電動(dòng)汽車(chē)充電站選址研究外文文獻(xiàn)

Contents lists available at ScienceDirect Computers Garcia Millet Tonnelier Richet Hern ndez Arauzo Puente Varela Jang Jeong Li Zhan Jong Liu Huang Shaukat et al 2018 Shi Wang Yang Zhang Song Baouche Billot Trigui Brooker Chen Kockelman Chung Frade Ribeiro Goncalves Gim nezgaydou Ribeiro Guti rrez Liu Shahraki Cai Turkay Xi Ramteen Yi You Zhu Gao Zheng Pashajavid Sadeghi Barzani Rajabi Ghahnavieh Dashora Barnes Combs Hilliard Davidov Dong Liu Hafez Khalkhali Abapour Moghaddas Tafreshi Kou Liu Lin et al 2014 Liu et al 2013 Micari Polimeni Napoli Andaloro Nie Sathaye Wang Xu Wen Xiang et al 2016 Yassir Zeng Feng Zhang Cim nez Gaydou Ribeiro Guri rrez Huang Kanaroglou Li Huang Shareef Islam Shi Xu Miao Zhang Andrenacci Ragona He Wu Yin Suganya Raja Yao et al 2014 It can be seen that almost all the studies applied the multi objective decision methods to the problems mentioned above such as linear nonlinear programming mixed integer programming cluster analysis etc Most studies take some quantitative indicators into account such as con struction cost daily operation and maintenance cost and annual profi ts and ignore some qualitative factors Guo Son Son 2015 2016 Thong Wei 2016 Wei Alsaadi Hayat Xu 2004 Standard deviation method Deng Yeh Cui and Huang 2018 Fan Ma Chan Kahraman Ertay if the tth expert holds neutral attitude towards the EVCS siteAiwith respect to the sub cri terionCjl then dH lt ij 2 if the tth expert holds negative attitude towards the EVCS siteAiwith respect to the sub criterionCjl then dH lt ij 3 if the tth expert refuses to evaluate the EVCS siteAiwith respect to the sub criterionCjl then dH lt ij 4 According to Eq 13 we can further con struct the corresponding indication matrix 14 whereIlt ij isavector i e IIIII lt ij lt ij lt ij lt ij lt ij 1234 Theelement Ih 1 2 3 4 lth ij in vectorIlt ij is a 0 1 variable where I1 lth ij if Table 2 Linguistic scales for importance Kahraman et al 2006 Linguistic scales for importance Triangular fuzzy scale Triangular fuzzy reciprocal scale Just equal JE 1 1 1 1 1 1 Equally important EI 1 2 1 3 2 2 3 1 2 Weakly more important WMI 1 3 2 2 1 2 2 3 1 Strongly more important SMI 3 2 2 5 2 2 5 1 2 2 3 Very strongly more important VSMI 2 5 2 3 1 3 2 5 1 2 Absolutely more important AMI 5 2 3 7 2 2 7 1 3 2 5 Fig 3 The intersection betweenm andm 12 Chang 1996 Y Ju et al Computers Industrial Engineering 135 2019 1271 1285 1276 dHh 1 2 3 4 lt ij h otherwise I0 lth ij Then letqjlh i denote the number of experts who holds the attitudeHhto express the evaluation on EVCS siteAiwith respect to the sub criterionCjl According to the indication matrix II ij lt ij nT j in Eq 14 qjlh i can be calculated by Eq 15 qIim jn lnh 1 2 1 2 1 2 1 2 3 4 jlh i t T lth ij j 1 15 According to Defi nition 1 we can get the picture fuzzy evaluation in formation for EVCS siteAiwith respect to the sub criterionCjl au vim jn ln 1 2 1 2 1 2 jl i jl i jl i jl i j 16 where uqT jl i jl i 1 qT jl i jl i 2 vqT jl i jl i 3 and T is the number of ex perts Obviously the following expression holds u v1 jl i jl i jl i Further we can construct the following picture fuzzy matrix Ga jjl i m njwith respect to the sub criteria Cln 1 2 jlj be longing to the criterionCjaccording to the picture fuzzy information in Eq 16 17 For the picture fuzzy matrix in Eq 17 we can determine the ag gregated result ru v ijij ij ij for each EVCS siteAiwith respect to the criterionCjby using proposed PFWIG operator in Eq 6 rPFWIG aaa a v v u vv v u vim jn 1 1 1 1 1 1 1 2 1 2 ijj i j i jn i l n jl iw l n jl i jl iw l n jl i jl i jl iw l n jl iw l n jl i jl iw l n jl iw ij ij ij 12 1 11 11 1 j j jl j jl j jl j jl j jl j jl 18 wherewjlis the local weight of the sub criterionCjl which can be cal culated by Eq 12 Further we can construct the following comprehensive picture fuzzy decision matrix Rr ij m nby Eq 19 19 4 3 The extended GRP method to select optimal EVCS site For the comprehensive picture fuzzy decision matrix shown in Eq 19 we will extend the traditional GRP method to solve EVCS site selection problem under picture fuzzy environment The specifi c pro cedure of the extended GRP method is briefl y described as follows Step 1 Build the EVCS site evaluation index system Step 2 Determine the weight vector wwww n T 12 of criteria C jn 1 2 j and the local weight vector wwww sub j jjjn T 12 j of the sub criteria Cln 1 2 jlj with respect to the criteria C jn 1 2 j using FAHP method Step 3 Construct comprehensive picture fuzzy decision matrix by Eq 19 Step 4 Determine the picture fuzzy positive ideal solution PF PIS and the picture fuzzy negative ideal solution PF NIS of the com prehensive picture fuzzy decision matrix in Eq 19 respectively Rrrr n12 20 Rrrr n12 21 where rrrS r max jljljimij1 rrrS r min jljljimij1 jn1 2 and S r ij can be calculated by Eq 2 Step 5 Construct the grey relational coeffi cient matrices For the comprehensive picture fuzzy decision matrix in Eq 19 the grey relational coeffi cient between r ijand rjcan be calculated by Eq 22 d rr d rr d rr d rr min min max max max max ij ijijjijijj ijjijijj 22 where 0 1 is distinguishing coeffi cient and d rr ijj is the dis tance between r ijand rj which can be calculated by Eq 4 In general 0 5 Similarly the grey relational coeffi cient between r ijand rjcan be calculated by Eq 23 d rr d rr d rr d rr min min max max max max ij ijijjijijj ijjijijj 23 where d rr ijj is the distance between r ijand rj and it can be cal culated by Eq 4 Based on ijand im jn 1 2 1 2 ij the following two grey relational coeffi cient matrices can be constructed ij m n n n mmmn 11121 21222 12 24 ij m n n n mmmn 11121 21222 12 25 where ij m n is the grey relational coeffi cient matrix between all EVCS sites and the PF PIS and ij m nis the grey relational coeffi cient matrix between all EVCS sites and the PF NIS From Eq 22 we know that the grey relational coeffi cient vector between the PF PIS and itself is 1 1 1 0 Similarly the grey relational coeffi cientvectorbetweenthePF NISanditselfis 1 1 1 0 Step 6 Determine the weighted grey relational coeffi cient matrices Two weighted grey relational coeffi cient matrices ij m nand ij m ncan be calculated by Eqs 26 and 27 respectively ij m n n n mmmn 11121 21222 12 26 Y Ju et al Computers Industrial Engineering 135 2019 1271 1285 1277 ij m n n n mmmn 11121 21222 12 27 where w ij j ij w ij j ij wj is the weight of the criterionCj and it can be calculated by Eq 12 From Eqs 22 and 26 we know that the weighted grey relational coeffi cient vector between the PF PIS and itself is www n 0 12 Similarly the weighted grey relational coeffi cient vector between the PF NIS and itself is www n 0 12 Step 7 Calculate the grey relational projections of each site Ai i 1 2 m on the PF PIS and PF NIS respectively Eachlineintheweightedgreyrelation coeffi cientmatrix ij m nis considered as a row vector iiiin12 which corresponds to the EVCS site Ai Therefore for the EVCS site Ai the grey relational projection of iiiin12 on the weighted grey rela tional coeffi cient vector www n 0 12 can be calculated by Eq 28 w w im cos 1 2 iii j n jij j n j 0 1 2 1 2 28 Similarly the grey relational projection of the EVCS site Ai i 1 2 m ontheweightedgreyrelational coeffi cientvector www n 0 12 can be calculated by Eq 29 w w im cos 1 2 iii j n jij j n j 0 1 2 1 2 29 Step 8 Calculate the relative grey relational projection of each EVCS site The relative grey relational projection of each site to the PF PIS www n 0 12 is defi ned as follows im 1 2 i i ii 30 Step 9 Sort the values of im 1 2 i in a descending sequence and select the most desirable EVCS site s If one site has the highest i then it is the most desirable one 5 Empirical example In this section the proposed framework is employed to select the optimal EVCS site from all the feasible sites To satisfy the increasing needs of EVCS in Beijing one electric vehicle charging pile limited company wants to determine the optimal site from six pre selected sites Due to confi dentiality reasons these six feasible sites are denoted by AAAAAAA 123456 whose geographical locations are shown in Fig 4 As is described previously the evaluation index system of EVCS site selection consists of four criteria Environment Economy Society and Technology and fourteen sub criteria which is shown in Fig 1 In order to determine the optimal EVCS site ten experts with expertise in the fi elds of land utilization site selection electric power system and transportation system are invited The set of experts is denoted by EEEE 1210 5 1 Determine the weights of criteria and sub criteria To gather data needed for comparing the importance of criteria and sub criteria the staff s of the company gave a deep interview with the expert team Pairwise comparison matrices can be formed by the expert team using the scale given in Table 2 Fuzzy evaluations are performed in the pairwise comparisons by the expert team as follows Environment C1 and Economy C2 are compared using the question How im portant is Environment C1 when it is compared to Economy C2 and if the answer is Strongly more important SMI then the triangular fuzzy number corresponding this linguistic scale is 3 2 2 5 2 The pairwise comparison matrix for the criteria is shown in Table 3 Simi larly we can construct the pairwise comparison matrices for the sub criteria which are shown in Tables 4 7 Weights of the criteria can be determined by using the fuzzy com parison values in Table 3 through Chang s extent analysis method By Eq 7 we can get the following results S 3 50 5 00 6 50 1 24 1 16 33 1 11 67 0 1458 0 3061 0 5571 C1 S 2 67 4 00 6 00 1 24 1 16 33 1 11 67 0 1111 0 2449 0 5143 C2 S 2 83 3 67 6 00 1 24 1 16 33 1 11 67 0 1181 0 2245 0 5143 C3 S 2 67 3 67 5 50 1 24 1 16 33 1 11 67 0 1111 0 2245 0 4714 C4 Using these vectors we can obtain some degrees of possibility by Eq 10 V SSV SSV SS 1 000 1 000 1 000 CCCCCC 121314 V SSV SSV SS 0 858 1 000 1 000 CCCCCC 212324 V SSV SSV SS 0 819 0 952 1 000 CCCCCC 313234 V SSV SSV SS 0 800 0 946 1 000 CCCCCC 414243 Further the weight vector of criteria can be determined by Eq 12 W 0 288 0 247 0 235 0 230 T Similarly we can determine the local weight vector of the sub criteria which are given in Tables 4 7 5 2 Determine comprehensive picture fuzzy decision matrix The comprehensive picture fuzzy decision matrix is constructed according to the local weights and ratings of sub criteria To gather the ratings of sub criteria provided by the experts the staff s in the company explain the detailed description of sub criteria to them and use the elements in the set H positive H1 neutral H2 negative H3 re fusal H4 to represent the attitude of each expert for rating of EVCS siteAiwith respect to the sub criterionCjl and further construct the evaluation matrix Ddim jn 1 2 1 2 ij lt ij nT j by Eq 13 Take the EVCS siteA1with respect to the sub criteriaC11for an example According to the evaluation information for the EVCS siteA1 with respect to the sub criteriaC11 C12 C13andC14provided by ten experts wecanconstructthefollowingevaluationmatrix Dd lt11 11 4 10by Eq 13 31 According to Eq 31 we can further construct the corresponding indication matrix II lt11 11 4 10by Eq 14 where the elements in the fi rstrowofthematrix II lt11 11 4 10 aregivenasfollows I 1 0 0 0 11 11 I 0 0 1 0 12 11 I 1 0 0 0 13 11 I 0 1 0 0 14 11 Y Ju et al Computers Industrial Engineering 135 2019 1271 1285 1278 I 1 0 0 0 15 11 I 0 0 1 0 16 11 I 1 0 0 0 17 11 I 0 0 1 0 18 11 I 0 1 0 0 19 11 and I 0 0 0 1 110 11 By Eq 15 we can calculate the number of experts who adopts Hh 1 2 3 h to express the evaluation on EVCS siteA1with respect to the sub criterionC11 q4 111 1 q2 112 1 q3 113 1 Then we can obtain the picture fuzzy evaluation value au v 11 1 11 1 11 1 11 1 for the EVCS siteA1with respect to the sub criterion C11byEq 16 uq 100 40 11 1 111 1 q 100 20 11 1 112 1 vq 100 30 11 1 113 1 i e a0 40 0 20 0 30 11 1 Similarly we can ob tain the picture fuzzy evaluation value of EVCS siteA1with respect to thesub criteriaC12 C13andC14 a0 30 0 30 0 30 12 1 a0 20 0 30 0 40 13 1 a0 40 0 20 0 30 14 1 which are shown in the fi rst row of Table 8 In this way we can determine the picture fuzzy decision matrix with respect to the sub criteria Cln 1 2 jlj be longing to criteria C j 2 3 4 j which are shown in Tables 9 11 Further we can determine the comprehensive picture fuzzy decision matrix Rr ij 4 4in Eq 19 according to the proposed PFWIG op erator which is shown in Table 12 Taking r 11for an example we can get the following aggregated result by Eq 18 Fig 4 The geographical locations of six alternative EVCS sites in Beijing Table 3 Local weights and pairwise comparison matrix of the criteria CriteriaC1C2C3C4Weights Environment C1 1 1 1 1 2 1 3 2 1 3 2 2 1 3 2 2 0 288 Economy C2 2 3 1 2 1 1 1 1 2 1 3 2 1 2 1 3 2 0 247 Society C3 1 2 2 3 1 2 3 1 2 1 1 1 2 3 1 2 0 235 Technology C4 1 2 2 3 1 2 3 1 2 1 2 1 3 2 1 1 1 0 230 Table 4 Local weights and pairwise comparison matrix with respect to Environment C1 Sub criteriaC11C12C13C14Local weights Destruction degree on urban vegetation and landscape C11 1 1 1 1 2 2 3 1 1 2 1 3 2 1 2 2 3 1 0 190 Waste discharge C12 1 3 2 2 1 1 1 3 2 2 5 2 1 2 1 3 2 0 316 Greenhouse gas and fi ne particulate matter emission reduction C13 2 3 1 2 2 5 1 2 2 3 1 1 1 2 3 1 2 0 224 Easiness of extension and reconstruction in the future C14 1 2 3 2 2 3 1 2 1 2 1 3 2 1 1 1 0 270 Table 5 Local weights and pairwise comparison matrix with respect to Economy C2 Sub CriteriaC21C22C22Local weights Construction cost C21 1 1 1 2 5 1 2 2 3 1 2 13 2 0 206 Daily operation and maintenance cost C22 3 2 2 5 2 1 1 1 1 3 2 2 0 506 Annual profi ts C23 2 3 1 2 1 2 2 3 1 1 1 1 0 288 Y Ju et al Computers Industrial Engineering 135 2019 1271 1285 1279 rPFWIG aaaa 0 4 0 2 0 30 3 0 3 0 30 2 0 3 0 4 0 4 0 2 0 3 1 0 3 0 2 1 0 3 0 3 1 0 4 0 3 1 0 3 0 2 1 0 3 0 2 0 4 1 0 3 0 3 0 3 1 0 4 0 3 0 2 1 0 3 0 2 0 4 1 0 3 1 0 3 1 0 4 1 0 3 1 0 3 0 2 1 0 3 0 3 1 0 4 0 3 1 0 3 0 2 1 1 0 3 1 0 3 1 0 4 1 0 3 0 32 0 26 0 32 1111 1 12 1 13 1 14 1 0 1900 3160 224 0 270 0 1900 3160 224 0 2700 190 0 3160 224 0 270 0 1900 3160 2240 270 0 1900 316 0 2240 270 0 1900 3160 2240 270 5 3 Select the optimal EVCS site based on the extended GRP method For the comprehensive picture fuzzy decision matrix shown in Table 12 we use the extended GRP method to select the optimal EVCS site The specifi c calculation process is briefl y described as follows Step 1 Determine the PF PIS and PF NIS of the comprehensive picture fuzzy decision matrix in Table 12 by Eqs 20 and 21 respectively R 0 35 0 18 0 30 0 45 0 23 0 22 0 47 0 24 0 17 35 0 23 0 26 R 0 32 0 26 0 32 0 27 0 23 0 41 0 31 0 22 0 36 0 25 0 23 0 39 Step2 Determinethegreyrelational coeffi cientmatrices ij 4 3and ij 4 3by Eqs 24 and 25 respectively 0 5883 1 0000 1 0000 1 0000 0 5695 0 4235 0 3400 0 7643 0 7062 0 3333 0 4436 0 4464 1 0000 0 6176 0 4880 0 5891 0 6934 0 4180 0 6753 0 7565 0 4408 0 4168 0 4983 0 5969 ij 6 4 Table 6 Local weights and pairwise comparison matrix with respect to society C3 Sub criteriaC31C32C33C34Local weights Convenience of accessing public transport C31 1 1 1 3 2 2 5 2 1 3 2 2 3 2 2 5 2 0 426 Scale of construction and peripheral population density C32 2 5 1 2 2 3 1 1 1 1 1 1 1 2 1 3 2 0 093 Service radius C33 1 2 2 3 1 1 1 1 1 1 1 2 3 1 2 0 270 Harmonization of EVCS with urban development and state grid planning C34 2 5 1 2 2 3 3 2 1 2 1 2 1 3 2 1 1 1 0 211 Table 7 Local weights and pairwise comparison matrix with respect to technology C4 Sub criteriaC41C42C43Local weights Reliability in the future C41 1 1 1 1 3 2 2 1 3 2 2 0 393 Possibility of off ering suitable services to the drivers at the EVCS in the future C42 1 2 2 3 1 1 1 1 1 2 1 3 2 0 328 Security and ability to deal with emergency in the future C43 1 2 2 3 1 2 3 1 2 1 1 1 0 279 Table 8 Picture fuzzy decision matrix with respect to the sub criteria belonging to Environment C1 C11C12C13C14 A1 0 40 0 20 0 30 0 30 0 30 0 30 0 20 0 30 0 40 0 40 0 20 0 30 A2 0 40 0 20 0 20 0 30 0 40 0 20 0 50 0 20 0 20 0 20 0 20 0 40 A3 0 40 0 20 0 20 0 40 0 20 0 30 0 30 0 30 0 30 0 20 0 10 0 50 A4 0 30 0 20 0 30 0 40 0 10 0 30 0 40 0 10 0 30 0 30 0 30 0 30 A5 0 40 0 10 0 30 0 30 0 30 0 20 0 30 0 20 0 30 0 30 0 20 0 30 A6 0 20 0 20 0 40 0 40 0 30 0 20 0 30 0 40 0 20 0 30 0 40 0 20 Table 9 The picture fuzzy evaluation matrix with respect to the sub criteria belonging to Economy C2 C21C22C23 A1 0 40 0 20 0 30 0 50 0 20 0 20 0 40 0 30 0 20 A2 0 30 0 40 0 20 0 20 0 20 0 40 0 50 0 10 0 20 A3 0 30 0 20 0 40 0 20 0 20 0 50 0 40 0 30 0 20 A4 0 40 0 10 0 30 0 40 0 20 0 20 0 30 0 40 0 20 A5 0 30 0 30 0 30 0 30 0 20 0 40 0 40 0 20 0 30 A6 0 20 0 30 0 40 0 40 0 20 0 20 0 20 0 20 0 40 Table 10 The picture fuzzy evaluation matrix with respect to the sub criteria belonging to Society C3 C31C32C33C34 A1 0 50 0 20 0 20 0 40 0 30 0 20 0 50 0 30 0 10 0 40 0 20 0 20 A2 0 20 0 20 0 50 0 30 0 10 0 40 0 40 0 30 0 20 0 50 0 20 0 20 A3 0 40 0 20 0 20 0 20 0 20 0 50 0 20 0 30 0 40 0 60 0 20 0 10 A4 0 30 0 30 0 20 0 30 0 20 0 30 0 40 0 20 0 20 0 40 0 20 0 30 A5 0 40 0 20 0 20 0 40 0 30 0 20 0 40 0 40 0 10 0 50 0 20 0 10 A6 0 40 0 30 0 20 0 40 0 30 0 10 0 50 0 30 0 10 0 20 0 20 0 50 Table 11 The picture fuzzy evaluation matrix with respect to the sub criteria belonging to Technology C4 C41C42C43 A1 0 20 0 20 0 40 0 50 0 20 0 10 0 40 0 30 0 20 A2 0 40 0 30 0 20 0 30 0 20 0 40 0 40 0 30 0 20 A3 0 20 0 30 0 40 0 20 0 10 0 50 0 40 0 30 0 20 A4 0 30 0 20 0 40 0 40 0 20 0 30 0 30 0 20 0 30 A5 0 40 0 20 0 30 0 30 0 40 0 20 0 40 0 20 0 30 A6 0 20 0 30 0 20 0 40 0 30 0 20 0 20 0 20 0 50 Table 12 The comprehensive picture fuzzy decision matrix C1C2C3C4 A1 0 32 0 26 0 32 0 45 0 23 0 22 0 47 0 24 0 17 0 35 0 23 0 26 A2 0 34 0 27 0 26 0 30 0 22 0 31 0 31 0 22 0 36 0 36 0 26 0 27 A3 0 33 0 19 0 34 0 27 0 23 0 41 0 35 0 24 0 27 0 25 0 23 0 39 A4 0 35 0 18 0 30 0 37 0 24 0 22 0 35 0 24 0 23 0 34 0 20 0 34 A5 0 32 0 21 0 27 0 33 0 22 0 35 0 42 0 27 0 15 0 36 0 27 0 27 A6