Gapst of GT problem
Type	Nodes	Arcs	Comms	Lower Bound/ Gurobi/ 120h	Upper Bound/ Gurobi/ 120h	CPLEX	CPLEX SP	IP SEARCH	PARLS	Capacity Scaling and Neighbor Search750	Capacity Scaling and Neighbor Search750  Best
F_L	500	2000	50	3496049	3742004	3882110	3726114	3823610	3722839	3703340	3684997
F_L	500	2000	100	5612839	6194571	6706100	6404834	6453880	6005177	6030640	6004733
F_L	500	2000	150	6863228	7691938	8205000	7886028	8081600	7510651	7548055	7496026
F_L	500	2000	200	8165040	9183930	10181700	10376103	9828350	9338097	8986462	8980066
F_L	500	2500	50	3211475	3544207	3818440	3507652	3612030	3491664	3517483	3439095
F_L	500	2500	100	5144270	5860749	6893490	6187629	6400140	5909401	5775371	5735142
F_L	500	2500	150	6818030	8447780	10022900	9520783	9089920	8138918	7997256	7895858
F_L	500	2500	200	8061178	10853172	11937300	11566824	10099200	9788913	9307056	9273254
F_L	500	3000	50	2989771	3396814	3668660	3492641	3457280	3369303	3309589	3309589
F_L	500	3000	100	5012129	5834588	6692780	6187593	6015950	5773133	5620093	5564106
F_L	500	3000	150	6449785	7819641	9378030	9479082	8919720	7741294	7571267	7471066
F_L	500	3000	200	7459169	9332126	11240900	11291918	10040000	9195115	8763465	8729617
F_T	500	2000	50	4217499	5109233	5038580	5100186	4949780	4892012	4891370	4851979
F_T	500	2000	100	6380988	7478374	7592260	7381313	7619670	7273916	7390874	7248610
F_T	500	2000	150	7256504	8237938	8640390	9083303	8807650	8014986	8047994	7916400
F_T	500	2000	200	8852715	11187154	11858000	11213371	11893100	10617796	10540260	10452886
F_T	500	2500	50	3837741	4587008	4585510	4448739	4600200	4406080	4364086	4364086
F_T	500	2500	100	5301129	6586216	6942260	6559397	6953660	6365848	6392506	6282050
F_T	500	2500	150	6120540	7036284	8094410	7978909	7571640	7037860	6878660	6878660
F_T	500	2500	200	8611901	10969518	11963100	11911900	11452900	10727261	10429633	10429633
F_T	500	3000	50	3496170	4321728	4333310	4069239	4262350	4035362	4164508	4060444
F_T	500	3000	100	5408225	6880936	7164410	7046750	7186810	6634387	6565356	6518955
F_T	500	3000	150	6260998	7750637	8773910	8172602	8709390	7517445	7526917	7442878
F_T	500	3000	200	7673931	9756073	11236600	11354647	10390700	9751002	9581707	9498508
Average				5945888	7158442	7868756	7664482	7509147	6969103	6870998	6813693
Gaps
Type	Nodes	Arcs	Comms	Lower Bound/ Gurobi/ 120h	Upper Bound/ Gurobi/ 120h	CPLEX	CPLEX SP	IP SEARCH	PARLS	Capacity Scaling and Neighbor Search750	Capacity Scaling and Neighbor Search750  Best
F_L	500	2000	50	-	7.0%	11.0%	6.6%	9.4%	6.5%	5.9%	5.4%
F_L	500	2000	100	-	10.4%	19.5%	14.1%	15.0%	7.0%	7.4%	7.0%
F_L	500	2000	150	-	12.1%	19.6%	14.9%	17.8%	9.4%	10.0%	9.2%
F_L	500	2000	200	-	12.5%	24.7%	27.1%	20.4%	14.4%	10.1%	10.0%
F_L	500	2500	50	-	10.4%	18.9%	9.2%	12.5%	8.7%	9.5%	7.1%
F_L	500	2500	100	-	13.9%	34.0%	20.3%	24.4%	14.9%	12.3%	11.5%
F_L	500	2500	150	-	23.9%	47.0%	39.6%	33.3%	19.4%	17.3%	15.8%
F_L	500	2500	200	-	34.6%	48.1%	43.5%	25.3%	21.4%	15.5%	15.0%
F_L	500	3000	50	-	13.6%	22.7%	16.8%	15.6%	12.7%	10.7%	10.7%
F_L	500	3000	100	-	16.4%	33.5%	23.5%	20.0%	15.2%	12.1%	11.0%
F_L	500	3000	150	-	21.2%	45.4%	47.0%	38.3%	20.0%	17.4%	15.8%
F_L	500	3000	200	-	25.1%	50.7%	51.4%	34.6%	23.3%	17.5%	17.0%
F_T	500	2000	50	-	21.1%	19.5%	20.9%	17.4%	16.0%	16.0%	15.0%
F_T	500	2000	100	-	17.2%	19.0%	15.7%	19.4%	14.0%	15.8%	13.6%
F_T	500	2000	150	-	13.5%	19.1%	25.2%	21.4%	10.5%	10.9%	9.1%
F_T	500	2000	200	-	26.4%	33.9%	26.7%	34.3%	19.9%	19.1%	18.1%
F_T	500	2500	50	-	19.5%	19.5%	15.9%	19.9%	14.8%	13.7%	13.7%
F_T	500	2500	100	-	24.2%	31.0%	23.7%	31.2%	20.1%	20.6%	18.5%
F_T	500	2500	150	-	15.0%	32.2%	30.4%	23.7%	15.0%	12.4%	12.4%
F_T	500	2500	200	-	27.4%	38.9%	38.3%	33.0%	24.6%	21.1%	21.1%
F_T	500	3000	50	-	23.6%	23.9%	16.4%	21.9%	15.4%	19.1%	16.1%
F_T	500	3000	100	-	27.2%	32.5%	30.3%	32.9%	22.7%	21.4%	20.5%
F_T	500	3000	150	-	23.8%	40.1%	30.5%	39.1%	20.1%	20.2%	18.9%
F_T	500	3000	200	-	27.1%	46.4%	48.0%	35.4%	27.1%	24.9%	23.8%
Average Gaps				-	19.5%	30.5%	26.5%	24.8%	16.4%	15.0%	14.0%
Computation Times
Type	Nodes	Arcs	Comms	Lower Bound/ Gurobi/ 120h	Upper Bound/ Gurobi/ 120h	CPLEX	CPLEX SP	IP SEARCH	PARLS	Capacity Scaling and Neighbor Search750	Capacity Scaling and Neighbor Search750  Best
F_L	500	2000	50	432000	432000	18000	18000	3600	3600	6304	5545
F_L	500	2000	100	432000	432000	18000	18000	3600	3600	9041	5456
F_L	500	2000	150	432000	432000	18000	18000	3600	3600	9630	19228
F_L	500	2000	200	432000	432000	18000	18000	3600	3600	12410	15962
F_L	500	2500	50	432000	432000	18000	18000	3600	3600	4335	4870
F_L	500	2500	100	432000	432000	18000	18000	3600	3600	9577	13858
F_L	500	2500	150	432000	432000	18000	18000	3600	3600	17284	29721
F_L	500	2500	200	432000	432000	18000	18000	3600	3600	20788	19606
F_L	500	3000	50	432000	432000	18000	18000	3600	3600	5983	5983
F_L	500	3000	100	432000	432000	18000	18000	3600	3600	10657	15333
F_L	500	3000	150	432000	432000	18000	18000	3600	3600	18574	33774
F_L	500	3000	200	432000	432000	18000	18000	3600	3600	38514	29030
F_T	500	2000	50	432000	432000	18000	18000	3600	3600	7004	5539
F_T	500	2000	100	432000	432000	18000	18000	3600	3600	7095	9268
F_T	500	2000	150	432000	432000	18000	18000	3600	3600	12884	15090
F_T	500	2000	200	432000	432000	18000	18000	3600	3600	12652	15776
F_T	500	2500	50	432000	432000	18000	18000	3600	3600	3673	3673
F_T	500	2500	100	432000	432000	18000	18000	3600	3600	11606	12520
F_T	500	2500	150	432000	432000	18000	18000	3600	3600	24606	24606
F_T	500	2500	200	432000	432000	18000	18000	3600	3600	17873	17873
F_T	500	3000	50	432000	432000	18000	18000	3600	3600	7073	6048
F_T	500	3000	100	432000	432000	18000	18000	3600	3600	9686	11477
F_T	500	3000	150	432000	432000	18000	18000	3600	3600	14562	20761
F_T	500	3000	200	432000	432000	18000	18000	3600	3600	16129	19860
Average				432000	432000	18000	18000	3600	3600	12831	15036
Lower Bound/ Gurobi7/ 60h				N. Katayama by Gurobi Ver7, 2018.
Upper Bound/ Gurobi/ 60h				N. Katayama by Gurobi Ver7, 2018.
CPLEX				L.M. Munguía, S. Ahmed, D.A. Bader, G.L. Nemhauser, V. Goel, Y. Shao, A parallel local search framework for the Fixed-Charge Multicommodity Network Flow problem, Computers & Operations Research, 77, 44-57, 2017.
CPLEX SP				L.M. Munguía, S. Ahmed, D.A. Bader, G.L. Nemhauser, V. Goel, Y. Shao, A parallel local search framework for the Fixed-Charge Multicommodity Network Flow problem, Computers & Operations Research, 77, 44-57, 2017.
IP SEARCH				M. Hewitt, G. L. Nemhauser, and M. Savelsbergh. Combining exact and heuristics approaches for the capacitated fixed charge network flow problem. Journal on Computing, 22, 314-325, 2010.
PARLS				L.M. Munguía, S. Ahmed, D.A. Bader, G.L. Nemhauser, V. Goel, Y. Shao, A parallel local search framework for the Fixed-Charge Multicommodity Network Flow problem, Computers & Operations Research, 77, 44-57, 2017.
Capacity Scaling and Neighbor Search				Naoto Katayama, Working Paper, 2018.