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                    自適應變化響應的動態多目標進化算法

                    梁正平 李輝才 王志強 胡凱峰 朱澤軒

                    梁正平, 李輝才, 王志強, 胡凱峰, 朱澤軒. 自適應變化響應的動態多目標進化算法. 自動化學報, 2021, x(x): 1001?1018 doi: 10.16383/j.aas.c210121
                    引用本文: 梁正平, 李輝才, 王志強, 胡凱峰, 朱澤軒. 自適應變化響應的動態多目標進化算法. 自動化學報, 2021, x(x): 1001?1018 doi: 10.16383/j.aas.c210121
                    Liang Zheng-Ping, Li Hui-Cai, Wang Zhi-Qiang, Hu Kai-Feng, Zhu Ze-Xuan. Dynamic multi-objective evolutionary algorithm with adaptive change response. Acta Automatica Sinica, 2021, x(x): 1001?1018 doi: 10.16383/j.aas.c210121
                    Citation: Liang Zheng-Ping, Li Hui-Cai, Wang Zhi-Qiang, Hu Kai-Feng, Zhu Ze-Xuan. Dynamic multi-objective evolutionary algorithm with adaptive change response. Acta Automatica Sinica, 2021, x(x): 1001?1018 doi: 10.16383/j.aas.c210121

                    自適應變化響應的動態多目標進化算法

                    doi: 10.16383/j.aas.c210121
                    基金項目: 國家自然科學基金(61871272); 廣東省自然科學基金(2020A1515010479, 2021A1515011911); 深圳市穩定支持面上項目(20200811181752003)
                    詳細信息
                      作者簡介:

                      梁正平:深圳大學計算機與軟件學院副教授. 2006年獲武漢大學博士學位. 主要研究方向為計算智能, 大數據分析與應用等. 本文通訊作者. E-mail: liangzp@szu.edu.cn

                      李輝才:深圳大學計算機與軟件學院碩士生. 主要研究方向為計算智能及應用. E-mail: 1810273028@email.szu.edu.cn

                      王志強:深圳大學計算機與軟件學院教授. 主要研究方向為計算智能, 大數據分析與應用, 多媒體技術與應用等. E-mail: wangzq@szu.edu.cn

                      胡凱峰:深圳大學信息中心工程師. 2019年獲深圳大學碩士學位. 主要研究方向為計算智能及其應用. E-mail: kaifeng@szu.edu.cn

                      朱澤軒:深圳大學計算機與軟件學院副教授. 2006年獲武漢大學博士學位. 主要研究方向為計算智能, 大數據分析與應用等. 本文通訊作者. E-mail: zhuzx@szu.edu.cn

                    Dynamic Multi-objective Evolutionary Algorithm with Adaptive Change Response

                    Funds: National Natural Science Foundation of China (61871272); Natural Science Foundation of Guangdong, China (2020A1515010479, 2021A1515011911); Shenzhen Fundamental Research Program (20200811181752003)
                    More Information
                      Author Bio:

                      LIANG Zheng-Ping Associate professor at the School of Computer Science & Software Engineering, Shenzhen University. He received his Ph. D. degree from Wuhan University in 2006. His research interests include computational intelligence, big data analysis and application

                      LI Hui-Cai Master student at the School of Computer Science & Software Engineering, Shenzhen University. His research interests include computational intelligence and applications

                      WANG Zhi-Qiang Professor at the School of Computer Science & Software Engineering, Shenzhen University. His research interests include computational intelligence, big data analysis and applications, multimedia technology and applications

                      HU Kai-Feng Engineer at Information Center of Shenzhen University. He received his master degree from Shenzhen University in 2019. His research interests include computational intelligence and applications

                      ZHU Ze-Xuan Professor at the School of Computer Science & Software Engineering, Shenzhen University. He received his Ph. D. degree from Nanyang Technological University in 2008. His research interests include computational intelligence, machine learning and bioinformatics

                    • 摘要: 動態多目標優化問題的目標函數發生變化時, 需要采取變化響應策略對種群進行重新初始化, 以快速追蹤新環境中的最優解集. 現有動態多目標優化算法對不同個體不同維度的決策變量缺乏針對性的變化響應, 導致重新初始化的效果尚存在較大改進空間. 為此, 本文提出了一種對不同個體不同維度的決策變量分別進行自適應變化響應的動態多目標進化算法(DMOEA-ACR). 該算法包括兩個核心部分, 首先是對t時間步最優種群和t?1時間步最優種群中對應個體各維度決策變量之間的差異進行計算, 自適應選擇變異策略或預測策略重新初始化不同個體不同維度的決策變量. 其次, 在每輪迭代或重新初始化后, 對非支配個體進行存檔, 基于存檔中心構建預測策略. 為了驗證DMOEA-ACR的有效性, 將其與動態多目標優化領域的6種先進算法在最新測試問題集SDP和DF上進行對比, 實驗結果表明DMOEA-ACR在求解動態多目標優化問題時具有明顯的優勢.
                    • 圖  1  二維決策空間最理想情形下的重新初始化示意圖

                      Fig.  1  Reinitialization illustration of the most ideal situation in 2D decision space

                      圖  2  自適應變化響應示意圖

                      Fig.  2  Illustration of adaptive change respond

                      圖  3  基于存檔中心的預測策略示意圖

                      Fig.  3  Illustration of prediction strategy based on the central of archive

                      圖  4  DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, MOEA/D-MoE和DMOEA-ACR在SDP1, SDP5,SDP6, DF3, DF5, DF8問題上的log(IGD)均值變化比較

                      Fig.  4  Comparison of average log(IGD) trends of DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, MOEA/D-MoE and DMOEA-ACR on SDP1, SDP5, SDP6, DF3, DF5, DF8

                      圖  5  DNSGA-II-A, DNSGA-II-B, MOEA/D-KF和SGEA在SDP1, SDP6, DF3, DF8問題上得到的PF圖

                      Fig.  5  PF graph obtained by DNSGA-II-A, DNSGA-II-B, MOEA/D-KF and SGEA on SDP1, SDP6, DF3, DF8

                      圖  6  Tr-DMOEA, MOEA/D-MoE和DMOEA-ACR在SDP1, SDP6, DF3, DF8問題上得到的PF圖

                      Fig.  6  PF graph obtained by Tr-DMOEA, MOEA/D-MoE and DMOEA-ACR on SDP1, SDP6, DF3, DF8

                      圖  7  τt 分別為5,10,20時DMOEA-ACR在SDP1(2), SDP5(2),SDP6(2), DF3, DF5,DF8問題上的log(IGD)均值變化比較

                      Fig.  7  Comparison of average log(IGD) trends of DMOEA-ACR on SDP1(2), SDP5(2), SDP6(2), DF3, DF5, DF8 where τt is 5, 10 and 20 respectively

                      表  1  DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE和DMOEA-ACR在SDP上獲得的MIGD均值和標準差

                      Table  1  The mean and standard deviation of MIGD of DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE and DMOEA-ACR were obtained on SDP

                      ProblemsMDNSGA-II-ADNSGA-II-BMOEA/D-KFSGEATr-DMOEAMOEA/D-MoEDMOEA-ACR
                      SDP122.03×10?2
                      (6.73×10?3)(?)
                      2.01×10?2
                      (5.34×10?3)(?)
                      6.69×10?1
                      (2.61×10?3)(?)
                      1.66×10?2
                      (5.12×10?3)(≈)
                      2.53×10?1
                      (2.65×10?2)(?)
                      5.78×10?1
                      (3.13×10?4)(?)
                      1.65×10?2
                      (3.67×10?3)
                      32.26×10?1
                      (3.02×10?3)(?)
                      2.32×10?1
                      (6.78×10?3)(?)
                      7.74×10?1
                      (6.35×10?3)(?)
                      1.40×10?1
                      (4.74×10?3)(?)
                      1.44×10?1
                      (7.32×10?2)(?)
                      7.46×10?1
                      (2.14×10?3)(?)
                      1.32×10?1
                      (5.44×10?3)
                      SDP221.75×10?2
                      (7.58×10?3)(+)
                      1.74×10?2
                      (7.05×10?3)(+)
                      4.38×10?2
                      (4.34×10?3)(+)
                      1.00×100
                      (3.17×10?3)(?)
                      4.93×100
                      (5.43×10?1)(?)
                      3.23×10?2
                      (8.38×10?3))(+)
                      1.14×10?1
                      (4.35×10?3)
                      32.87×10?1
                      (7.18×10?3)(?)
                      3.60×10?1
                      (8.31×10?3)(?)
                      3.36×10?1
                      (7.67×10?4)(?)
                      9.23×10?1
                      (1.59×10?2)(?)
                      4.80×10?1
                      (6.61×10?2)(?)
                      3.34×10?1
                      (1.39×10?3)(?)
                      2.42×10?1
                      (7.12×10?3)
                      SDP321.76×100
                      (6.74×10?2)(+)
                      1.81×10?1
                      (3.97×10?2)(+)
                      6.37×10?2
                      (4.18×10?3)(+)
                      2.07×10?1
                      (2.04×10?3)(+)
                      1.45×10+1
                      (3.41×10?1)(+)
                      4.58×10?1
                      (1.30×10?3)(+)
                      4.74×100
                      (6.38×10?2)
                      37.01×100
                      (8.34×10?2)(?)
                      8.51×100
                      (7.37×10?2)(?)
                      8.54×10?1
                      (1.43×10?2)(+)
                      3.74×10?1
                      (3.55×10?3)(+)
                      2.36×10?1
                      (3.67×10?2)(+)
                      5.47×10?1
                      (4.42×10?3)(+)
                      3.33×100
                      (8.53×10?2)
                      SDP421.14×10?1
                      (6.19×10?3)(?)
                      7.86×10?2
                      (3.07×10?2)(?)
                      5.63×10?2
                      (1.01×10?3)(?)
                      5.56×10?2
                      (4.76×10?3)(?)
                      3.65×100
                      (4.09×10?1)(?)
                      5.54×10?2
                      (3.61×10?3)(?)
                      5.08×10?2
                      (5.03×10?3)
                      32.44×10?1
                      (5.08×10?3)(?)
                      2.26×10?1
                      (7.48×10?2)(?)
                      1.81×10?1
                      (3.28×10?3)(?)
                      1.95×10?1
                      (2.43×10?3)(?)
                      1.74×10?1
                      (5.48×10?2)(?)
                      1.79×10?1
                      (2.71×10?2)(?)
                      1.69×10?1
                      (8.25×10?3)
                      SDP529.40×10?2
                      (4.21×10?3)(?)
                      6.27×10?1
                      (8.05×10?3)(?)
                      9.74×10?2
                      (4.07×10?3)(?)
                      7.19×10?1
                      (2.79×10?2)(?)
                      8.35×10?1
                      (7.87×10?3)(?)
                      9.86×10?2
                      (4.37×10?4)(?)
                      6.81×10?3
                      (4.92×10?4)
                      31.41×10?1
                      (6.08×10?2)(?)
                      5.24×10?1
                      (3.43×10?2)(?)
                      1.54×10?1
                      (7.81×10?3)(?)
                      8.68×10?2
                      (7.15×10?3)(?)
                      1.46×10?1
                      (6.43×10?2)(?)
                      1.50×10?1
                      (7.61×10?3)(?)
                      6.38×10?2
                      (6.06×10?3)
                      SDP622.47×10?2
                      (1.53×10?3)(?)
                      3.14×10?2
                      (5.92×10?3)(?)
                      2.45×10?2
                      (3.69×10?3)(?)
                      8.56×10?2
                      (2.72×10?3)(?)
                      4.28×10?1
                      (5.97×10?3)(?)
                      2.41×10?2
                      (5.81×10?3)(?)
                      4.26×10?3
                      (7.43×10?4)
                      31.61×10?1
                      (6.44×10?2)(?)
                      1.79×10?1
                      (6.45×10?2)(?)
                      1.03×10?1
                      (6.61×10?3)(?)
                      5.38×10?2
                      (6.05×10?3)(?)
                      6.60×10?1
                      (6.06×10?3)(?)
                      5.33×10?2
                      (3.86×10?2)(?)
                      5.17×10?2
                      (5.86×10?3)
                      SDP725.15×10?2
                      (2.46×10?3)(+)
                      2.96×10?2
                      (7.28×10?3)(+)
                      3.49×10?1
                      (3.54×10?3)(?)
                      2.67×10?1
                      (6.73×10?3)(?)
                      8.12×10?1
                      (3.78×10?3)(?)
                      3.11×10?1
                      (6.65×10?3)(?)
                      2.15×10?1
                      (1.68×10?2)
                      32.41×10?1
                      (3.12×10?3)(?)
                      2.87×10?1
                      (8.30×10?2)(?)
                      3.76×10?1
                      (5.71×10?3)(?)
                      2.59×10?1
                      (2.72×10?2)(?)
                      3.71×10?1
                      (4.97×10?2)(?)
                      3.55×10?1
                      (8.36×10?2)(?)
                      2.24×10?1
                      (5.11×10?3)
                      SDP821.40×10?1
                      (6.12×10?2)(?)
                      1.56×10?1
                      (6.91×10?3)(?)
                      1.15×10?1
                      (1.31×10?3)(?)
                      1.27×10?1
                      (4.95×10?3)(?)
                      2.77×10?1
                      (5.62×10?2)(?)
                      1.07×10?1
                      (1.63×10?3)(?)
                      3.14×10?2
                      (4.26×10?3)
                      33.45×10?1
                      (8.76×10?2)(?)
                      2.97×10?1
                      (3.58×10?3)(?)
                      1.36×10?1
                      (4.87×10?3)(?)
                      1.21×10?1
                      (6.82×10?3)(+)
                      1.39×10?1
                      (9.61×10?2)(?)
                      1.03×10?1
                      (4.73×10?3)(+)
                      1.29×10?1
                      (6.43×10?3)
                      SDP928.95×10?2
                      (7.09×10?3)(?)
                      6.67×10?1
                      (5.94×10?3)(?)
                      1.64×10?1
                      (8.52×10?4)(?)
                      2.45×10?1
                      (2.06×10?3)(?)
                      1.35×10?1
                      (3.25×10?2)(?)
                      1.56×10?1
                      (6.23×10?3)(?)
                      8.13×10?2
                      (7.92×10?3)
                      34.01×10?1
                      (8.98×10?3)(?)
                      3.67×10?1
                      (4.08×10?3)(?)
                      4.93×10?1
                      (6.03×10?3)(?)
                      3.61×10?1
                      (3.74×10?2)(≈)
                      4.28×10?1
                      (4.56×10?2)(?)
                      4.45×10?1
                      (9.13×10?3)(?)
                      3.60×10?1
                      (8.03×10?2)
                      SDP1028.67×10?2
                      (7.72×10?2)(?)
                      1.15×10?1
                      (8.31×10?2)(?)
                      9.39×10?2
                      (4.94×10?3)(?)
                      2.23×10?1
                      (1.75×10?2)(≈)
                      2.35×100
                      (3.74×10?1)(?)
                      9.19×10?2
                      (7.02×10?4)(?)
                      2.21×10?2
                      (1.67×10?3)
                      33.05×10?1
                      (5.73×10?2)(?)
                      2.56×10?1
                      (9.76×10?2)(?)
                      1.85×10?1
                      (6.51×10?3)(?)
                      4.51×10?1
                      (8.06×10?2)(?)
                      3.48×10?1
                      (7.43×10?2)(?)
                      1.79×10?1
                      (3.63×10?3)(?)
                      1.74×10?1
                      (3.58×10?3)
                      SDP1121.61×10?2
                      (6.36×10?3)(?)
                      7.40×10?3
                      (7.67×10?4)(+)
                      3.02×10?2
                      (3.14×10?3)(?)
                      3.36×10?2
                      (6.91×10?3)(?)
                      9.18×10?1
                      (3.64×10?3)(?)
                      2.43×10?2
                      (3.26×10?3)(?)
                      1.36×10?2
                      (8.16×10?3)
                      31.49×10?1
                      (7.48×10?3)(?)
                      1.23×10?1
                      (5.98×10?2)(?)
                      9.77×10?2
                      (2.81×10?2)(?)
                      1.47×10?1
                      (1.08×10?2)(?)
                      8.98×10?2
                      (6.05×10?3)(?)
                      9.57×10?2
                      (5.15×10?3)(?)
                      8.77×10?2
                      (9.65×10?3)
                      SDP1222.20×10?2
                      (4.03×10?3)(?)
                      2.52×10?2
                      (3.08×10?3)(?)
                      9.16×10?3
                      (2.78×10?3)(?)
                      4.11×10?3
                      (5.38×10?2)(?)
                      8.09×10?2
                      (4.65×10?2)(?)
                      6.38×10?3
                      (8.83×10?4)(?)
                      4.04×10?3
                      (2.17×10?4)
                      32.22×10?1
                      (8.66×10?2)(?)
                      2.15×10?1
                      (6.79×10?2)(?)
                      8.66×10?2
                      (3.59×10?3)(?)
                      9.97×10?2
                      (7.02×10?2)(?)
                      7.66×10?2
                      (6.93×10?2)(?)
                      8.13×10?2
                      (4.16×10?3)(?)
                      7.63×10?2
                      (5.63×10?4)
                      +/?/≈3/21/04/20/03/21/03/18/32/22/04/20/0
                      下載: 導出CSV

                      表  2  DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE和DMOEA-ACR在DF上獲得的MIGD均值和標準差

                      Table  2  The mean and standard deviation of MIGD of DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE and DMOEA-ACR were obtained on DF

                      ProblemsMDNSGA-II-ADNSGA-II-BMOEA/D-KFSGEATr-DMOEAMOEA/D-MoEDMOEA-ACR
                      DF123.31×10?2
                      (8.35×10?3)(?)
                      4.24×10?2
                      (3.91×10?3)(?)
                      1.85×10?2
                      (4.47×10?3)(?)
                      1.22×10?2
                      (1.38×10?3)(?)
                      6.42×10?2
                      (3.34×10?3)(?)
                      1.54×10?2
                      (3.97×10?3)(?)
                      9.15×10?3
                      (3.67×10?3)
                      DF225.75×10?3
                      (7.61×10?4)(+)
                      5.76×10?3
                      (2.08×10?4)(+)
                      3.81×10?2
                      (5.02×10?3)(+)
                      1.22×10?1
                      (2.76×10?2)(?)
                      5.46×10?3
                      (5.21×10?3)(+)
                      3.10×10?2
                      (5.23×10?3)(+)
                      5.80×10?2
                      (7.85×10?3)
                      DF329.48×10?2
                      (5.32×10?3)(?)
                      1.48×10?1
                      (7.35×10?3)(?)
                      2.85×10?2
                      (3.32×10?3)(?)
                      2.61×10?1
                      (4.58×10?2)(?)
                      3.90×10?1
                      (7.31×10?3)(?)
                      2.10×10?2
                      (7.52×10?3)(?)
                      1.99×10?2
                      (3.20×10?3)
                      DF422.78×10?1
                      (7.38×10?2)(?)
                      3.81×10?1
                      (2.79×10?2)(?)
                      9.85×10?2
                      (4.59×10?3)(?)
                      5.56×10?2
                      (7.88×10?3)(?)
                      8.67×10?1
                      (6.82×10?2)(?)
                      9.09×10?2
                      (2.81×10?3)(?)
                      2.89×10?2
                      (5.19×10?3)
                      DF528.05×10?2
                      (6.39×10?2)(?)
                      8.11×10?2
                      (5.65×10?3)(?)
                      2.20×10?2
                      (4.03×10?3)(?)
                      1.45×10?2
                      (4.31×10?3)(?)
                      2.99×10?2
                      (4.34×10?3)(?)
                      2.13×10?2
                      (1.24×10?3)(?)
                      9.32×10?3
                      (6.01×10?4)
                      DF622.33×10?1
                      (8.01×10?3)(+)
                      2.40×10?1
                      (8.18×10?3)(+)
                      5.04×100
                      (9.92×10?2)(?)
                      1.51×100
                      (8.39×10?2)(?)
                      5.32×100
                      (7.31×10?1)(?)
                      2.98×100
                      (7.68×10?1)(?)
                      1.14×100
                      (4.23×10?1)
                      DF721.56×10?2
                      (4.33×10?3)(≈)
                      1.85×10?2
                      (6.02×10?3)(?)
                      3.66×10?2
                      (6.39×10?3)(?)
                      2.08×10?1
                      (5.04×10?3)(?)
                      6.54×100
                      (5.37×10?1)(?)
                      3.72×10?2
                      (2.29×10?3)(?)
                      1.57×10?2
                      (3.67×10?3)
                      DF828.82×10?2
                      (7.13×10?2)(?)
                      8.17×10?2
                      (7.14×10?3)(?)
                      7.94×10?2
                      (3.68×10?3)(?)
                      2.07×10?2
                      (5.98×10?3)(?)
                      2.85×10?1
                      (6.81×10?2)(?)
                      7.73×10?2
                      (6.64×10?3)(?)
                      1.70×10?2
                      (5.68×10?3)
                      DF927.82×10?2
                      (9.75×10?3)(?)
                      8.69×10?2
                      (9.98×10?3)(?)
                      9.52×10?2
                      (7.87×10?3)(?)
                      2.57×10?1
                      (6.30×10?2)(?)
                      5.33×10?1
                      (2.76×10?2)(?)
                      7.09×10?2
                      (5.31×10?2)(?)
                      6.87×10?2
                      (4.97×10?3)
                      DF1032.88×10?1
                      (8.10×10?3)(?)
                      2.76×10?1
                      (6.31×10?3)(?)
                      1.80×10?1
                      (3.51×10?2)(?)
                      1.19×10?1
                      (5.26×10?2)(?)
                      8.51×10?1
                      (8.61×10?2)(?)
                      1.86×10?1
                      (2.21×10?2)(?)
                      1.05×10?1
                      (8.18×10?2)
                      DF1135.77×10?1
                      (7.57×10?2)(?)
                      5.80×10?1
                      (3.59×10?3)(?)
                      1.53×10?1
                      (4.06×10?2)(?)
                      8.20×10?2
                      (3.14×10?2)(?)
                      6.53×10?2
                      (4.05×10?2)(?)
                      1.50×10?1
                      (3.72×10?3)(?)
                      6.38×10?2
                      (5.07×10?3)
                      DF1232.18×10?1
                      (8.61×10?2)(?)
                      2.34×10?1
                      (2.36×10?2)(?)
                      1.41×10?1
                      (3.38×10?2)(?)
                      1.47×10?1
                      (2.78×10?2)(?)
                      4.25×10?1
                      (7.63×10?3)(?)
                      1.00×10?1
                      (6.98×10?2)(?)
                      9.49×10?2
                      (6.53×10?3)
                      DF1331.80×10?1
                      (5.32×10?2)(?)
                      1.87×10?1
                      (8.95×10?2)(?)
                      2.79×10?1
                      (5.72×10?2)(?)
                      1.28×10?1
                      (6.52×10?2)(?)
                      1.37×100
                      (2.71×10?1)(?)
                      2.68×10?1
                      (1.25×10?2)(?)
                      1.15×10?1
                      (4.38×10?2)
                      DF1431.35×10?1
                      (5.31×10?2)(?)
                      1.22×10?1
                      (4.32×10?2)(?)
                      6.91×10?2
                      (3.31×10?2)(?)
                      5.19×10?2
                      (4.06×10?2)(?)
                      1.15×100
                      (3.59×10?2)(?)
                      6.88×10?2
                      (5.81×10?2)(?)
                      4.28×10?2
                      (5.56×10?3)
                      +/?/≈2/11/12/12/01/13/00/14/01/13/01/13/0
                      下載: 導出CSV

                      表  3  DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE和DMOEA-ACR在SDP(包括2目標和3目標)上的性能綜合排名

                      Table  3  Performance comprehensive ranking of DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE and DMOEA-ACR on SDP (including 2 goals and 3 goals)

                      AlgorithmsSDP1SDP2SDP3SDP4SDP5SDP6SDP7SDP8SDP9SDP10SDP11SDP12Average
                      rank
                      DNSGA-II-A3177252624574
                      DNSGA-II-B4346763555266
                      MOEA/D-KF7514536473445
                      SGEA2623344346733
                      Tr-DMOEA5755677737657
                      MOEA/D-MoE6432425162322
                      DMOEA-ACR1261111211111
                      下載: 導出CSV

                      表  4  DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE和DMOEA-ACR在DF的性能綜合排名

                      Table  4  Performance comprehensive ranking of DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE and DMOEA-ACR algorithms on DF

                      AlgorithmsDF1DF2DF3DF4DF5DF6DF7DF8DF9DF10DF11DF12DF13DF14Average
                      rank
                      DNSGA-II-A524561163665364
                      DNSGA-II-B635672354576456
                      MOEA/D-KF453446445353645
                      SGEA276224626234223
                      Tr-DMOEA717757777727777
                      MOEA/D-MoE342335532442532
                      DMOEA-ACR161113211111111
                      下載: 導出CSV

                      表  5  DMOEA-ACR-D1, DMOEA-ACR-D2, DMOEA-ACR-D3與DMOEA-ACR在DF上獲得的MIGD均值和標準差

                      Table  5  The mean and standard deviation of MIGD of DMOEA-ACR-D1, DMOEA-ACR-D2, DMOEA-ACR-D3 and DMOEA-ACR were obtained on DF

                      ProblemsMDMOEA-ACR-D1DMOEA-ACR-D2DMOEA-ACR-D3DMOEA-ACR
                      DF121.99×10?2
                      (1.62×10?2)(?)
                      2.58×10?2
                      (1.51×10?2)(?)
                      1.50×10?2
                      (4.12×10?3)(?)
                      9.15×10?3
                      (3.67×10?3)
                      DF221.22×10?1
                      (7.57×10?3)(?)
                      2.54×10?2
                      (4.08×10?3)(+)
                      5.93×10?2
                      (4.18×10?2)(?)
                      5.80×10?2
                      (7.85×10?3)
                      DF321.99×10?1
                      (2.61×10?3))(?)
                      2.33×10?1
                      (4.52×10?3))(?)
                      4.44×10?2
                      (1.04×10?3))(?)
                      1.99×10?2
                      (3.20×10?3)
                      DF425.28×10?2
                      (7.05×10?3)(?)
                      2.70×10?2
                      (6.82×10?3)(+)
                      4.17×10?2
                      (5.17×10?3)(?)
                      2.89×10?2
                      (5.19×10?3)
                      DF521.74×10?2
                      (6.41×10?3)(?)
                      5.05×10?2
                      (3.69×10?3)(?)
                      2.09×10?2
                      (3.65×10?4)(?)
                      9.32×10?3
                      (6.01×10?4)
                      DF622.88×100
                      (8.39×10?1)(?)
                      6.44×100
                      (5.07×10?1)(?)
                      1.23×100
                      (7.47×10?1)(?)
                      1.14×100
                      (4.23×10?1)
                      DF721.85×10?1
                      (2.66×10?3)(?)
                      1.42×10?2
                      (7.06×10?3)(+)
                      1.99×10?2
                      (2.61×10?3)(?)
                      1.57×10?2
                      (3.67×10?3)
                      DF821.65×10?2
                      (7.09×10?3)(+)
                      1.56×10?2
                      (5.13×10?3)(+)
                      1.91×10?2
                      (6.05×10?3)(?)
                      1.70×10?2
                      (5.68×10?3)
                      DF924.15×10?1
                      (4.72×10?2)(?)
                      1.21×10?1
                      (4.81×10?3)(?)
                      1.11×10?1
                      (5.82×10?3)(?)
                      6.87×10?2
                      (4.97×10?3)
                      DF1033.01×10?1
                      (5.11×10?2)(?)
                      1.48×10?1
                      (1.42×10?2)(?)
                      2.43×10?1
                      (3.47×10?2)(?)
                      1.05×10?1
                      (8.18×10?2)
                      DF1136.65×10?2
                      (5.31×10?3)(?)
                      7.76×10?2
                      (6.37×10?3)(?)
                      6.85×10?2
                      (4.21×10?3)(?)
                      6.38×10?2
                      (5.07×10?3)
                      DF1232.24×10?1
                      (6.99×10?2)(?)
                      2.62×10?1
                      (8.70×10?2)(?)
                      1.84×10?1
                      (7.17×10?2)(?)
                      9.49×10?2
                      (6.53×10?3)
                      DF1332.36×10?1
                      (5.77×10?2)(?)
                      1.62×10?1
                      (3.91×10?2)(?)
                      1.36×10?1
                      (5.32×10?2)(?)
                      1.15×10?1
                      (4.38×10?2)
                      DF1437.19×10?2
                      (9.54×10?3)(?)
                      6.25×10?2
                      (4.32×10?3)(?)
                      5.29×10?2
                      (8.02×10?3)(?)
                      4.28×10?2
                      (5.56×10?3)
                      +/?/≈1/13/04/10/00/14/0
                      下載: 導出CSV

                      表  6  DMOEA-ACR-D1, DMOEA-ACR-D2, DMOEA-ACR-D3與DMOEA-ACR在SDP上獲得的MIGD均值和標準差

                      Table  6  The mean and standard deviation of MIGD of DMOEA-ACR-D1, DMOEA-ACR-D2, DMOEA-ACR-D3 and DMOEA-ACR were obtained on SDP

                      ProblemsMDMOEA-ACR-D1DMOEA-ACR-D2DMOEA-ACR-D3DMOEA-ACR
                      SDP122.51×10?2
                      (4.25×10?3)(?)
                      1.78×10?2
                      (3.03×10?3)(?)
                      1.67×10?2
                      (5.12×10?3)(≈)
                      1.65×10?2
                      (3.67×10?3)
                      31.68×10?1
                      (5.34×10?2)(?)
                      1.54×10?1
                      (4.31×10?2)(?)
                      1.41×10?1
                      (4.08×10?2)(?)
                      1.32×10?1
                      (5.44×10?3)
                      SDP226.47×10?1
                      (2.27×10?2)(?)
                      1.12×10?1
                      (6.26×10?2)(≈)
                      2.15×10?1
                      (3.38×10?2)(?)
                      1.14×10?1
                      (4.35×10?3)
                      34.05×10?1
                      (3.15×10?2)(?)
                      3.94×10?1
                      (7.58×10?2)(?)
                      5.64×10?1
                      (4.15×10?2)(?)
                      2.42×10?1
                      (7.12×10?3)
                      SDP328.91×100
                      (6.55×10?1)(?)
                      4.81×100
                      (1.06×10?2)(?)
                      4.99×100
                      (7.21×10?1)(?)
                      4.74×100
                      (6.38×10?2)
                      33.91×100
                      (7.60×10?1)(?)
                      4.40×100
                      (4.96×10?1)(?)
                      4.47×100
                      (6.06×10?1)(?)
                      3.33×100
                      (8.53×10?2)
                      SDP426.96×10?2
                      (6.16×10?3)(?)
                      7.85×10?2
                      (6.31×10?2)(?)
                      1.60×10?1
                      (5.51×10?2)(?)
                      5.08×10?2
                      (5.03×10?3)
                      32.10×10?1
                      (4.01×10?2)(?)
                      2.68×10?1
                      (3.07×10?2)(?)
                      1.89×10?1
                      (4.19×10?2)(?)
                      1.69×10?1
                      (8.25×10?3)
                      SDP527.76×10?2
                      (6.63×10?3)(?)
                      7.40×10?3
                      (2.25×10?3)(?)
                      9.52×10?3
                      (5.12×10?3)(?)
                      6.81×10?3
                      (4.92×10?4)
                      36.85×10?2
                      (9.08×10?3)(?)
                      6.71×10?2
                      (6.91×10?3)(?)
                      7.26×10?2
                      (7.61×10?3)(?)
                      6.38×10?2
                      (6.06×10?3)
                      SDP627.98×10?3
                      (4.37×10?3)(?)
                      6.84×10?3
                      (4.66×10?3)(?)
                      6.83×10?3
                      (2.03×10?3)(?)
                      4.26×10?3
                      (7.43×10?4)
                      36.05×10?2
                      (8.12×10?3)(?)
                      1.16×10?1
                      (3.30×10?3)(?)
                      5.14×10?2
                      (4.60×10?3)(+)
                      5.17×10?2
                      (5.86×10?3)
                      SDP722.70×10?1
                      (5.59×10?2)(?)
                      2.34×10?1
                      (7.57×10?2)(?)
                      2.25×10?1
                      (4.89×10?2)(?)
                      2.15×10?1
                      (1.68×10?2)
                      32.62×10?1
                      (3.67×10?2)(?)
                      1.14×100
                      (3.86×10?2)(?)
                      2.17×10?1
                      (2.61×10?2)(+)
                      2.24×10?1
                      (5.11×10?3)
                      SDP829.54×10?2
                      (6.63×10?3)(?)
                      6.28×10?2
                      (6.73×10?3)(?)
                      4.53×10?2
                      (5.15×10?3)(?)
                      3.14×10?2
                      (4.26×10?3)
                      33.46×10?1
                      (3.10×10?2)(?)
                      2.79×10?1
                      (2.50×10?2)(?)
                      3.21×10?1
                      (2.07×10?2)(?)
                      1.29×10?1
                      (6.43×10?3)
                      SDP921.47×10?1
                      (5.06×10?2)(?)
                      1.28×10?1
                      (4.65×10?2)(?)
                      1.35×10?1
                      (3.23×10?2)(?)
                      8.13×10?2
                      (7.92×10?3)
                      33.66×10?1
                      (8.15×10?2)(?)
                      4.01×10?1
                      (4.08×10?2)(?)
                      3.54×10?1
                      (6.61×10?2)(+)
                      3.60×10?1
                      (8.03×10?2)
                      SDP1026.36×10?2
                      (2.03×10?3)(?)
                      2.61×10?2
                      (7.38×10?3)(?)
                      3.75×10?2
                      (2.25×10?3)(?)
                      2.21×10?2
                      (1.67×10?3)
                      31.68×10?1
                      (6.22×10?2)(+)
                      2.41×10?1
                      (1.36×10?2)(?)
                      3.86×10?1
                      (5.46×10?2)(?)
                      1.74×10?1
                      (3.58×10?3)
                      SDP1123.80×10?2
                      (7.32×10?3)(?)
                      4.83×10?2
                      (5.21×10?3)(?)
                      3.26×10?2
                      (8.06×10?3)(?)
                      1.36×10?2
                      (8.16×10?3)
                      31.47×10?1
                      (9.08×10?3)(?)
                      9.68×10?2
                      (6.52×10?3)(?)
                      1.96×10?1
                      (6.21×10?3)(?)
                      8.77×10?2
                      (9.65×10?3)
                      SDP1224.53×10?3
                      (3.18×10?3)(?)
                      1.62×10?2
                      (2.06×10?3)(?)
                      1.40×10?2
                      (1.32×10?3)(?)
                      4.04×10?3
                      (2.17×10?4)
                      31.62×10?1
                      (5.34×10?2)(?)
                      1.96×10?1
                      (3.73×10?2)(?)
                      1.02×10?1
                      (2.17×10?2)(?)
                      7.63×10?2
                      (5.63×10?4)
                      +/?/≈1/23/00/23/13/20/1
                      下載: 導出CSV

                      表  7  DMOEA-ACR-P1, DMOEA-ACR-P2, DMOEA-ACR-P3, DMOEA-ACR-P4與DMOEA-ACR在SDP上獲得的MIGD的均值和標準差

                      Table  7  The mean and standard deviation of MIGD of DMOEA-ACR-P1, DMOEA-ACR-P2, DMOEA-ACR-P3, DMOEA-ACR-P4 and DMOEA-ACR were obtained on SDP

                      ProblemsMDMOEA-ACR-P1DMOEA-ACR-P2DMOEA-ACR-P3DMOEA-ACR-P4DMOEA-ACR
                      SDP127.80×10?2
                      (2.17×10?3)(?)
                      1.87×10?2
                      (7.05×10?3)(?)
                      6.34×10?2
                      (4.24×10?3)(?)
                      1.73×10?2
                      (5.76×10?3)(?)
                      1.65×10?2
                      (3.67×10?3)
                      36.69×10?1
                      (4.82×10?3)(?)
                      1.53×10?1
                      (3.62×10?3)(?)
                      5.50×10?1
                      (4.01×10?3)(?)
                      1.81×10?2
                      (6.20×10?3)(?)
                      1.32×10?1
                      (5.44×10?3)
                      SDP221.78×10?1
                      (3.16×10?3)(?)
                      2.02×10?1
                      (4.91×10?3)(?)
                      2.25×10?1
                      (3.97×10?3)(?)
                      2.36×10?1
                      (6.32×10?3)(?)
                      1.14×10?1
                      (4.35×10?3)
                      35.82×10?1
                      (8.04×10?3)(?)
                      3.25×10?1
                      (6.51×10?3)(?)
                      3.11×10?1
                      (5.26×10?3)(?)
                      3.21×10?1
                      (4.58×10?3)(?)
                      2.42×10?1
                      (7.12×10?3)
                      SDP325.15×100
                      (3.66×10?2)(?)
                      4.85×100
                      (1.35×10?2)(?)
                      5.14×100
                      (6.59×10?2)(?)
                      4.83×100
                      (4.76×10?2)(?)
                      4.74×100
                      (6.38×10?2)
                      31.99×100
                      (5.14×10?2)(+)
                      3.83×100
                      (2.94×10?2)(?)
                      3.88×100
                      (5.68×10?2)(?)
                      3.91×100
                      (6.20×10?2)(?)
                      3.33×100
                      (8.53×10?2)
                      SDP424.67×10?2
                      (5.16×10?3)(+)
                      8.35×10?2
                      (5.91×10?3)(?)
                      1.02×10?1
                      (4.85×10?3)(?)
                      7.58×10?2
                      (6.24×10?3)(?)
                      5.08×10?2
                      (5.03×10?3)
                      31.76×10?1
                      (4.21×10?3)(?)
                      2.13×10?1
                      (3.89×10?3)(?)
                      1.65×10?1
                      (3.56×10?3)(+)
                      2.02×10?1
                      (5.81×10?3)(?)
                      1.69×10?1
                      (8.25×10?3)
                      SDP523.66×10?2
                      (5.41×10?3)(?)
                      7.63×10?3
                      (3.00×10?4)(?)
                      7.13×10?3
                      (6.35×10?4)(?)
                      8.08×10?3
                      (6.10×10?4)(?)
                      6.81×10?3
                      (4.92×10?4)
                      33.96×10?1
                      (8.79×10?2)(?)
                      6.43×10?2
                      (6.84×10?3)(?)
                      6.49×10?2
                      (2.96×10?3)(?)
                      6.57×10?2
                      (5.39×10?3)(?)
                      6.38×10?2
                      (6.06×10?3)
                      SDP626.48×10?3
                      (5.61×10?4)(?)
                      4.62×10?3
                      (8.91×10?4)(?)
                      4.36×10?3
                      (6.03×10?4)(?)
                      4.31×10?3
                      (5.28×10?4)(?)
                      4.26×10?3
                      (7.43×10?4)
                      31.51×10?1
                      (7.36×10?3)(?)
                      5.27×10?2
                      (7.18×10?3)(?)
                      5.43×10?2
                      (6.23×10?3)(?)
                      5.20×10?2
                      (5.98×10?3)(?)
                      5.17×10?2
                      (5.86×10?3)
                      SDP721.60×10?1
                      (5.31×10?2)(+)
                      3.26×10?1
                      (6.94×10?2)(?)
                      2.32×10?1
                      (3.28×10?2)(?)
                      2.46×10?1
                      (4.51×10?2)(?)
                      2.15×10?1
                      (1.68×10?2)
                      35.98×10?2
                      (6.60×10?3)(+)
                      2.56×10?1
                      (6.59×10?2)(?)
                      2.43×10?1
                      (4.67×10?3)(?)
                      2.53×10?1
                      (5.81×10?3)(?)
                      2.24×10?1
                      (5.11×10?3)
                      SDP821.23×10?1
                      (6.57×10?2)(?)
                      4.70×10?2
                      (5.48×10?3)(?)
                      2.70×10?2(
                      4.90×10?3)(+)
                      2.55×10?2
                      (5.84×10?3)(+)
                      3.14×10?2
                      (4.26×10?3)
                      31.37×10?1
                      (4.96×10?3)(?)
                      1.81×10?1
                      (3.69×10?3)(?)
                      1.55×10?1
                      (1.86×10?3)(?)
                      1.40×10?1
                      (7.82×10?3)(?)
                      1.29×10?1
                      (6.43×10?3)
                      SDP921.85×10?1
                      (8.80×10?3)(?)
                      1.29×10?1
                      (7.61×10?3)(?)
                      1.50×10?1
                      (8.55×10?3)(?)
                      1.32×10?1
                      (6.27×10?3)(?)
                      8.13×10?2
                      (7.92×10?3)
                      34.94×10?1
                      (9.43×10?2)(?)
                      3.79×10?1
                      (8.99×10?2)(?)
                      3.67×10?1
                      9.08×10?2)(?)
                      3.69×10?1
                      (4.20×10?2)(?)
                      3.60×10?1
                      (8.03×10?2)
                      SDP1021.12×10?1
                      (3.13×10?3)(?)
                      3.28×10?2
                      (4.10×10?3)(?)
                      2.23×10?2
                      (2.15×10?3)(?)
                      3.63×10?2
                      (2.23×10?3)(?)
                      2.21×10?2
                      (1.67×10?3)
                      31.87×10?1
                      (5.78×10?2)(?)
                      2.80×10?1
                      (3.65×10?2)(?)
                      1.79×10?1
                      (6.03×10?2)(?)
                      1.92×10?1
                      (2.65×10?3)(?)
                      1.74×10?1
                      (3.58×10?3)
                      SDP1122.28×10?2
                      (9.14×10?3)(?)
                      3.60×10?2
                      (7.61×10?3)(?)
                      2.38×10?2
                      (9.03×10?3)(?)
                      3.34×10?2
                      (8.16×10?3)(?)
                      1.36×10?2
                      (8.16×10?3)
                      38.83×10?2
                      (8.87×10?3)(?)
                      1.04×10?1
                      (8.17×10?3)(?)
                      8.79×10?2
                      (5.96×10?3)(?)
                      1.18×10?1
                      (9.08×10?3)(?)
                      8.77×10?2
                      (9.65×10?3)
                      SDP1224.52×10?3
                      (3.75×10?3)(?)
                      4.94×10?3(
                      3.65×10?3)(?)
                      4.37×10?3
                      (7.29×10?3)(?)
                      4.60×10?3
                      (6.94×10?3)(?)
                      4.04×10?3
                      (2.17×10?4)
                      32.17×10?1
                      (5.02×10?2)(?)
                      2.65×10?1
                      (4.10×10?2)(?)
                      1.06×10?1
                      (3.08×10?2)(?)
                      3.23×10?1
                      (5.24×10?2)(?)
                      7.63×10?2
                      (5.63×10?4)
                      +/?/≈4/20/00/24/02/22/01/23/0
                      下載: 導出CSV

                      表  8  DMOEA-ACR-P1, DMOEA-ACR-P2, DMOEA-ACR-P3, DMOEA-ACR-P4與DMOEA-ACR在DF上獲得的MIGD的均值和標準差

                      Table  8  The mean and standard deviation of MIGD of DMOEA-ACR-P1, DMOEA-ACR-P2, DMOEA-ACR-P3, DMOEA-ACR-P4 and DMOEA-ACR were obtained on DF

                      ProblemsMDMOEA-ACR-P1DMOEA-ACR-P2DMOEA-ACR-P3DMOEA-ACR-P4DMOEA-ACR
                      DF129.28×10?3
                      (6.51×10?3)(?)
                      1.82×10?2
                      (1.39×10?2)(?)
                      9.47×10?3
                      (8.94×10?3)(?)
                      1.73×10?2
                      (5.06×10?3)(?)
                      9.15×10?3
                      (3.67×10?3)
                      DF221.01×10?1
                      (3.16×10?2)(?)
                      6.98×10?2
                      (2.48×10?3)(?)
                      1.16×10?1
                      (3.90×10?2)(?)
                      5.17×10?2
                      (8.26×10?3)(+)
                      5.80×10?2
                      (7.85×10?3)
                      DF322.64×10?2
                      (4.09×10?3)(?)
                      2.89×10?2
                      (6.71×10?3)(?)
                      2.04×10?2
                      (5.66×10?3)(≈)
                      2.91×10?2
                      (4.18×10?3)(?)
                      1.99×10?2
                      (3.20×10?3)
                      DF422.38×10?2
                      (6.23×10?3)(+)
                      3.99×10?2
                      (4.20×10?3)(?)
                      2.94×10?2
                      (6.81×10?3)(?)
                      2.77×10?2
                      (7.11×10?3)(+)
                      2.89×10?2
                      (5.19×10?3)
                      DF528.51×10?3
                      (8.38×10?3)(+)
                      2.48×10?2
                      (4.82×10?3)(?)
                      8.83×10?3
                      (6.22×10?4)(+)
                      2.27×10?2
                      (3.10×10?3)(?)
                      9.32×10?3
                      (6.01×10?4)
                      DF622.26×100
                      (7.82×10?1)(?)
                      1.46×100
                      (6.33×10?1)(?)
                      1.16×100
                      (5.67×10?1)(?)
                      1.60×100
                      (4.28×10?1)(?)
                      1.14×100
                      (4.23×10?1)
                      DF721.62×10?2
                      (4.61×10?3)(?)
                      1.84×10?2
                      (5.14×10?3)(?)
                      1.45×10?2
                      (7.12×10?3)(+)
                      1.48×10?2
                      (5.04×10?3)(+)
                      1.57×10?2
                      (3.67×10?3)
                      DF821.65×10?2
                      (4.77×10?3)(+)
                      2.87×10?2
                      (4.00×10?3)(?)
                      1.71×10?2
                      (6.54×10?3)(≈)
                      1.68×10?2
                      (5.26×10?3)(+)
                      1.70×10?2
                      (5.68×10?3)
                      DF929.75×10?2
                      (4.63×10?2)(?)
                      9.32×10?2
                      (3.91×10?3)(?)
                      6.93×10?2
                      (5.73×10?3)(?)
                      1.10×10?1
                      (6.05×10?3)(?)
                      6.87×10?2
                      (4.97×10?3)
                      DF1031.92×10?1
                      (9.39×10?2)(?)
                      4.59×10?1
                      (8.35×10?2)(?)
                      2.37×10?1
                      (3.07×10?2)(?)
                      1.51×10?1
                      (7.99×10?2)(?)
                      1.05×10?1
                      (8.18×10?2)
                      DF1137.43×10?2
                      (5.86×10?3)(?)
                      8.51×10?2
                      (4.81×10?3)(?)
                      6.42×10?2
                      (6.03×10?3)(?)
                      6.57×10?2
                      (5.87×10?3)(?)
                      6.38×10?2
                      (5.07×10?3)
                      DF1231.75×10?1
                      (3.23×10?2)(?)
                      3.29×10?1
                      (2.02×10?2)(?)
                      2.60×10?1
                      (6.17×10?2)(?)
                      1.16×10?1
                      (4.03×10?2)(?)
                      9.49×10?2
                      (6.53×10?3)
                      DF1331.19×10?1
                      (4.91×10?2)(?)
                      2.57×10?1
                      (2.68×10?2)(?)
                      1.20×10?1
                      (3.16×10?2)(?)
                      2.48×10?1
                      (4.82×10?2)(?)
                      1.15×10?1
                      (4.38×10?2)
                      DF1434.43×10?2
                      (6.09×10?3)(?)
                      6.32×10?2
                      (4.17×10?3)(?)
                      4.59×10?2
                      (3.21×10?3)(?)
                      5.95×10?2
                      (6.61×10?3)(?)
                      4.28×10?2
                      (5.56×10?3)
                      +/?/≈3/11/00/14/02/10/24/10/0
                      下載: 導出CSV

                      表  9  $\tau_t $ 分別為5,10,20時DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE和DMOEA-ACR在SDP和DF上獲得的顯著差異統計結果

                      Table  9  Significant difference statistical results of DNSGA-II-A, DNSGA-II-B, MOEA/D-KF, SGEA, Tr-DMOEA, MOEA/D-MoE and DMOEA-ACR were obtained on SDP and DF where $\tau_t $ is 5, 10 and 20 respectively

                      Problems$\tau_t $DNSGA-II-ADNSGA-II-BMOEA/D-
                      KF
                      SGEATr-DMOEAMOEA/D-
                      MoE
                      DMOEA-
                      ACR
                      SDP54/19/14/20/03/21/02/22/00/24/01/23/0+/?/≈
                      103/21/04/20/03/21/03/18/32/22/04/20/0
                      203/21/05/19/01/21/25/18/12/22/03/21/0
                      DF52/12/02002-11-11/13/01/13/00/14/01/13/0+/?/≈
                      102002-11-12/12/01/13/00/14/01/13/01/13/0
                      202/12/02/12/01/13/02/12/02001-12-12001-12-1
                      下載: 導出CSV
                      360彩票
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