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1 12 Exploration Method of Various Routes with Genetic Algorithm

2 ( Genetic Algorithm: GA ) GA 2 3 Dijkstra Dijkstra i

3 Abstract Exploration Method of Various Routes with Genetic Algorithm Inoue Yusuke There is the shortest route decision in the navigation system for the car as one of the applications of the route search method. In this paper I would like to propose the technique of exploring route of denotation map file with a Genetic Algorithm (GA). When the feature of multi point search of GA is made the best use of, and it searches for the route, this technique is able not only to search for the shortest route but also decide the 2nd and the 3rd a short route. Such a route cannot be easily chosen by the Dijkstra method which has been used about the shortest route problem so far.in addition, this technique can decide two or more routes to which the route length is short and the node passed is not similar at the same time by introducing two or more evaluation functions which put different weight.moreover, the effectiveness of this technique was confirmed by doing the experiment which adjusted to the data of an actual map. key words genetic algorithm, shortest route, two or more routes, Dijkstra method ii

4 GA iii

5 A 29 B 32 iv

6 2.1 Dijkstra Dijkstra (a) (b) a b a b c d 24 v

7 vi

8 Depth First Search: DFS Breadth First Search: BFS [1] 1 Dijkstra Dijkstra [2] [3] Genetic Algorithm: GA [4] [5] 1

9 GA GA [6] 3 4 GA 5 Dijkstra GA 6 7 2

10 2 2 1 DFS BFS 1 DFS BFS DFS BFS Dijkstra Dijkstra Step 1 Step a 2.1 b 3

11 Step 3 Step c Step 5 Step (a) (b) (c) 2.1 Dijkstra Dijkstra 2.2 V U p V q U 2.2 Dijkstra U V 4

12 U p p V p p V V p V p 2.2 q p V q q p 0 V q p p p q q p Dijkstra 5

13 3 John Holland GA 3.1 GA 3.1 6

14 GA 7

15 4 GA NULL 2 0 NULL NULL NULL (a) (b) 4.1 (a) (b) 8

16 b a NULL (a) (b) 4.2 a b 4.2 a

17

18 [ ] [ ] ( Fitness ) F itness = 1 N rlength(i) i 11

19 4.3 N rlength i i i F = N i=1 f i F f i N p i p i = f i F (i = 1,2,,N) q i q i q i = i p j = 1 F j=1 i j=1 f j (i = 1,2,,N) r q i r q i <r<q i+1 (i = 0,1,,N-1, q 0 =0) i +1 N N q i+1 q i r 12

20 4.4 q i+1 q i = p i q q 2 1 p N-1 p N p 1 p 2 p 3 p i

21 [] Parent1 [ ] Parent2 [ ] P1 : P2 : Offspring1 [ ] Offspring2 [ ] O1 : O2 :

22 Parent Parent1 [ ] Parent2 [ ] P1 : P2 : Offspring1 [ ] Offspring2 [ ] O1 : O2 : Offspring n M n M M 15

23 [ ] [ ]

24 A A B Dijkstra 17

25 5.2 2 (m) A J I 3000 B (m) s Dijkstra s 5.2 Dijkstra Dijkstra CPU PentiumII-400MHz GA Dijkstra 18

26 5.2 2 (m) A J I 3000 B (m) Dijkstra 5.2 Dijstra 60 Route length in generation change The best Route The second Route Route length (Km) Number of generations

27 I J (m) A J I 3000 B (m) 5.4 A B I J Dijkstra 20

28 A Dijkstra GA Dijkstra 2 3 Dijkstra 21

29 6 Dijkstra GA Step 1 Step 2 Step 3 Step 4 Step 5 Step 6 Step3 22

30 6.2 Dijkstra GA (m) 2500 Y X (m) X Y X-Y 6.1 B 23

31 (m) (m) 2500 Y 2500 Y X 1500 X (a) (m) (c) (m) (m) (m) 2500 Y 2500 Y X 1500 X (m) (m) (b) (d) 6.2 a b c d 6.2 a d GA 24

32 Dijkstra Dijkstra Dijkstra 25

33 7 GA Dijkstra GA 1 GA GA 1 GA Dijkstra 26

34 GA

35 [1] 2000 [2] Brian W.Kernighan Dennis M.Ritchie C [3] [4] Melanie Mitchell [5] [6] (D-I) vol.j82-d-i no.8 pp Aug

36 A 5 M Tstop Pc Pm M=50 T=20 10 Pc\Pm

37 M=50 T =30 10 Pc\Pm M=50 T =40 10 Pc\Pm

38 M=50 T =50 10 Pc\Pm Cost Time Time (s) M 50 T 40 Pc 0.2 Pm Pc 0.2 Pm M 50 T 50 Pc 0.3 Pm Pc 0.9 Pm

39 B 6 M = 150 T=60 10 Pc\Pm ,308,421,300, ,252,525,259, ,243,806,490, ,395,552,453, ,229,638,608, ,280,634,547, ,235,524,491, ,251,447,451, ,232,541,690, ,245,534,599, ,232,597,547, ,259,576,408, ,234,790,574, ,222,818,550, ,233,268,815, ,262,262,647, ,253,365,408, ,224,345,478, ,271,394,294, ,242,557,502, ,233,423,429, ,367,399,436, ,276,362,258, ,244,531,298, ,243,427,236, ,255,324,383, ,223,278,357,384 32

40 Pc\Pm ,243,578,742, ,255,258,439, ,234,644,603, ,261,464,429, ,222,384,570, ,244,429,484, ,251,377,357, ,223,637,770, ,246,394,523, ,266,423,639, ,226,621,647, ,222,379,483, ,246,343,397, ,267,311,782, ,240,475,433, ,249,744,361, ,234,269,383, ,357,308,242, ,226,432,385, ,237,522,371, ,233,467,358, ,235,378,255, ,260,268,362, ,252,300,236, ,235,331,409, ,248,256,240, ,234,381,236,359 Pc\Pm ,258,562,398, ,251,442,637, ,229,354,367, ,249,445,818, ,238,273,307, ,231,311,236, ,234,517,820, ,267,356,432, ,237,256,390, ,240,380,335, ,235,441,255, ,222,331,382, ,374,559,363, ,228,282,233, ,225,402,228, ,222,359,251, ,243,547,313, ,276,454,311, ,252,539,363, ,244,297,334, ,279,288,242, ,258,347,428, ,263,467,266, ,247,256,335, ,222,256,236, ,256,425,236, ,359,450,236,383 33

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