job-shop.dvi
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1 21 GA GA for job-shop scheduling problem by plural chromosome expression
2 GA 1,,,,,,,, 4, 4,, i
3 Abstract GA for job-shop scheduling problem by plural chromosome expression Tatsuki Shinohara Genetic algorithm imitates evolution of life a kind of approximate solution of optimization problem Express practicable answer of problem as chromosome, select, cross over and mutation genetic operation repeat generation find approximate solution Each chromosome corresponds to solution possible, therefore ability is understood, ability is called fitness value Selection of chromosome left in next generation is chosen by fitness value Cross over and mutation are operation to cause the variety of the solution In this paper, four kind of chromosome expression to job-shop scheduling problem was considered In the experiment a result, best solution among four kinds chromosome expression is Operation Permutation Adjust parameters such as cross over probability, mutation probability, approximate solution of Operation Permutation key words genetic algorithm, job-shop scheduling problem, chromosome expression ii
4 JSP iii
5 511 (PMX) (CX) iv
6 GA J J J J J J J J J v
7 PMX PMX PMX PMX CX CX , , , , vi
8 21 JSP makespan %, 10% %, 50% 26 vii
9 1,,,,,,,, NP, 1,,,,,
10 ,, 5 6 2
11 2 21 (job-shop scheduling problem: JSP),, ( ) (makespan),, (makespan) 1 ( ) JSP, 21 4, 3 4 J 1,J 2,J 3,J 4, 3 M 1,M 2,M 3 3
12 22 21 JSP J 1 (M 2,4) (M 3,3) (M 1,2) J 2 (M 2,2) (M 1,1) (M 3,1) J 3 (M 1,4) (M 3,1) (M 2,1) J 4 (M 1,2) (M 3,1) (M 2,3) J 1 1 (M 2,4), J 1 M 2 4 1, J 1 M 2, M 3, M 1 J 2 J 4 makespan, M 2 10, makespan 10 JSP
13 22,, makespan 11 M 1 J 4,J 2,J 3,J 1 21 M 2 J 1 J 2 2, 2, M 2 J 1 J 2, 21 M 2 J 2 J 1 3, 21 M 2 2 J J 1 21, M 2 J 2, M 2 J 1 22 makespan 10,
14 3 31 (Genetic Algorithm: GA),,, [1] ( ) ( ) ( ) GA 31 GA 6
15 , , 2, ( ), 2 [1],,, ( ), 0, 1, 2,, [2] 7
16 ( ), 324 GA, 8
17 4 JSP JSP, [3] 1,, makespan J 1 (M 2,4) (M 3,3) (M 1,2) J 2 (M 2,2) (M 1,1) (M 3,1) J 3 (M 1,4) (M 3,1) (M 2,1) J 4 (M 1,2) (M 3,1) (M 2,3) 41 41, ( 1 ) 41 J 4,J 2,J 1,J 3 1 9
18 , 2 J 4 2 3, J 2 2, 3 43 makespan , J 4 10
19 42 1 J J 1 1, M 2 J 2 1 M 2, J 1 1 1, 1 makespan J 1 1 J 2 2 makespan 46, J 2 47 J 2 11
20 42 1 makespan J 1 J makespan J J 4 1, makespan 10 12
21 J , 1 1, , f 1, o 1, f
22 43 o 1 J 1 2, 3, J 4,J 2 J makespan , 1 makespan 43 42, 1 15, , , , , 14
23 44 44, 1, , 1 15, , , , makespan upper bound, lower bound [4][5] upper bound 1, (= * ), ( ) 4, ,
24 45, 2 J J J , J J J 3 3 J makespan J
25 , 420 M 1 J 4 J 3 1 1, makespan, 1 15, , , , , 15, JSP, 17
26 5 51, 1 *, 4, , (PMX) (partial mapped crossover: PMX), 2 ( ) 1 2, 53 2 P 1, P 2 18
27 51 53 PMX P 1 P 2, P 2 P 1 P 1 P 2 P 1 4 7, PMX 1 55 PMX 2 P P 2 P 2 P 1, 56 C 1, C 2 C 1 P 2, C 2 P 1 56 PMX,,, 19
28 (CX) (cycle crossover: CX), 2 1, 1 57 P 1, P 2 57 CX, P 1 8 P 2 3 P 1 3 P 1 3 P , P 1 P 2 59, P 1, P 2 C 1, C 2 20
29 52 59 CX , %
30 %, 50% 50%, 50% 54 makespan, makespan, 1, 1,, , 2, 22
31 55 51 PMX( ) PMX( ) PMX( ) PMX( ) CX , , PMX, makespan 51 PMX, PMX 55, , makespan makespan 23
32 , , , , , 1500, ,
33 %, 10% 61, 55%, 50% 62, 61, ( 511 ), 75% 4 1, 10% 3 75%, 10% 55%, 50%, 2, 55% , 2 makespan 61 25
34 %, 10%, PMX( ) PMX( ) 10, , , , , , , %, 50%, PMX( ) PMX( ) 10, , , , , , , , 5 makespan 62 10, 10 PMX( ) makespan 10, 10, makespan, 61, 62 upper bound 1 26
35 62 62, 4, 10, 5 15, 15 makespan,, upper bound upper bound upper bound 15, 5 20, 5 30, 10, 30, 20 50, , 20 PMX( ), 62, M 2 1, ( J 1 ), J 1 2 M (M 1 ) 1 (J 2 ), J 1 2 J 1 1, J 2 M 1 J 1 2 J 2 1, 62 M 1 27
36 62 62,, J 1 3,, 62 = (1, 1, 2, ), 1,
37 ,,,,,,, 29
38 [1],, 1998 [2] L Dabis, Handbook of Genetic Algorithms (,,, 1944) [3], NEH, No [4] OR-Library, /12/18 [5] CP2SAT:JSS benchmark redults, /1/27 [6], /12/18 30
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