集的调整等方面进行改进,改进后的算法称为SPEA2[11]。SPEA2较传统进化算法具有更好的收敛性和更均匀广泛的分布性,其具体步骤如下。
Step 1:种群初始化。产生一个初始群体P0,同时使归档集Q0为空。
Step 2:适应度分配。根据SPEA2的适应度分配策略,计算Pt和Qt中所有个体的适应度。
Step 3:环境选择。将Pt和Qt中所有非支配个体保存到Qt+1中。若Qt+1的大小超过归档集最大容量N,则利用修剪操作降低其大小;否则,从Pt和Qt中选取支配个体填满Qt+1。
Step 4:终止条件。若t>T,或其他终止条件满足,Qt+1中的所有非支配个体作为返回结果;否则,执行Step 5。
Step 5:配对选择。对Qt+1执行二元锦标赛选择。
Step 6:进化操作。对Qt+1执行交叉、变异操作,并将结果保存到Pt中,t=t+1,转Step 2。
2.2 熵加权TOPSIS
熵权法是一种基于信息熵理论的客观赋权方法,通过计算每个指标的信息熵和信息效用值,来确定每个指标的权重[12]。熵权法根据数据的变异程度进行赋权,能够避免主观赋权的随意性。TOPSIS是一种逼近理想解排序法,通过计算评价对象与最优方案和最劣方案之间的距离,得出评价对象与最优方案的相对接近程度,从而进行排序[13]。TOPSIS能够充分利用原始数据的信息,使得结果精确反映各方案之间的差距。熵加权TOPSIS算法通过将熵权法和TOPSIS法相结合,利用熵权法确定各指标的权重,然后将权重应用于TOPSIS的计算过程中[14-16]。熵加权TOPSIS算法,既能充分考虑数据的客观信息,又能准确反映各评价方案之间的差距,使得评价结果更加客观和准确;用于确定Pareto最优解集中最优方案的熵加权TOPSIS算法如下。
Step 1:构造原始决策矩阵,即Pareto最优解集。原始决策矩阵可表示为
$F=\left[\begin{array}{llll}{f}_{11}& {f}_{12}& \dots & {f}_{1m}\\ {f}_{21}& {f}_{22}& \dots & {f}_{2m}\\ ︙& ︙& ︙& ︙\\ {f}_{n1}& {f}_{n2}& \dots & {f}_{nm}\end{array}\right]$
式中:F初始决策矩阵,即Pareto最优解集;fij表示第i个方案中第j个优化目标的值,i=1,2,…,n,j=1,2,…,m。
Step 2:决策矩阵归一化。为了消除决策矩阵中各个元素的单位不同,根据式(16)对决策矩阵进行归一化处理。
${\stackrel{-}{f}}_{ij}=\frac{{f}_{ij}}{\sqrt{{\sum }_{i=1}^{m}({f}_{ij}{)}^{2}}}$
Step 3:计算优化目标的比重。设pij为第i个方案中第j个优化目标值在该优化目标总和中的比重,其计算式为
${p}_{ij}=\frac{{f}_{ij}}{{\sum }_{i=1}^{n}{f}_{ij}}$
Step 4:计算熵值和变异程度。根据式(18)和式(19)分别计算各个优化目标的熵值和变异程度。
${E}_{j}=\frac{1}{\mathrm{l}\mathrm{n}m}\stackrel{n}{\sum _{i=1}}{p}_{ij}\mathrm{l}\mathrm{n}{p}_{ij}$
Dj=1-Ej,(19)
式中:Ej为第j个优化目标的熵值;Dj表示第j个优化目标的变异程度。
Step 5:计算各个优化目标的熵权。熵权越大,表示该优化目标越重要,对Pareto最优解集中的方案影响力越大。
${W}_{j}=\frac{{D}_{j}}{\stackrel{m}{\sum _{j=1}}{D}_{j}},$
式中:Wj为第j个优化目标的熵权。
Step 6:构造加权归一化决策矩阵。
$R=\left[\begin{array}{llll}{\stackrel{-}{f}}_{11}& {\stackrel{-}{f}}_{12}& \dots & {\stackrel{-}{f}}_{1m}\\ {\stackrel{-}{f}}_{21}& {\stackrel{-}{f}}_{22}& \dots & {\stackrel{-}{f}}_{2m}\\ ︙& ︙& ︙& ︙\\ {\stackrel{-}{f}}_{n1}& {\stackrel{-}{f}}_{n2}& \dots & {\stackrel{-}{f}}_{nm}\end{array}\right]\times [{W}_{1},{W}_{2},\dots,{W}_{m}]=\left[\begin{array}{llll}{W}_{1}{\stackrel{-}{f}}_{11}& {W}_{2}{\stackrel{-}{f}}_{12}& \dots & {W}_{m}{\stackrel{-}{f}}_{1m}\\ {W}_{1}{\stackrel{-}{f}}_{21}& {W}_{2}{\stackrel{-}{f}}_{22}& \dots & {W}_{m}{\stackrel{-}{f}}_{2m}\\ ︙& ︙& ︙& ︙\\ {W}_{1}{\stackrel{-}{f}}_{n1}& {W}_{2}{\stackrel{-}{f}}_{n2}& \dots & {W}_{m}{\stackrel{-}{f}}_{nm}\end{array}\right]$
式中:R为加权归一化决策矩阵。
Step 7:根据式(22)和式(23)确定正理想解和负理想解。
${R}_{j}^{+}=\mathrm{m}\mathrm{i}{\mathrm{n}}_{i}\{{W}_{j}{\stackrel{-}{f}}_{ij},i=\mathrm{1,2},\dots,n\}$
${R}_{j}^{-}=\mathrm{m}\mathrm{a}{\mathrm{x}}_{i}\{{W}_{j}{\stackrel{-}{f}}_{ij},i=\mathrm{1,2},\dots,n\}$
式中:${R}_{j}^{+}$和 ${R}_{j}^{-}$分别为第j个优化目标的正理想解和负理想解。
Step 8:根据式(24)和式(25)计算各解决方案到正理想解和负理想解的欧式空间距离。
${d}_{i}^{+}=\sqrt{\stackrel{m}{\sum _{j=1}}{R}_{ij}-{R}_{j}^{+}}$
${d}_{i}^{-}=\sqrt{\stackrel{m}{\sum _{j=1}}{R}_{ij}-{R}_{j}^{-}}$
式中:${d}_{i}^{+}$和${d}_{i}^{-}$分别为第i个解决方案到正理想解和负理想解的距离。Rij为加权归一化决策矩阵第i行第j列元素。
Step 9:计算各解决方案的相对贴合度(RCi)。各个解决方案以相对贴合度为准,进行大小优劣排序,相对贴合度较高的解决方案表现更佳,排名更高,反之则更差。
$R{C}_{i}=\frac{{d}_{i}^{-}}{{d}_{i}^{+}+{d}_{i}^{-}}$
式中:RCi为第i个解决方案的相对贴合度。
3 多目标优化流程
收起
提出一种基于SPEA2和熵加权TOPSIS的露天矿多金属精细化配矿多目标优化方法,用于降低矿石品位的波动和运输成本。该方法通过SPEA2算法求解露天矿多金属精细化配矿多目标优化数学模型,得到最优的Pareto前沿解集。最后,采用基于熵加权TOPSIS从Pareto最优解集中确定最优解。露天矿多金属精细化配矿多目标优化流程见图1。
4 工程应用
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4.1 上房沟钼矿基本概况
上房沟钼矿是特大型斑岩-矽卡岩型钼矿床,位于栾川县冷水乡上房沟村。上房沟钼矿为栾川钼矿田的一部分,矿区面积1.207 3平方千米,矿体厚大而集中,东西长1 125 m、南北宽825 m,保有工业矿石储量5.15亿吨,钼金属量66.5万吨,钼平均品位0.129%,共生铁矿石量186.20万吨,伴生铁矿石量4 999.16万吨,属于埋藏浅、品位高的特大型钼矿床(图2)。目前露天采场长900 m、宽500 m,生产台阶高15 m,采用潜孔钻穿孔—挖掘机铲装—汽车运输台阶式采剥工艺。
该露天采场共有4台挖机和1个破碎站,其工作效率分别为650 t/h和870 t/h。在配矿计划中,钼矿和磁铁矿的目标品位分别为0.12%和4.53%。该采场某生产作业计划周期内的矿石目标产量为5 000 t,所有矿石来自10个出矿点,各出矿点的矿物品位、岩性及其与受矿点的距离见表1。矿用卡车型号为YTK89A,载重量为60 t,重载运输费用和空载运输费用分别为50元/km和30元/km。
4.2 多目标配矿优化结果
采用该露天矿多金属精细化配矿多目标优化方法,对上房沟钼矿某生产作业计划周内的配矿计划进行优化。SPEA2算法种群规模为20,最大迭代次数为100 000。分别求解脱泥配矿计划和不脱泥配矿计划,并将2次求解的Pareto最优解集合并。对合并后的集合进行非支配排序,得到最优的Pareto解集。最后,采用熵加权TOPSIS算法进行排序,得到最优配矿计划方案。优化后的Pareto最优解集见表2。原配矿计划和最优配矿计划及其各项指标分别见表3~表4。
从表2~表4可知,采用SPEA2算法得出的配矿计划的矿石品位偏差均优于由人工编制的原配矿计划。采用熵加权TOPSIS优选后的最优配矿计划的矿石品位偏差为0.696 0%,运输成本为4 580.28元;与原配矿计划相比,矿石品位偏差降低了73.60%,运输成本降低了20.99%。与人工编制的配矿计划相比,基于SPEA2和熵加权TOPSIS的露天矿多金属精细化配矿多目标优化方法,能够快速且准确地得到满足要求的配矿计划,有效性好。
5 结论
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1)建立的露天多金属精细化矿配矿多目标优化模型,提高了资源利用率,降低了矿企的运输成本,并提高了企业配矿管理水平,可为智能矿山和绿色矿山建设提供技术支持。
2)基于SPEA2和熵加权TOPSIS算法的露天矿多金属精细化配矿多目标优化方法,解决了对多目标优化模型求解难和Pareto解集选择难的问题,得益于SPEA2优秀的寻优能力和熵加权TOPSIS的客观准确性,该方法为露天矿配矿问题提供了新的解决思路。
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2024年第43卷第4期
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doi: 10.13426/j.cnki.yky.2024.04.04
  • 接收时间：2024-04-05
  • 首发时间：2025-07-04
  • 出版时间：2024-11-20
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  • 收稿日期：2024-04-05
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    1 洛阳富川矿业有限公司, 河南 洛阳 471500
    2 洛阳栾川钼业集团股份有限公司, 河南 洛阳 471500
    3 长沙迪迈科技股份有限公司, 湖南 长沙 410221
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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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