1、“ Q 5 ? T E陈建岭(山东交通学院交通工程系,山东济南 250023)K1:“ Q F5, NP-Hard5, p 4,B ? TZE 。“ Q 54 B ? T E, E “ :”F ,YVB。YV L E zr L。1 o M:“ Q ; ? T Ems |:U492.3 DS M :A cI|:1672-0032(2005)03-0053-04l :2005-04-10Te:陈建岭(1974-),男,山东菏泽人,山东交通学院助教,工学硕士.“ Q 5 | Z T“ Q,V7KvK4“ Q bW? 。“ Q 5 Vss。Dyckhoff|“ Q 5s3/B/O3/V/I,9“ Q“
2、 Q 。Bortfeldt5 s,| 0( )s 、 s 、 s, 0M f , s 0 1 f ,7 s 0 f1 。 “Sf Hqs,“ Q 5 V +M T:H , “Sf “ QKl; T , “Sf “ Q bW qKv;QQ , “Sf “ Q K ;QQ , “Sf “ Q Kl。V ,“ Q 5 bWg A5, 5$ NP-Hard5, 4 p, “ - ? TZEs K2-5 ,“ Q 54 B ? T E, | zrT。m1 集装箱坐标系1 5 5 |Bt 0vl“QV7 P“ Q bW qKv f,9“ Q 5。L,S /L:1)“ Q、 z、sYV 5:US“X ,Y
3、, ZZ_,US - P/(“ Q ), m1 U。2) Z80 =,0 V“ Q ,V=WHD ,W,H,DsYV U“ Q =r z、r r ;n ;i I|, i =1, , n;xi QM,xi = 0, Q1, Q;wii z;hii ;dii 。2 ? T E“ Q 5, AZ T1 “ :”Z T6 ,|“ QZ_(9XUSZ_)yB“ “”。 EG Z T,V “”| sB“ “H”,V7| “H” A p “H”5。 H z, BK , 6 V | i h bW 3。2.1 4 “” “H” z z4“ Q bW qvY, X f I n V ? z, “ d v。 , E
4、zK , I n Bs0。 I nM1 “”M2 “H” z, E ?G t4j aR。yN, I n/ZE:1)V A 4C qKvj,4 vV ?5 “”。2)4C q9Kvj, QV : 4jKv PC Qv B$ C q。 sM1#M2 z, V p5ZE “H” 。2.2 FZEYV F V ?5 ,h bW , bW q。 /:n5, j Pdj d, 7(j)=vj/(wjhjd)=dj/d, (2)s i(i j), P dj +did, 7(i ,j)=(vi +vj)/(dmaxwi ,wjmaxhi ,hj). (3)T(i ,j)(i ,j),|iF;5,4 i ,iS
5、zS:。 3B vk, jwk =max(wi ,wj),hh =max(hi,hj),dk =d. (4) ij HV “M , $Q4。2.3 “H” A5 VB5,B “H”, ! zw,d。n5, Pwj w,dj d,i Phj V ?l; T j a,| b V “D;5, 7aj =hj , vj =wjhjdj(j (N D). (5)V7 “Sf max j(N D)vjxj , (6) Hqj(N D)ajxj b;xj 0,1,j(N D), (7)T N D Hq “;b “H”。N T5 V ?E %, HWO(nb), n= N D 。54 Y2005 M9 13
6、m2 程序总流程图E :B 0“N,“ Q bdX 8V,YVB 4 VBVchoosedepth()M1 “”。 “”d, P 1 ,FVbestmatch()| F。 (WHd),B Vfilllayer() “H”。V “M - “L,|“L8FX 8 ,9 “ Q :,Vchoosedepth()。 bW B H,Kv 8, E 。 E P M XVsYV U -KMKv 8, S H, V=0。 ECI LC, mnm2。BVfilllayer “ (WHd),X 8UV U。 V “H” 3, -1 “N5) ,YV j a “H” z。BV P M LU,sYV U -KD “M
7、8。3 ECI,9 (1.2GHzCPU, 128RAM) YV。 ? HWW |, |M1=4,M2=8。“Q?S=20ft,MW=H=230cm, D=590cm。 L D7 3,0js uW25,115 =,0 20, 8“ Q 90%, L 060130W。 20,0 # B 0 f A,0 s s f 。 TnV1。V1 T i0 ni bW q/% 0 HW/s1 76 90.5 0 37.652 92 90.1 0 44.493 66 90.4 0 20.704 68 91.4 0 52.685 65 90.3 0 11.656 74 91.0 0 1.847 105 90.3
8、0 7.648 73 90.6 0 7.729 88 90.7 0 2.6410 78 90.5 0 3.4811 73 91.6 0 58.4912 102 92.4 0 64.7713 127 90.2 0 182.0914 86 91.6 0 22.0015 86 90.6 0 16.5716 114 90.2 0 20.9417 98 90.7 0 24.1818 83 92.1 0 99.2319 72 90.6 0 13.0120 92 90.0 0 9.75 (85.90 90.8 0 35.073 y 4:“ Q 5 ? T E55m3 实例13的优化解V1 V A, E20
9、3 L ( ?。m3 L 13 m,d , LL L 。 s, V , s s 5, E ?r “ Q 。NZE$ 9 m、 o/ , 7? 9 v “d,|“d“ Q 、 , w, ?4Tr q, P H,4 Z i q,i A6rm。 ID:1 Dyckhoff HATypologyof CuttingandPackingProblemsJ .EuropeanJournal of Operational Research,1990,44:145-159.2 DowslandKA, Dowsland WB.PackingProblemsJ .EuropeanJournal ofOperati
10、onal Research, 1992,56:2-14.3 Bortfeldt AAGeneticAlgorithmfortheContainerLoadingProblemM .Singapore:Proceedingsof theConferenceofIndustrialAutomation, 1994.115-126.4 邢文讯,谢金星.现代优化计算方法M .北京:清华大学出版社,1999.5 GilmorePC, GomoryR E.TheTheoryandComputationof KnapsackFunctionJ .Operations Research, 1966,14:10
11、45-1074.6 GeorgeJ A, RobinsonD F.A HeuristicforPacking BoxesintoaContainerJ .Computers andOperations Research, 1980,7:147-156.7 Hemminki J.ContainerLoadingwith VariableStrategies inEachLayerA .ESI-XC .France, 1994.Optimal Heuristic Algorithm for Container Loading ProblemCHEN Jian-ling(Department of
12、Traffic Engineering, Shandong Jiaotong University , Jinan, 250023, China)Abstract:The containers matched loading is a complicated combinatorial optimization problem with manyconstraints, whichbelongs to theNP-Hardproblem.Generally it isdifficult to obtainitsprecise solution, andinmost cases the heur
13、istic algorithm is employed to obtain its approximate solution.This paper proposes aheuristicalgorithmbasedonthebackpackcontainerloading problems, using thenew“wall-building”mechanismandcargo-pairingstrategytoobtaintheoptimalsolutionthroughtherecursivemethod.Itprovesthroughanexamplethatthisalgorithmismoreeffectiveandpractical.Key words:containerload;backpack;heuristicalgorithm(3 I : )56 Y2005 M9 13
