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1 Memetic 26 2 (125T208T)

2

3 Abstract The Facility Dispersion Problem(FDP) is compinatorial optimization problem which is selecting facilities to maximize each distance as far as possible in case of selecting facilities in given facility arrange candidates. Practically, it uses for determining selection of facilities which are undesirable to arrange closely; such as chemical plants and power stations. It also uses for determining hamming codes in the field of coding theory. As to approaches for FDP, there are exact algorithm using linear programming, greedy randomized adaptive search procedure and heuristic approach based on genetic algorithm. Yamada et al. proposed the algorithm based on genetic algorithm which treat the population of solutions, so the method inclued initial solutions generation process, mutation process, selection process and so on. Especially, Yamada et al. proposed new method called partial reconstruction in the mutation process. Ordinarily, mutaion process alters the solution randomly, so it makes the accuracy of solution worse, but spreads the solution search space. But, it was confirtmed that partial reconstruction can secure the search space and keep the solution accuracy by computer experiments. In this research, we aimed to reduce execution time by improving the method based on genetic algorithm using hash. Because, proposed partial reconstruction has high ratio toward entire execution time. Hash used for keeping and adding the information which are needed in partial reconstruction. And Yamada s method fixed the number of deleting vertices in partial reconstruction, but we changed the number, and checked the influence to solution accuracy. We made computer experiments that the input datas are availablebenchmark problems, and compared with Yamada s method Consequently, proposed method can reduce the total execution time while keeping the solution accuracy. Also, the percentage of the time of parial reconstruction toward entire time was decreasing. So, we confirmed the efficiency of proposed method which keeps and adds the information of partial reconstction using hash.

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5 1 1 [2] [3]. GRASP Resende (2010)[6] Porumbel (2011)[4] 2012 [8] Memetic Algorithm ()??

6 2 G(V, E) V = {v 1, v 2,..., v n } V 2 d(, ) k V S ( S = k) f (S ) = min 1 i< j k d(s i, s j )

7 :

8 n k ( ) :

9 5 s p l s l k/2 2 1 s s s Procedure.1 Procedure 1 Input: V d s = {s 1, s 2,..., s p } l 1: s {s 1, s 2,..., s p l } // 2: for i = 1 to l do 3: s V \ s s 4: end for Output: s

10 n, k p O(kp) O(kn) O(knp) 2 O(k 2 ) O(k 2 p) 2p O(p log p) p 2 O(k) O(p 2 ) O(kp 2 ) p n

11 7 3.2 ( 3.1) 3.1:

12 8 s L s ()

13 CPU : Intel(R) Xeon(R) 2.00GHz OS : Linux ( Centos 6.5 ) : 64.0GB : Java Geo Ran Glover [1] n = 100, 250, 500 k = 0.1n( 01 10), 0.3n( 11 20) Silva [7] ( ) Geo n = 100, 250, 500 kk = 0.1n( 01 10), 0.3n( 11 20) n = 500, k = n 20 l

14 [5] ( 4.1,4.2) 4.1: Geo [%] 2 k/4 k/2 Geo_100_ Geo_100_ Geo_250_ Geo_250_ Geo_500_ Geo_500_ : Ran [%] 2 k/4 k/2 Ran_100_ Ran_100_ Ran_250_ Ran_250_ Ran_500_ Ran_500_ k/2() 2, k/4, k/2 3

15 : : 250 Geo_500_ %Geo_100_11 20

16 12 4.3: 500 k/4 1% Ran_100_11 20( k/4 ) Geo_100_11 20( k/2 ) % ( 4.3) 4.3: [MB] n=100 n=250 n=500 2 Geo_n_ Geo_n_ Ran_n_ Ran_n_ k/4 Geo_n_ Geo_n_ Ran_n_ Ran_n_ k/2 Geo_n_ Geo_n_ Ran_n_ Ran_n_

17 13 8GB n = MB n n = n ( ) 4.4: (n = 100)

18 14 4.5: (n = 250) 4.6: (n = 500)

19 15 5 Facility Dispersion GB

20 16

21 17 [1] Fred Glover, Ching-Chung Kuo, and Krishna S Dhir. Heuristic algorithms for the maximum diversity problem. Journal of Information and Optimization Sciences, Vol. 19, No. 1, pp , [2] Michael J Kuby. Programming models for facility dispersion: The p-dispersion and maxisum dispersion problems. Geographical Analysis, Vol. 19, No. 4, pp , [3] Ching-Chung Kuo, Fred Glover, and Krishna S Dhir. Analyzing and modeling the maximum diversity problem by zero-one programming*. Decision Sciences, Vol. 24, No. 6, pp , [4] Daniel Cosmin Porumbel, Jin-Kao Hao, and Fred Glover. A simple and effective algorithm for the maxmin diversity problem. Annals of Operations Research, Vol. 186, No. 1, pp , [5] Mauricio GC Resende, Rafael Martí, Micael Gallego, and Abraham Duarte. Optiscom project - maxmin diversity problem. [6] Mauricio GC Resende, Rafael Martí, Micael Gallego, and Abraham Duarte. Grasp and path relinking for the max min diversity problem. Computers & Operations Research, Vol. 37, No. 3, pp , [7] Geiza C Silva, Luiz S Ochi, and Simone L Martins. Experimental comparison of greedy randomized adaptive search procedures for the maximum diversity problem. In Experimental and Efficient Algorithms, pp Springer, [8],,,. GA Facility Dispersion. 2012, pp. S1 18, 2012.

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23 19 5.1: 2 (Geo) Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_

24 20 5.2: 2 (Ran) Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_

25 21 5.3: k/4 (Geo) Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_

26 22 5.4: k/4 (Ran) Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_

27 23 5.5: k/2 (Geo) Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_100_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_250_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_ Geo_500_

28 24 5.6: k/2 (Ran) Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_100_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_250_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_ Ran_500_

29 25 5.7: (n = 100) 2 Geo_100_ Geo_100_ p Geo_100_ Geo_100_ p Geo_100_ Geo_100_ Ran_100_ Ran_100_ p Ran_100_ Ran_100_ p Ran_100_ Ran_100_ : (n = 250) 2 Geo_250_ Geo_250_ p Geo_250_ Geo_250_ p Geo_250_ Geo_250_ Ran_250_ Ran_250_ p Ran_250_ Ran_250_ p Ran_250_ Ran_250_

30 26 5.9: (n = 500) 2 Geo_500_ Geo_500_ p Geo_500_ Geo_500_ p Geo_500_ Geo_500_ Ran_500_ Ran_500_ p Ran_500_ Ran_500_ p Ran_500_ Ran_500_

31 27 [1],,,, Edge concentration GA, 2012 CD-ROM, S2-8, [2],,,,, 25,G10-6,2013.

n 2 n (Dynamic Programming : DP) (Genetic Algorithm : GA) 2 i

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