Mathematical Problems in Engineering

Research Article

An Improved Shuffled Frog Leaping Algorithm and Its Application in Dynamic Emergency Vehicle Dispatching

Table 11

The shortest travel time path of the illustrative examples based on the prediction link travel speed.


Vehicle no.	Example no.	Prediction error (km/h)	Accident no.
Vehicle no.	Example no.	Prediction error (km/h)	1	2	3	4

1	I	0	3, 2, 10, 21	3, 2, 1, 6	3, 12, 13, 14, 27	--
		±3	3, 2, 10, 21	3, 2, 1, 6	3, 12, 13, 14, 27	--
		±5	3, 12, 11, 22, 21	3, 2, 1, 6	3, 12, 13, 14, 27	--
		±10	3, 12, 11, 22, 21	3, 2, 1, 6	3, 12, 13, 14, 27	--
	II	0	3, 2, 10, 21	3, 2, 1, 6	3, 12, 13, 14, 27	3, 2, 1, 6, 18, 17, 16
		±3	3, 2, 10, 21	3, 2, 1, 6	3, 12, 13, 14, 27	3, 2, 1, 6, 18, 17, 16
		±5	3, 12, 11, 22, 21	3, 2, 1, 6	3, 12, 13, 14, 27	3, 2, 1, 6, 18, 17, 16
		±10	3, 12, 11, 22, 21	3, 2, 1, 6	3, 12, 13, 14, 27	BL

2	I	0	8, 9, 20, 21	8, 7, 18, 6	BL	--
		±3	8, 9, 20, 21	8, 7, 18, 6	BL	--
		±5	8, 9, 20, 21	8, 7, 1, 6	BL	--
		±10	8, 9, 20, 21	8, 7, 18, 6	BL	--
	II	0	8, 9, 20, 21	8, 7, 18, 6	BL	8, 7, 18, 17, 16
		±3	8, 9, 20, 21	8, 7, 18, 6	BL	8, 7, 18, 17, 16
		±5	8, 9, 20, 21	8, 7, 1, 6	BL	8, 7, 18, 17, 16
		±10	8, 9, 20, 21	8, 7, 18, 6	BL	8, 7, 18, 17, 16

3	I	0	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	--
		±3	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	--
		±5	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	--
		±10	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	--
	II	0	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 4, 5, 15, 16
		±3	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 4, 5, 15, 16
		±5	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	BL
		±10	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 14, 15, 16

4	I	0	17, 18, 6, 1, 2, 10, 21	17, 18, 6	17, 16, 15, 14, 27	--
		±3	17, 18, 6, 1, 2, 10, 21	17, 18, 6	17, 16, 15, 14, 27	--
		±5	17, 18, 7, 8, 19, 20, 21	17, 18, 6	17, 16, 15, 14, 27	--
		±10	17, 18, 6, 1, 2, 10, 21	17, 18, 6	17, 16, 15, 14, 27	--
	II	0	17, 18, 6, 1, 2, 10, 21	17, 18, 6	BL	17, 16
		±3	17, 18, 6, 1, 2, 10, 21	17, 18, 6	BL	17, 16
		±5	17, 18, 7, 8, 19, 20, 21	17, 18, 6	BL	17, 16
		±10	17, 18, 6, 1, 2, 10, 21	17, 18, 6	BL	17, 16

5	I	0	29, 15, 5, 6, 1, 2, 10, 21	29, 15, 5, 6	29, 28, 27	--
		±3	29, 15, 5, 6, 1, 2, 10, 21	29, 15, 5, 6	29, 28, 27	--
		±5	29, 15, 5, 6, 1, 2, 10, 21	29, 15, 5, 6	29, 28, 27	--
		±10	29, 15, 5, 6, 1, 9, 20, 21	29, 15, 5, 6	29, 28, 27	--
	II	0	29, 15, 5, 6, 1, 2, 10, 21	29, 15, 5, 6	29, 28, 27	29, 15, 16
		±3	29, 15, 5, 6, 1, 2, 10, 21	29, 15, 5, 6	29, 28, 27	29, 15, 16
		±5	29, 15, 5, 6, 1, 2, 10, 21	29, 15, 5, 6	29, 28, 27	29, 15, 16
		±10	29, 15, 5, 6, 1, 9, 20, 21	29, 15, 5, 6	29, 28, 27	29, 30, 16

6	I	0	25, 24, 23, 22, 21	BL	25, 26, 27	--
		±3	25, 24, 23, 22, 21	25, 24, 13, 4, 5, 6	25, 26, 27	--
		±5	25, 24, 23, 22, 21	25, 24, 13, 4, 5, 6	25, 26, 27	--
		±10	25, 24, 23, 22, 21	25, 24, 13, 4, 5, 6	25, 26, 27	--
	II	0	25, 24, 23, 22, 21	BL	25, 26, 27	BL
		±3	25, 24, 23, 22, 21	25, 24, 13, 4, 5, 6	25, 26, 27	25, 24, 13, 4, 5, 15, 16
		±5	25, 24, 23, 22, 21	25, 24, 13, 4, 5, 6	25, 26, 27	BL
		±10	25, 24, 23, 22, 21	25, 24, 13, 4, 5, 6	25, 26, 27	BL

7	I	0	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 28, 27	--
		±3	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 28, 27	--
		±5	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 28, 27	--
		±10	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 43, 42, 41, 27	--
	II	0	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 28, 27	31, 30, 16
		±3	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 28, 27	31, 30, 16
		±5	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 28, 27	31, 30, 16
		±10	31, 32, 33, 19, 20, 21	31, 17, 18, 6	31, 30, 29, 43, 42, 41, 27	31, 30, 16

8	I	0	32, 33, 19, 20, 21	32, 18, 6	BL	--
		±3	32, 33, 19, 20, 21	32, 18, 6	BL	--
		±5	32, 33, 19, 20, 21	32, 18, 6	BL	--
		±10	32, 33, 19, 20, 21	32, 18, 6	BL	--
	II	0	32, 33, 19, 20, 21	32, 18, 6	BL	32, 18, 17, 16
		±3	32, 33, 19, 20, 21	32, 18, 6	BL	32, 18, 17, 16
		±5	32, 33, 19, 20, 21	32, 18, 6	BL	32, 18, 17, 16
		±10	32, 33, 19, 20, 21	32, 18, 6	BL	32, 18, 17, 16

9	II	0	33, 19, 20, 21	33, 32, 18, 6	BL	33, 32, 18, 17, 16
		±3	33, 19, 20, 21	33, 32, 18, 6	BL	33, 32, 18, 17, 16
		±5	33, 19, 20, 21	33, 32, 18, 6	BL	33, 32, 31, 30, 16
		±10	33, 19, 20, 21	33, 32, 18, 6	BL	33, 32, 18, 17, 16

10	II	0	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 4, 5, 15, 16
		±3	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 4, 5, 15, 16
		±5	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 4, 5, 15, 16
		±10	13, 12, 11, 22, 21	13, 4, 5, 6	13, 14, 27	13, 14, 15, 16

Note. BL means that the travel time of the optimal path exceeds the upper limit of the time window.