Optimizing the Location of Virtual Stations in Free-Floating Bike-Sharing Systems with the User Demand during Morning and Evening Rush Hours

Table 3

Performance analysis of CPLEX and the clustering algorithm. K = 5.

N	CPLEX		Our method
	Obj.	CPU(s)	Avg. Obj.	Avg. gap	Best Obj.	Best gap	Avg. CPU(s)
30	15	64.231	14.6	2.67	15	0.00	38.841
50	32	650.289	30.8	3.75	31	3.13	43.142
70	49	2275.631	47.1	3.88	48	2.04	54.260
90	68	7200	65.3	3.97	66	2.94	60.394
110	85	7200	81.5	4.12	82	3.53	69.787
150	114	7200	108.1	5.18	109	4.39	81.140
190		7200	149.5		153		89.769
230		7200	176.8		190		96.145

Avg. Obj: average objective value; Best Obj: best objective value; Avg. CPU: average CPU time after 100 runs.