Continuous Time Formulation and Lagrangian Relaxation Algorithm for the Gate Assignment Problem

Table 2

Comparison between SOCP and sum of squares model.

Problem			Avg. CPU time (s)		MIP gap (%)
|N|	|M|	T	SOCP	Sum of squares	SOCP	Sum of squares
10	3	360	0.43	0.57	0.00	0.00
12	5	360	8.06	292.27^{4}	0.00	7.42
14	5	360	45.38	394.75^{5}	0.01	13.38
16	5	360	94.82	387.25^{6}	0.01	35.25
18	5	360	213.83^{2}	493.04^{8}	0.42	45.24
20	5	360	108.23^{1}	442.84^{7}	0.05	27.21

^{•}The number of instances not optimally solved in 600 s, and CPU time is set to 600 s.