A Simulated Annealing Approach for the Train Design Optimization Problem

Table 8

Relevant data (columns I, II) and results (columns III, IV, and V) of 50 runs of SA on 20 random instances. A lower bound—explained in Section 5.3—on the optimal solution cost is shown in column VI. The last column is an indicator of the solution quality.

I	II	III	IV	V	VI	VII
Instance	Number of; stations, blocks, arcs, crew segments	Minimum cost; ()	Average cost	Avg time; (sec)	Lower bound; ()	Difference in %
p5_7D	5 7 5 6	47,193	47,193	1	32,957	43.18
p5_10D	5 10 4 6	77,691	77,726	1	60,336	28.76
p10_15D	10 15 11 14	224,186	226,845	4	187,862	19.34
p10_20D	10 20 8 13	294,595	299,021	4	248,649	18.48
p20_30D	20 30 13 25	297,952	301,013	13	243,932	22.15
p20_40D	20 40 15 25	336,651	339,876	13	267,840	25.69
p40_60D	40 60 22 45	565,954	576,906	49	446,538	26.74
p40_80D	40 80 21 45	568,089	573,991	46	446,411	27.26
p80_120D	80 120 38 86	791,072	800,660	124	614,225	28.79
p80_160D	80 160 38 89	987,646	997,005	168	791,041	24.85
p160_240D	160 240 62 169	2,214,593	2,240,989	376	1,791,395	23.62
p160_320D	160 320 72 169	2,201,347	2,221,606	320	1,765,637	24.68
p200_300D	200 300 82 216	4,043,845	4,071,617	409	3,306,843	22.29
p200_400D	200 400 81 210	1,591,058	1,607,980	463	1,203,586	32.19
p250_375D	250 375 96 261	2,518,148	2,548,918	856	1,958,093	28.60
p250_500D	250 500 104 260	1,881,881	1,905,522	723	1,445,175	30.22
p300_450D	300 450 117 311	8,919,042	8,969,957	606	7,480,671	19.23
p300_600D	300 600 115 313	10,419,523	10,453,791	744	8,782,219	18.64
p320_480D	320 480 138 333	8,172,082	8,218,034	662	6,676,505	22.40
p320_640D	320 640 138 332	2,053,295	2,077,627	900	1,516,815	35.37