Simulated Annealing-Based Ant Colony Algorithm for Tugboat Scheduling Optimization

Table 5

Results with different proportion of the shifting berth operation.

Number of ships	Results with different proportion of the shifting-berth operation
	0%^1	5%^2	GAP1^a	10%^3	GAP2^b	15%^4	GAP3^c	20%^5	GAP4^d
10	2675	2845	6.36%	3076	13.04%	3224	20.52%	3415	27.66%
15	3952	4205	6.40%	4518	12.53%	4703	19.00%	4961	25.53%
20	5206	5485	5.36%	5824	10.61%	6121	17.58%	6452	23.93%
25	6503	6857	5.44%	7331	11.29%	7715	18.64%	8035	23.56%
30	7951	8381	5.41%	9122	12.84%	9423	18.51%	9731	22.39%
Average	/	/	5.79%	/	12.06%	/	18.85%	/	24.61%

a(value of 2 − value of 1)/value of 1 × 100%; b(value of 3 − value of 1)/value of 1 × 100%; c(value of 4 − value of 1)/value of 1 × 100%; ^d(value of 5 − value of 1)/value of 1 × 100%.